# CSST Strong Lensing Preparation: a Framework for Detecting Strong Lenses in
the Multi-color Imaging Survey by the China Survey Space Telescope (CSST)

Xu Li  College of Electronic Information and Optical Engineering, Taiyuan
University of Technology, Taiyuan, 030024, China  Ruiqi Sun 111The first two
authors contribute equally to this paper. College of Electronic Information
and Optical Engineering, Taiyuan University of Technology, Taiyuan, 030024,
China  Jiameng Lv  College of Electronic Information and Optical Engineering,
Taiyuan University of Technology, Taiyuan, 030024, China  Peng Jia College of
Electronic Information and Optical Engineering, Taiyuan University of
Technology, Taiyuan, 030024, China<EMAIL_ADDRESS>Nan Li National
Astronomical Observatories, Beijing, 100101,China<EMAIL_ADDRESS>Chengliang Wei  Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  Zou Hu  National Astronomical Observatories, Beijing,
100101,China  Xinzhong Er  South-Western Institute for Astronomy Research,
Yunnan University, Kunming, Yunnan 65000, P.R. China  Yun Chen  Key Laboratory
for Computational Astrophysics, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing 100101, China  Zhang Ban  Changchun Institute of
Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun,
130033, China  Yuedong Fang  University Observatory, Faculty of Physics,
Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany  Qi Guo
National Astronomical Observatories, Beijing, 100101,China  Dezi Liu  South-
Western Institute for Astronomy Research, Yunnan University, Kunming, 650500,
China  Guoliang Li  Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  Lin Lin  Shanghai Astronomical Observatory, Chinese
Academy of Sciences, Shanghai 200030, PR China  Ming Li  National Astronomical
Observatories, Beijing, 100101,China  Ran Li  National Astronomical
Observatories, Beijing, 100101,China  Institute for Frontiers in Astronomy and
Astrophysics, Beijing Normal University, Beijing 102206, China  School of
Astronomy and Space Science, University of Chinese Academy of Science, Beijing
100049, China  Xiaobo Li  Changchun Institute of Optics, Fine Mechanics and
Physics, Chinese Academy of Sciences, Changchun, 130033, China  Yu Luo  Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
Xianmin Meng  National Astronomical Observatories, Beijing, 100101,China
Jundan Nie  National Astronomical Observatories, Beijing, 100101,China
Zhaoxiang Qi  Shanghai Astronomical Observatory, Chinese Academy of Sciences,
Shanghai 200030, PR China  School of Astronomy and Space Science, University
of Chinese Academy of Science, Beijing 100049, China  Yisheng Qiu  Institute
for Astronomy, School of Physics, Zhejiang University, Hangzhou 310027, China
Li Shao  National Astronomical Observatories, Beijing, 100101,China  Hao Tian
National Astronomical Observatories, Beijing, 100101,China  Lei Wang  Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China  Wei
Wang  Changchun Institute of Optics, Fine Mechanics and Physics, Chinese
Academy of Sciences, Changchun, 130033, China  Jingtian Xian  Changchun
Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences,
Changchun, 130033, China  Youhua Xu  National Astronomical Observatories,
Beijing, 100101,China  Tianmeng Zhang  National Astronomical Observatories,
Beijing, 100101,China  Xin Zhang  National Astronomical Observatories,
Beijing, 100101,China  Zhimin Zhou  National Astronomical Observatories,
Beijing, 100101,China

###### Abstract

Strong gravitational lensing is a powerful tool for investigating dark matter
and dark energy properties. With the advent of large-scale sky surveys, we can
discover strong lensing systems on an unprecedented scale, which requires
efficient tools to extract them from billions of astronomical objects. The
existing mainstream lens-finding tools are based on machine learning
algorithms and applied to cut-out-centered galaxies. However, according to the
design and survey strategy of optical surveys by CSST, preparing cutouts with
multiple bands requires considerable efforts. To overcome these challenges, we
have developed a framework based on a hierarchical visual Transformer with a
sliding window technique to search for strong lensing systems within entire
images. Moreover, given that multi-color images of strong lensing systems can
provide insights into their physical characteristics, our framework is
specifically crafted to identify strong lensing systems in images with any
number of channels. As evaluated using CSST mock data based on an Semi-
Analytic Model named CosmoDC2, our framework achieves precision and recall
rates of 0.98 and 0.90, respectively. To evaluate the effectiveness of our
method in real observations, we have applied it to a subset of images from the
DESI Legacy Imaging Surveys and media images from Euclid Early Release
Observations. 61 new strong lensing system candidates are discovered by our
method. However, we also identified false positives arising primarily from the
simplified galaxy morphology assumptions within the simulation. This
underscores the practical limitations of our approach while simultaneously
highlighting potential avenues for future improvements.

Strong gravitational lensing (1643), Astronomy image processing (2306), Neural
networks (1933), Space telescopes (1547)

##  1 Introduction

Strong Gravitational Lensing represents a significant category of celestial
phenomena, occurring as light emitted by distant cosmic entities traverses
regions occupied by supermassive objects such as galaxies, galaxy clusters, or
black holes (Birrer et al., 2022; Meneghetti et al., 2013; Treu, 2010; Shajib
et al., 2022; Treu et al., 2022; Kneib & Natarajan, 2011; Vegetti et al.,
2023). Strong lensing systems play a vital role in measuring mass
distributions, confining cosmological parameters like the Hubble constant and
dark energy density, and affords scientists the opportunity to investigate
properties of remote celestial objects (Bradač et al., 2002; Treu & Koopmans,
2002; Auger et al., 2010; Sonnenfeld et al., 2015). It furnishes invaluable
insights into understanding the early universe and the evolution of the
cosmos.

Currently, our knowledge of strong lensing systems is limited to a few hundred
instances. However, with ongoing and forthcoming surveys (Oguri & Marshall,
2010; Jacobs et al., 2017), such as the Legacy Survey of Space and Time (LSST)
(Ivezić et al., 2019; Jacobs et al., 2017), Euclid (Laureijs et al., 2011),
and the China Space Station Telescope (CSST) (Zhan, 2021), we anticipate a
substantial increase in the identification of strong lensing systems. The task
of detecting them in future surveys presents a formidable challenge. The
intricate shapes of images, including arcs and multiple images, often stem
from the complex interplay of strong lensing systems influenced by the
internal structures of galaxies and their surrounding environments.
Furthermore, additional sources of interference, such as the interal structure
of galaxies, noise from background and effects brought by the point spread
function (PSF), add to the complexity, rendering the detection of strong
lensing systems an even more daunting endeavor.

As the volume of observation data continue to expand, the manual approach of
visually inspecting strong lensing systems has proven insufficient. Therefore,
the adoption of appropriate automated algorithms for detection of strong
lensing systems become imperative. Previous automated detection methods have
adopted various strategies. These include the search for distinctive features
of strong lensing systems, such as arcs and rings, the fitting of geometric
parameters to quantify the extent of these features, and searching for blue
residuals in images extracted from the galaxy (Webster et al., 1988; Bacon et
al., 2000; Courbin et al., 2000; Smith et al., 2001; Lenzen et al., 2004;
Alard, 2006; Estrada et al., 2007; Seidel & Bartelmann, 2007; More et al.,
2012; Gavazzi et al., 2014; Jacobs et al., 2017). Another approach has
involved generating models of potential lensing galaxies and comparing them
with real observation data to pinpoint potential lensing occurrences (Brault &
Gavazzi, 2015; Jacobs et al., 2017). Certain methods have involved the removal
of galaxies from observation images (Chan et al., 2015; More et al., 2016;
Jacobs et al., 2017), while others have delved into the analysis of colors and
shapes of lensed quasars, employing parameterization techniques for subsequent
analysis (Brault & Gavazzi, 2015; Jacobs et al., 2017). The aforementioned
approaches have indeed discovered a notable amount of strong lensing system
candidates. However, these methods necessitate the manual identification of
candidates of strong lensing systems, alongside intricate data analysis. Due
to the limitations of modern monitors, which can only display images with a
finite range of gray scale levels and channels, many of the physical
properties associated with strong lensing systems, contained within variations
in gray scale or color, cannot be fully utilized in the detection process.
Moreover, the elevated computational intricacy associated with these methods
renders them unsuitable for processing a huge volume of data.

With the development of machine learning techniques, their application within
the field of astronomy has increased. Compared to traditional methods, machine
learning algorithms exhibit a heightened ability to efficiently manage large
datasets and distinguish valuable features from them. Their swift adaptability
to new observation data and robust generalization capabilities render them
especially fitting for a large volume of astronomical data. In particular, in
2015, researchers introduced a deep neural network model designed to classify
galaxy morphology. This model leveraged the translational and rotational
symmetries inherent in galaxy images to achieve classification and redshift
estimation (Dieleman et al., 2015; Jacobs et al., 2017). Within the realm of
galaxy evolution studies, Schawinski et al. (2017) have proposed deep
generative models, notably generative adversarial networks (GANs) (Goodfellow
et al., 2014; Jacobs et al., 2017), and devised an innovative deconvolution
technique to recover features from SDSS galaxy images.

In the realm of strong lensing systems detection, Petrillo et al. (2017) have
conducted an analysis of Kilo Degree Survey (KiDS) data using Convolutional
Neural Networks (CNN). Their efforts yielded successful identification of
several candidates of strong lensing systems within the KiDS dataset. Metcalf
et al. (2019) have implemented a variety of methods, including visual
inspection, arc and ring finders, support vector machines (SVM), and
convolutional neural networks (CNN) in detection of strong lensing systems.
These methods provided approaches for strong lensing systems finding and
classification in Euclid data. Jia et al. (2022) have introduced a
transformer-based deep neural network (DETR) for strong lensing systems
detection, which demonstrated noteworthy proficiency in identifying strong
lensing systems on the scale of galaxy clusters. The transformer model is
designed to concentrate its attention on key regions like distorted images or
arcs during the process of strong lensing systems detection. Through its
adaptive allocation of attention across different components, the algorithm
effectively captures both local and global information, thereby enhancing the
efficiency of the detection process.

Building upon the methodology introduced in Jia et al. (2022), we have further
implemented additional efforts. These enhancements incorporate the utilization
of a visual transformer employing a sliding window strategy (Liu et al.,
2021). This mechanism divides the image into an array of overlapping sub-
windows, treating each sub-window as an input for processing, which addresses
the impact of input length restrictions and the imbalance of positive and
negative samples on the results. By operating at the window level, the model
gains the ability to effectively capture features of diminutive and densely
clustered objects, thereby augmenting its capability to detect targets. With
these adjustments, our approach is now capable of handling input data of
varying lengths, and it results in more equitable feature extraction for a
more comprehensive representation of strong lensing phenomena.

Furthermore, given the current limited number of detected strong lensing
instances and various forms of noise that affect observation images, we have
developed an end-to-end pipeline based on the previously discussed detection
strategy. This pipeline encompasses three distinct components: image
simulation for training data generation, image pre-processing, and target
detection. The image simulation component serves to generate a substantial
volume of simulated images. These simulated images incorporate prior knowledge
about strong lensing systems, which is then utilized to train the detection
algorithm. The subsequent image pre-processing step is employed to process
real observation images. This involves deconvolution of observation images
with predefined PSFs from the telescope and adjusting the grayscales of these
images. The image pre-processing component enhances the visibility of
celestial objects with low signal-to-noise ratios. For the detection
component, the simulated images are used as the training data set. After
training, real observation images known to contain strong lensing systems are
processed using the image pre-processing algorithm. The outcomes of the image
pre-processing algorithm are employed to fine-tune the previously trained
detection algorithm. Finally, all real observation images undergo pre-
processing before being subjected to the detection algorithm. This sequential
process facilitates the identification of strong lensing systems in the
observation data.

This paper is structured as follows. In Section 2, we elaborate on the
methodology employed to generate simulated images featuring strong lensing
systems. In this paper, we generate simulated images with both galaxy scale
and galaxy cluster scale strong lensing systems, therefore, our method could
detect strong lensing systems with both galaxy scale and galaxy cluster scale.
In this article, the primary focus is on detecting strong lensing systems at
the galaxy scale. In Section 3, we outline the procedures involved in data
pre-processing. In Section 4, we introduce the detection algorithm for strong
lensing systems, leveraging the attention mechanism. We subsequently evaluate
the efficiency of our model using simulated data acquired through the CSST. In
Section 5, we establish a comprehensive pipeline for detecting strong lensing
systems and assess its performance using public media images from Euclid Early
Release Observations and images from the Legacy Imaging Surveys. Finally, in
Section 6, we present our conclusions and anticipate potential avenues for
future research.

##  2 The Method to Generate Simulated Data

The China Space Station Telescope (CSST) is a 2-meter space telescope slated
to launch in approximately 2025, operating within the same orbit as the China
Manned Space Station (Zhan, 2021). As a significant scientific project within
the Space Application System of the China Manned Space Program, CSST is
designed to be a large field of view, covering around 1.1 square degrees, with
high spatial resolution of roughly 0.1500 arcseconds at 633 nm for its Survey
Camera (SC). This versatile telescope spans multiple wavelength bands, from
the near-ultraviolet (NUV) to the near-infrared (NIR), and it will
simultaneously conduct photometric and slitless spectral surveys across an
extended sky area of 17,500 square degrees.

Generating simulated data, as discussed in our previous papers (Jia et al.,
2022, 2023a), serves a crucial purpose in the detection of celestial objects,
particularly when sufficient training data is lacking. Simulated data provide
valuable prior information about the targets we aim to detect. These
simulations are important in training neural networks, enabling them to
swiftly adapt to real observation data through transfer learning.
Additionally, we leverage simulated CSST data to make predictions regarding
the scientific outcomes of the CSST in the realm of strong lensing detection.
The simulation code consists of two key components: the strong lensing
simulator and the imaging simulator tailored for the CSST, both of which will
be briefly introduced below.

We use the PICS strong lensing system simulator without introducing noise or
other effects (Li et al., 2016). Our simulation process, akin to Madireddy et
al. (2019), involves six steps: (1) generating lens and source populations
based on statistical properties, (2) constructing mass and light models for
foreground lensings, (3) calculating lens deflection fields, (4) creating
light profiles for background source galaxies, (5) conducting ray-tracing
simulations to generate strong lensing images using deflection fields and
source light profiles.

The populations of lenses and sources are built upon an advanced extragalactic
catalog (Korytov et al., 2019) named CosmoDC2, which is a synthetic galaxy
catalog to support precision science with the Legacy Survey of Space and
Time222 urlhttps://rubinobservatory.org/explore/lsst (LSST). It covers a
$440deg^{2}$ of sky area to a redshift of $z=3$ and is complete to a magnitude
depth of 28 in the r-band. Various properties, including stellar mass,
morphology, spectral energy distributions, broadband filter magnitudes, host
halo information, and weak lensing shear, characterize each galaxy in the
catalog. The CosmoDC2 has undergone a wide range of observation-based
validation tests to ensure consistency with real observations. The official
release of the cosmoDC2 dataset and documentation can be found
here333https://portal.nersc.gov/project/lsst/cosmoDC2/_README.html.

Lenses are modeled as a combination of dark matter halos and galaxies. The
dark matter halo follows the Navarro, Frenk & White (NFW) model, given by
Navarro et al. (1996), as shown below:

$\rho(r)=\frac{\rho_{\mathrm{c}}}{(r/r_{s})(1+r/r_{s})^{2}}\,,$ (1)

where $\rho_{\mathrm{c}}$ is a characteristic density and $r_{s}$ a scale
radius. Its lensing potential is given by Golse & Kneib (2002),

$\varphi(x)=2\kappa_{s}\theta_{s}^{2}\,h(x)\,$ (2)

with $\kappa_{s}=\rho_{c}r_{s}\Sigma_{\mathrm{crit}}^{-1}$,
$\theta_{s}=r_{s}/D_{a}(z_{l})$, and $x=\theta/\theta_{s}$. Where
$D_{a}(z_{l})$ stands for the angular diameter distance from the observer to
the lens plane, and

$h(x)=\begin{cases}\displaystyle{\ln^{2}{\frac{x}{2}}-\mathrm{arcch}^{2}\frac{1}{x}}&(x<1)\\\
\displaystyle{\ln^{2}{\frac{x}{2}}+\arccos^{2}{\frac{1}{x}}}&(x\geq
1)\end{cases}$ (3)

To achieve an elliptical lensing potential
$\phi_{\epsilon}(x)\equiv\phi(x_{\epsilon})$, Golse & Kneib (2002) defined
$\varepsilon=(1-q^{2})/(1+q^{2})$ to create the below elliptical coordinate
system then substituted $x$ by $x_{\varepsilon}$.

$\left\\{\begin{array}[]{lcl}x_{1\epsilon}&=&\sqrt{1-\epsilon}\,x_{1}\\\
x_{2\epsilon}&=&\sqrt{1+\epsilon}\,x_{2}\\\
x_{\epsilon}&=&\sqrt{x_{1\epsilon}^{2}+x_{2\epsilon}^{2}}\ =\
\sqrt{a_{1\epsilon}x_{1}^{2}+a_{2\epsilon}x_{2}^{2}}\\\
\phi_{\epsilon}&=&\arctan\left(x_{2\epsilon}/x_{1\epsilon}\right)\end{array}\right.$
(4)

Then the deflection angles can be calculated numerically according to the
relation $\alpha_{1}=\partial\phi_{\epsilon}(x)/\partial x_{1}$ and
$\alpha_{2}=\partial\phi_{\epsilon}(x)/\partial x_{2}$. Therefore, the
deflection angles for the dark matter halos are described by
$\\{x_{nfw,1},x_{nfw,2},M_{vir},c_{vir},q_{nfw},\phi_{nfw},z_{l},z_{s}\\}$,
where $(x_{nfw,1},x_{nfw,2})$ is the angular position of the dark matter halo
in the field of view, $M_{vir}$ is the virial mass, $c_{vir}$ is the
concentration, $q_{nfw}$ and $\phi_{nfw}$ are the axis ratio and positional
angle. $z_{l}$ and $z_{s}$ represent the redshifts of the lens and source
planes, respectively.

The density profile of galaxies are modeled as a singular isothermal ellipsoid
(SIE), has deflection angles given by Kormann et al. (1994); Keeton (2001),

$\alpha_{1}=\frac{\sqrt{q}\,\theta_{\mathrm{E}}}{\sqrt{(1-q^{2})}}\tan^{-1}\left[\frac{\sqrt{1-q^{2}}x_{1}}{\sqrt{q^{2}x_{1}^{2}+x_{2}^{2}}}\right]\,\,,$
(5)
$\alpha_{2}=\frac{\sqrt{q}\,\theta_{\mathrm{E}}}{\sqrt{(1-q^{2})}}\tanh^{-1}\left[\frac{\sqrt{1-q^{2}}x_{2}}{\sqrt{q^{2}x_{1}^{2}+x_{2}^{2}}}\right]\,\,,$
(6)

where $q$ is the minor to major axis ratio and $\theta_{\mathrm{E}}$ is an
effective factor to represent Einstein radius,

$\theta_{\mathrm{E}}=4\pi\left(\frac{\sigma_{v}}{c}\right)^{2}\frac{D_{ls}}{D_{s}}\,\,.$
(7)

Therefore, the complete parameter set required by equations 5 to equation 7)
is $\\{x_{1},x_{2},\sigma_{v},q_{gal},\phi_{gal},z_{l}\\}$, where
$(x_{1},x_{2})$ is the angular position of the galaxy centers in the field of
View, $\sigma_{v}$ is the velocity dispersion of the galaxy, $q_{gal}$ is the
axis ratio, $\phi_{gal}$ is the position angle, and $z_{l}$ is the redshift of
the lens plane. The parameters ${x_{1},x_{2},q_{gal},\phi_{gal},z_{l}}$ are
taken directly from the cosmoDC2 catalog. $\sigma_{v}$ is derived from the
$L-\sigma$ scaling relation from the bright sample of Parker et al. (2007)
given by

$\sigma_{v}=142\left(\frac{L}{L_{\star}}\right)^{(1/3)}~{}{\rm
km~{}s}^{-1}\,\,,$ (8)

where, $\log_{10}(L/L_{\star})=-0.4(mag_{r}-mag_{r\star})$, and $mag_{r}$ is
the apparent $r$-band magnitude of the galaxy given by the cosmoDC2 catalog.
We use apparent r-band magnitudes ($magr$) from the CosmoDC2 catalog and adopt
an evolving $mag_{r\star}=+1.5(z-0.1)-20.44$ along with redshift as per More
et al. (2016) and Faber et al. (2007).

For a given lens, summing all gravitational lensing contribution of its
components together, we obtain the total deflection angle $\bf{\alpha_{tot}}$
then the lensing equation $\bf{y}=\bf{x}-\bf{\alpha_{tot}}$. Hence, the strong
lensed arcs can be generated by tracing light rays from the lens plane to the
source plane, where the source images are drawn according to their positions
and light profiles. To ensure prominent lensing features, we require
$z_{s}>z_{l}+0.5$ for source galaxies and locate one source manually by
randomly choosing source positions in regions with lensing magnifications
exceeding 20 on the source plane. Galaxies in the light cone, whether lensed
or not, are modeled with composite Sersic profiles based on CosmoDC2
parameters. Lensed arcs are rendered with Sersic profiles on ray-traced grids.

With the above strategy of generating strong lensing system images, we utilize
the CSST simulator, an End-to-End pipeline integrating cosmology simulation,
gravitational ray-tracing, optical instruments, and imaging, to generate mock
observation images444https://csst-tb.bao.ac.cn/code/csst_sim/csst-simulation.
In this simulator, galaxies consist of bulges and disks, which are modeled
with composite Sersic profiles based on CosmoDC2 parameters, and they are
convolved with simulated PSFs for CSST. These galaxies are then imaged onto
detectors with dimensions of $9216\times 9232$ pixels with pixelscale of 0.074
arcseconds. Then we choose strongly lensed arcs in three steps: (1) calculate
the reference Einstein Radii $\theta_{E,ref}$ of all galaxies and galaxy
clusters in the above field of view by setting $z_{s}=10.0$; (2) remove the
deflectors with $\theta_{E,ref})<0.2"$; (3) randomly choose $1\%$ of the rest
deflectors as lenses. We then generate strongly lensed arcs for the selected
lenses as described in the above paragraphs, and the pixelized images of the
strongly lensed arcs are passed into the CSST-image-simulator afterwards.
Subsequently, both galaxies and strong strong lensing systems are imaged
together onto the detectors.

Rather than relying on parametric models, the PSF is derived from an optical
design model. To produce a comprehensive set of realistic PSFs that consider
the impact brought by the optical system, an optical emulator is created to
simulate high-fidelity PSFs for CSST. This optical emulator for CSST comprises
six distinct modules, each simulating optical aberrations stemming from mirror
surface roughness, fabrication errors, CCD assembly errors, gravitational
distortions, and thermal distortions. Additionally, the simulated PSF
incorporates two dynamic errors arising from micro-vibrations and image
stabilization. We have further introduced various sources of noise into the
simulated CSST images, encompassing shot noise, sky background, and detector
effects. To accomplish this, we have employed Galsim (Rowe et al., 2015) to
simulate photon generation from a given galaxy, accounting for the throughputs
of the CSST system, including mirror efficiency, filter transmission, and
detector quantum efficiency. We have also introduced Poisson noise originating
from both the sky background and the dark current of the CCD detector.
Specifically, we have set the i-band background level to 0.212
$e^{-}$/pixel/s, with a dark current of 0.02 $e^{-}$/pixel/s, resulting in an
average of approximately 35 $\rm e^{-}$/pixel in a 150s exposure. Furthermore,
we have incorporated read noise using a Gaussian distribution with a standard
deviation of approximately 5.0 $e^{-}$/pixel. In simulating the creation of
mock galaxy images on the detector, we have also accounted for bias and
applied gain factor of the detector.

##  3 The Data Pre-processing Method

Within this section, we establish the data pre-processing method for images
captured by the CSST. It is worth noting that these steps can be adjusted, or
even omitted, when they are used to process observation data obtained by other
telescopes. Moreover, should the need arise, parameters within these processes
can be readily fine-tuned to adapt with images obtained by other surveys.

###  3.1 The Image Cropping Step

Given that images acquired by the CSST are relatively large, with size of
$9232\times 9216$ pixels, we find it is necessary to crop them into smaller
sections, each with size of $1000\times 1000$ pixels. This step is essential
to align with hardware constraints, as the detection algorithm needs
approximately 14.88 GB GPU memory for an image of dimensions $1000\times 1000$
pixels. Given that this study uses an RTX 3090 Ti GPU with a maximum memory
capacity of 24 GB, this image size represents the upper limit of what the GPU
can accommodate. Moreover, to ensure that images of strong lensing systems
remain intact and undivided, we have introduced overlapping segments, with
each segment featuring an overlap region of 80 pixels. This approach results
in the generation of 100 smaller images following the cropping of a single
original larger image. It is worth noting that the image cropping step can be
circumvented if access to a GPU with greater memory capacity is available.

###  3.2 The Image Deconvolution Step

Astronomical imaging faces inherent constraints in angular resolution,
primarily attributed to factors like atmospheric turbulence, diffraction,
instrumental effects, and others. This limitation is rooted in the
mathematical equivalence of Fraunhofer diffraction to a Fourier transform,
indicating the absence of signal on Fourier scales smaller than the
diffraction limit. Consequently, when the PSF sets the diffraction-limited
optics of the telescope, resulting in zero signal-to-noise ratio on scales
smaller than the PSF, the image information becomes incomplete. Additional
factors, such as jitter, may exacerbate the performance degradation.
Leveraging advancements in machine learning, deconvolution neural networks
have been employed to augment and suppress noise in astronomical images across
various wavelengths, with the goal of restoring diffraction-limited
performance Lauritsen et al. (2021). In this study, we assume that we can
obtain PSFs of the CSST and these images can be used to generate simulated
blurred images. These blurred images and the original images can be used as
the training set for deep learning based image restoration algorithms. We
employ the PSF-NET method for image deconvolution, as presented by Jia et al.
(2020). The PSF-NET contains two neural networks, a PSF neural network and a
restoration neural network. The PSF neural network models the PSF,
facilitating the conversion of high-resolution images into blurred
counterparts. The restoration neural network, named RESTORE, encapsulates the
deconvolution algorithm, thereby converting blurred images back to high-
resolution forms. Both of these neural networks include residual blocks, in
addition to multiple convolutional and transposed convolutional blocks, as
illustrated in Figure 1.

Figure 1: The flowchart of image restoration step, which contains an image
restoration neural network (RESTORE) and an image blurring neural network
(PSF).

During the training phase, both the PSF neural network and the RESTORE neural
network are trained. This approach enhances training efficiency while
mitigating the risk of overfitting. Subsequent to training, the RESTORE neural
network could be used directly to restore blurred images. In accordance with
the functionalities of these two networks, we adjust the loss function of
these neural networks as depicted in Equation 9, following the method proposed
in (Lv et al., 2022; Jia et al., 2024). Here, $L_{idet}$ signifies the
identity loss function, $L_{rec}$ denotes the cyclic loss function, and
$L_{fl}$ stands for the focal frequency loss function.

$\displaystyle Loss=L_{idet}+L_{rec}+L_{fl},$ (9) $\displaystyle
L_{idet}=\|PSF(Img_{org})-Img_{blur}\|_{2}$
$\displaystyle+\|Restore(Img_{blur})-Img_{org}\|_{2},$ $\displaystyle
L_{rec}=\|Restore(PSF(Img_{org}))-Img_{org}\|_{2}$
$\displaystyle+\|PSF(Restore(Img_{blur}))-Img_{blur}\|_{2},$ $\displaystyle
L_{ffl}=W\times L_{fl}.$

In the above equation, both $L_{idet}$ and $L_{rec}$ are used to minimize the
mean square error that exists between the original image and the image
restored by the neural network. The PSF neural network and the RESTORE neural
network share an encoder-decoder structure. However, the decoder section
encompasses several convolutional and upsampling layers. These layers
introduce gaps in the restored image, leading to loss of information and the
introduction of artifacts. Such issues can disrupt the accurate interpretation
and analysis of the image. To enhance the efficacy of our neural network, we
introduce a focal frequency loss, denoted as $L_{ffl}$ (Jiang et al., 2021).
This particular loss function contributes to the improvement of neural network
performance by incorporating regularization weights into the density of the
power spectrum, W. The loss of focal frequency, $L_{ffl}$, is equivalent to
the mean square error computed in the spatial frequency domain between the
restored image and the original image, as shown in Equation 10. In this
equation, $FFT$ denotes the Fast Fourier Transformation, and $\alpha$
corresponds to the regularization parameter, which is assigned a value of 1.

$\displaystyle
W=\left|FFT(Img_{org})-FFT(Restore(Img_{blur}))\right|^{\alpha},$ (10)
$\displaystyle L_{fl}=\|FFT(Img_{org})-FFT(Restore(Img_{blur}))\|^{2}.$

In the provided equation, $L_{idet}$ and $L_{rec}$ are employed to minimize
the mean squared error (MSE) between the original image and the image restored
by the neural network. Adhering to the image restoration principles discussed
earlier, we have performed restoration on the simulated data that contained
noise. Following this, we can compare the restored image with the original
noisy after applying the asinh transformation. The restoration results are
visualized in Figure 2. As shown in this figure, the quality of images have
been imporved with our method. We use the peak signal-to-noise ratio (PSNR)
defined in Wang et al. (2004); Xu et al. (2014) to evaluate the quality of
these images. In this case, the PSNR has been improved from 48.22 to 51.77 by
our method. This highlights how our method can effectively improve the signal-
to-noise ratio of faint celestial targets.

(a) (b) (c) (d)

Figure 2: We chose the r, g, and i bands to generate a color image. Figure (a)
shows the raw data, Figure (b) shows the data after the asinh transformation,
Figure (c) displays the restoration results and Figure (d) shows the restored
image after the asinh grayscale transformation. As depicted in these figures,
the incorporation of image restoration and grayscale transformation steps
significantly enhances the visibility of image details.

.

###  3.3 The Grayscale Transformation Step

In contrast to typical images, astronomical images frequently encompass
celestial objects with significantly wider grayscale ranges. Consequently,
certain images exhibiting a low signal-to-noise ratio might appear similarly
to the background when compared to the overall grayscale. While deep neural
networks are capable of acquiring non-linear mapping functions, it might be an
inefficient utilization of computational resources if we can establish
straightforward transformation functions. A grayscale transformation function
is one example of such functions. The asinh function, introduced by Lupton et
al. (2004), serves to enhance the signal-to-noise ratio of faint targets. This
function is defined by Equation 11,

$asinh(x)=ln(x+sqrt(x^{2}+1))$ (11)

where $x$ is a real number. When the value of $x$ is relatively large,
$asinh(x)$ can be approximated as $ln(x)$. When the value of $x$ is relatively
small, $asinh(x)$ can be approximated as $x$.

When handling these images, our initial step involves computing the maximum
and minimum values within the provided image to establish the data range. This
range is then used to derive the scaling factor for the data. It is important
to highlight that, when analyzing processed images using our method where the
flux has been calibrated across different bands, we can utilize the maximum
and minimum values. However, if dealing with real observation data, it is
crucial to meticulously choose suitable values based on the photometry zero
point and the full well depth of the observed images. The equation to
calculate this scaling factor in this paper is illustrated in Equation 12,

$scale\\_factor=asinh(0.5\times\frac{(max\\_value-
min\\_value)}{max\\_value}),$ (12)

where $max\\_value$ and $min\\_value$ respectively represent the maximum and
minimum values of the image. After calculating the scaling factor, the data
can be subjected to an asinh transformation, defined in equation 13,

$asinh\\_value=asinh(\frac{0.5\times(data\\_value-min\\_value)}{2\times
scale\\_factor}),$ (13)

where $data\\_value$ corresponds to the original data value, $asinh\\_value$
signifies the value after undergoing the asinh transformation, while
$min\\_value$ and $scale\\_factor$ respectively denote the minimum value and
the scaling factor determined during the scaling factor calculation. The
figure illustrates the image following the grayscale transformation process.
As shown in figure 2 (c), celestial objects with a low signal-to-noise ratio
become distinctly visible.

##  4 The Strong Lensing System Detection Algorithm Based on the Swin
Transformer

###  4.1 The Structure of the Strong Lensing System Detection Algorithm

The algorithm proposed in this paper is built upon the foundation of the
transformer model. The transformer, originally applied extensively in the
realm of Natural Language Processing (NLP), has yielded favorable outcomes in
numerous NLP tasks (Vaswani et al., 2017). Building on these successes, the
transformer architecture has been extended to tasks involving image
processing. However, in contemporary transformer-based neural networks, tokens
are confined to fixed sizes (Vaswani et al., 2017; Dosovitskiy et al., 2020;
Liu et al., 2021), thus restricting the input to a fixed number of dimensions.
This presents a challenge when it comes to images, which inherently possess
thousands of dimensions and requires precise predictions at the pixel level.
As a consequence, the transformer faces difficulties in effectively handling
high-resolution images, largely due to the quadratic increase in computational
complexity with respect to image size.

To surmount these challenges, we implement an enhancement to the transformer
architecture by incorporating the Swin Transformer model as a core feature
extraction module (Liu et al., 2021; Jia et al., 2023b). The Swin Transformer
has two noteworthy advantages. Firstly, its hierarchical structure aligns
seamlessly with the feature pyramid network (Lin et al., 2017; Liu et al.,
2021)) or the U-Net (Ronneberger et al., 2015; Liu et al., 2021), enhancing
its compatibility with such frameworks. Secondly, it introduces the concept of
moving windows, where self-attention calculations are confined to a local
window, as opposed to global attention calculations (Liu et al., 2021). This
architectural choice significantly mitigates model complexity, reducing the
quadratic complexity ($N^{2}$) to linear complexity. These attributes
collectively render the Swin Transformer an adaptable feature extraction
model, well-suited for a range of visual tasks.

The architecture of the model is shown in Figure 3. Here is an overview of its
structure: The initial step involves feeding preprocessed images into the Swin
Transformer, which serves as the feature extractor. Subsequently, the outputs
from the Swin Transformer are directed into the RPN network for binary
classification and regression of positions. Regions potentially containing
strong lensing systems are singled out, and using the ROIAlign layer, the
feature map is cropped and aligned to generate fixed-size feature tensors.
These tensors are then independently transmitted to the classification branch,
bounding box regression branch, and mask segmentation branch, each responsible
for different aspects of the object detection task. By amalgamating the
outputs from these three branches, the network can simultaneously provide
information about comprehensive insights regarding the position and the mask
of each detected strong lensing systems.

Figure 3: As depicted in this figure, our method initiates the feature
extraction process using the Swin Transformer. These extracted features are
subsequently compiled into a feature map, which is then utilized for box
regression and classification.

Figure 4 shows the precise architecture and data flow of the Swin Transformer.
An image, sized $H\times W\times C$, is divided into $4\times 4$ patches,
effectively transitioning from pixels to patches as the smallest unit of
representation. This procedure generates a feature map of
$\frac{H}{4}\times\frac{W}{4}\times(C\times 4\times 4)$. This feature map
undergoes three distinct stages. In the first stage, a linear embedding
transforms the feature map from $\frac{H}{4}\times\frac{W}{4}\times(C\times
4\times 4)$ to $\frac{H}{4}\times\frac{W}{4}\times Channel$. In the subsequent
three stages, patch merging is executed, performing operations subsequent to
the amalgamation of neighboring patches. For the classification networks, the
final output is obtained by connecting a Layer Norm layer, a global pooling
layer, and a fully connected layer.

Figure 4: The specific structure and data flow of the Swin Transformer. The
input image undergoes linear embedding, patch merging, Layer Norm, global
pooling, and fully connected layers to obtain the final output.

In each stage, the initial input undergoes downsampling via a Patch Merging
layer. This layer groups neighboring pixels into patches, which are
subsequently combined to form four feature maps. These four feature maps are
then merged in the depth dimension. Following this, a LayerNorm and fully
connected layer are employed to linearly adjust the depth of the feature map,
halving its original size to $\frac{C}{2}$. After traversing the Patch Merging
layer, the height and width of feature maps are halved, while its depth is
doubled. To manage high-resolution images with many tokens more effectively,
the Swin Transformer implements a technique known as local window self-
attention. This approach reduces computational complexity while maintaining
commendable outcomes. In essence, the model concentrates on local regions at a
given moment, rather than attempting to process the entire image concurrently.
This method facilitates a step-by-step image processing approach, making it
feasible to handle a lot of images without overwhelming computational
resources. To ensure coherence among windows and boost efficiency, the Swin
Transformer adopts a strategy called "shifted window partitioning". This
strategy mitigates computational load while ensuring interconnections among
the windows, as shown in Figure 5.

Figure 5: The diagram illustrates the computation diagram of self-attention
with a shifting window. In Layerl, each window is averaged, and the self-
attention is calculated independently for each window. In Layerl+1, the
windows are shifted systematically, generating new windows that maintain
connectivity between the windows when calculating attention.

As depicted in Figure 5, $Layerl$ contains only 4 windows, while $Layerl+1$
encompasses 9 layers. Multi-Scale Analysis (MSA) is executed within each of
these windows. To alleviate computational burden, an Efficient Batch
Computation approach is employed, utilizing shifted configurations for
resolution. This is shown in Figure 6. The method involves filling relatively
small windows to dimensions of $M\times M$ through a shifting operation, while
masking the areas that are filled with attention. In Figure 6, after
cyclically shifting to the upper left, the batch window encompasses several
sub-windows that are not adjacent in the feature map. The number of batch
windows aligns with the window partition count. During the computation step,
self-attention is applied solely to each sub-window, with a few others being
masked out. After the computation step, the sub-window is repositioned to its
original orientation. In simpler terms, this method enlarges windows by
shifting them and disregards specific values in the process. This approach
yields a batch window composed of disconnected sub-windows. Subsequently,
self-attention is carried out individually within each sub-window, and once
calculations conclude, the original arrangement is restored.

Figure 6: The figure illustrates an efficient batch processing approach used
for self-attention in the context of shifting window partitioning.

###  4.2 Training of the Strong Lensing System Detection Algorithm

Due to the large number of parameters of the Swin Transformer, utilizing
random weights for neural network training would consume substantial
computational resources. Therefore, we initialize the network with the weights
provided by K-H-Ismai 555https://github.com/SwinTransformer/Swin-Transformer-
Object-Detection#mask-r-cnn. As described in Section 2, the simulated data
serves as the training and validation datasets for the neural network. Our
simulation assumes a galaxy density of 55.6 galaxies per arcmin2 detectable by
the CSST, resulting in an expected 1.4 strong lensing systems per arcmin2.
This galaxy density aligns with the Stage IV galaxy surveys. The training
dataset consists of 3,000 images, each with dimensions of 1000 x 1000 pixels.
Training and validation sets are randomly split with a 7:3 ratio. It is worth
noting that if the model is intended for application with data from other sky
survey projects, utilizing images generated by specific simulation codes or
real observation data for fine-tuning would be necessary, given the
specialized nature of the CSST simulation code.

We generate labels for these images using the following approach. Images of
strong lensing systems are enclosed with bounding boxes, and we establish
these boxes using center coordinates and a fixed size. Since images of strong
lensing systems often exhibit varying sizes, we opt for bounding boxes with a
fixed dimension of $50\times 50$ pixels. This strategy enables precise object
localization, ensuring that a broader range of objects is captured while
minimizing the inclusion of extraneous background details. Consequently, this
approach enhances the efficacy of training the model. During the training
stage, the learning rate for the Swin Transformer is set as 0.001. As we train
the neural network, a consistent decrease in loss could be observed. After 100
epochs of training, which cost around 72 hours in a computer with one RTX 3090
Ti GPU, the loss stops decreasing, which shows that the model is convergence.
The learning curve is depicted in Figure 7.

Figure 7: This figure illustrates the learning curve observed throughout the
entire training and validation process. We can find that the model achieves
convergence at approximately 80 epochs.

##  5 Performance Evaluation of the Pipeline

In this section, we will assess the performance of the pipeline using
simulated CSST data and explore the potential scientific insights the CSST
could provide for studying strong lensing. Additionally, we will demonstrate
the essential nature of various stages within our pipeline.

###  5.1 Evaluation Metrics of the Detection Results

In object detection tasks, the accuracy of position prediction is often
evaluated using a metric known as Intersection over Union ($IOU$) ratio. This
ratio quantifies the degree of overlap between the predicted bounding box and
the actual (ground truth) box. Since the position and size of prediction
results are both important for object detection tasks, we calculate the $IOU$
value between our prediction and the ground truth box. A higher $IOU$ value
indicates more precise predictions. The $IOU$ calculation is defined by
Equation 14,

$IOU=\frac{Intersection}{Union},$ (14)

where $Intersection$ pertains to the overlap region between the predicted
bounding box and the actual (ground truth) bounding box, while $Union$
encompasses the entirety of the space covered by both the predicted bounding
box and the ground truth bounding box. In simpler terms, $Intersection$
corresponds to the shared area and $Union$ represents the total area covered
by both boxes. When evaluating object detection results using the IOU metric,
we need to select a specific threshold. If the value $IOU$ between the
predicted box and the ground truth box exceeds this threshold, we consider the
predicted box to have successfully detected the object, and the model
classifies it as true positive ($TP$). On the other hand, if the $IOU$ value
falls below the threshold, the predicted box is considered an unsuccessful
detection. In this case, the model designates it as either a false negative
($FN$) if it failed to detect a true object or a false positive ($FP$) if it
mistakenly identified a non-object region as an object. This threshold-based
approach helps us evaluate the performance of the model in distinguishing
between true positives, false negatives, and false positives.

In order to evaluate the performance of our model, we compute two crucial
metrics: precision and recall. Precision informs us about the ratio of
accurately classified positive results relative to all positive results, and
its calculation is based on the following equation 15,

$Precision=\frac{TP}{TP+FP}.$ (15)

The recall rate, often referred to as the "detection rate," defines the
percentage of accurately recognized bounding boxes out of all the actual
positive boxes. Its computation is determined by the formula depicted in
Equation 16,

$Recall=\frac{TP}{TP+FN}.$ (16)

The $Precision$ and $Recall$ are interconnected metrics with a reciprocal
relationship. As we elevate the $IOU$ threshold, both $Precision$ and $Recall$
typically experience a decrease. This signifies that the model becomes more
precise in recognizing true positives, yet it could overlook certain positive
instances, resulting in a decline in $Recall$. Conversely, by lowering the
threshold, the $Recall$ can increase as the model becomes more attuned to
positive instances. However, this improvement in $Recall$ comes with a trade-
off: the $Precision$ may decrease, potentially leading to more false positive
predictions by the model.

For an accurate model evaluation, achieving a balance between precision and
recall is essential, and this balance can be attained by determining an
optimal threshold. In this way, we can achieve a model that correctly
identifies positive samples while minimizing the occurrence of false
positives. To balance between these parameters, we need to use the Precision-
Recall (PR) curve. The PR curve illustrates the interplay between precision
and recall. Precision indicates the correctness of positive predictions, while
recall gauges the ability of the model to detect all actual positive
instances. On the PR curve, we plot recall on the x-axis and precision on the
y-axis. By examining this curve, we can make informed decisions about the
performance of the model and select the threshold that aligns with our
specific requirements. Typically, the closer the PR curve resides to the
upper-right corner, the better the performance is. To quantitatively measure
the trade-off between precision and recall for an individual class, we compute
the Average Precision (AP), which involves calculating the area under the
Precision-Recall curve. Additionally, the mean Average Precision (mAP)
represents the average AP value across all classes, offering an assessment of
the overall model performance. In this paper, we employ PR curves and mAP to
compare the performance of different trained models, aiding in our
comprehensive evaluation of their efficacy.

###  5.2 Performance Evaluation of the Detection Algorithm

In this subsection, we will show the performance of the detection algorithm
with the CSST simulation data. Since there are no data pre-processing steps
used in this subsection, we use the detection results as the baseline. Two
sets of simulated data are used in this subsection. The CSST simulation data
with no PSF variations, read out noise or back ground noise are considered as
clear data and CSST simulation data with realistic PSF variations and
different noises are considered as noisy data. Two neural networks are trained
with clean data and noisy data separately through the same procedure. The
results are shown in figure 8.

(a) (b)

Figure 8: Figure (a) presents the PR curve of detection results from clear,
unprocessed image, while Figure (b) displays the detection results from noisy,
unprocessed images. As shown in these figures, noise and blur will introduce
very strong effects to detection results and we need to design some algorithms
to reduce these effects. In these figures, we can find that if we set smaller
IOU, the AP will be larger, which means we can obtain higher recall rate and
precision rate at the cost of lower position regression accuracy.

We designate RT3 to denote clear data and RT4 for noisy data. As illustrated
in Figure 8(12(a)) and Table 1, setting $IOU$ to 0 yields a precision rate of
approximately 30%, while the recall rate is 90%. This indicates that the model
can effectively detect nearly all strong lensing systems, albeit with only 30%
of these detections being genuine strong lensing systems. However, when $IOU$
is set to 0.5, as shown in the RT3 column in Table 2, there is a noticeable
decrease in the recall rate to 70%, suggesting the model could identify
roughly 70% of all strong lensing systems. In Figure 8(12(b)) and Table 1, the
influence of noise becomes apparent, resulting in a detection accuracy of only
69.6% when $IOU$ is set at 0. With a recall rate of 80%, the precision rate
drops to merely 53.3%, indicating that only about half of the detected results
are strong lensing systems, while the majority are false positives. This low
precision rate would necessitate significant human intervention in practical
applications. Moreover, with increasing $IOU$ values, as exemplified by the
data in the RT4 column of Table 2, the accuracy rate sharply decreases,
reaching 25.5% when $IOU$ is set to 0.5. Based on the outcomes presented
above, it is apparent that while our methods can yield some results, there are
still certain aspects that need improvement. When employing a low $IOU$
threshold, it is expected that numerous detection results would exhibit
relatively low precision rates, demanding extensive subsequent human
interventions. Consequently, there is a need to further refine our approach
and develop complementary methods that can enhance the efficiency of
detection.

###  5.3 Performance Evaluation of the Detection Pipeline

As discussed earlier, in order to obtain scientific outcomes with acceptable
costs from observation data collected by the CSST, there is an urgent need to
enhance the detection capability of our algorithm. Given the impact of varying
levels of noise and variable PSFs on images, one strategy involves leveraging
image restoration algorithms such as the PSF-Net proposed by Lv et al. (2022);
Jia et al. (2024). This involves training the PSF-Net with CSST PSFs and
subsequently employing it to enhance the quality of observation images.
Considering that many strong lensing systems exhibit relatively low signal-to-
noise ratios, we advocate the utilization of the gray scale transformation
algorithm outlined in Lupton et al. (2004). This approach renders dim
celestial objects easier to be detected. Our proposed strategy involves
training the swin transformer-based detection algorithm with a mix of CSST
simulation data containing both noisy and clear images. Subsequently, we
deploy this trained swin transformer to process images at various stages
within the data processing pipeline, thereby providing clearer insights into
the necessity of developing a robust data detection pipeline.

We test the performance of our algorithm using three sets of simulated images,
and the results are depicted in Figure 9. In Figure 9(12(a)), it is evident
that clear images after gray scale transformation demonstrate outstanding
performance, achieving a precision of 99% within a recall range up to 80%.
This highlights the capability of the model to almost flawlessly identify
nearly all strong lensing systems with exceptional accuracy. A slight decline
is observed only at an IOU of 0.9, attributable to the stringent precision
requirement for localization, leading to potential undetected strong lensing
systems. In comparison to unprocessed clear images, the detection accuracy
rises to 0.975 at an IOU of 0.5, representing a substantial 66% enhancement.
The initial test indicates that gray scale transformation is a crucial step in
data preprocessing. We utilize the asinh transformation to process noisy
images, followed by employing the trained Swin Transformer to detect strong
lensing systems in these images. The detection results are presented in Figure
9(12(b)). We use RT3 as clear data, RT4 as noisy data, RT3+asinh and RT4+asinh
as asinh gray scale transformation, and RT4+restore+asinh as images after
restoration and asinh transformation. In both Table 1 and Table 2, when
comparing RT3+asinh and RT4+asinh, regardless of whether the IOU is 0 or 0.5,
the mAP of noisy images is smaller than that of clear images. Moreover, as the
recall rate ranges from 0.8 to 1.0, the precision decreases significantly,
resulting in the loss of many strong lensing events. Therefore, we have
decided to perform image restoration on the noisy images.

(a) (b) (c)

Figure 9: In Figure (a), the detection results of the clear image after gray scale transformation are depicted. Figure (b) illustrates the PR (Precision-Recall) curve of the noisy image after gray scale transformation, and Figure (c) displays the PR curve of noisy images after gray scale transformation and image restoration. Comparative to the PR curve shown in Figure 8, the image pre-processing method enhances the detection capabilities of our algorithm and mitigates the effects caused by noise and blur. Table 1: We chose an IOU of 0.0 to generate a table and assess the performance of the model on various datasets. In this table, RT3 denotes clear data, RT4 represents noisy data, RT3+asinh and RT4+asinh indicate data subjected to asinh grayscale transformation, and RT4+restore+asinh is used for noisy images that underwent both image restoration and asinh transformation. Recall Data Precision | RT3 | RT4 | RT3+asinh | RT4+asinh | RT4+restore+asinh
---|---|---|---|---|---
0.0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000
0.1 | 1.000 | 0.981 | 1.000 | 1.000 | 1.000
0.2 | 0.998 | 0.879 | 1.000 | 1.000 | 1.000
0.3 | 0.994 | 0.810 | 1.000 | 1.000 | 1.000
0.4 | 0.977 | 0.746 | 1.000 | 0.999 | 0.996
0.5 | 0.940 | 0.701 | 1.000 | 0.999 | 0.992
0.6 | 0.891 | 0.645 | 1.000 | 0.997 | 0.976
0.7 | 0.816 | 0.597 | 0.999 | 0.980 | 0.933
0.8 | 0.574 | 0.533 | 0.998 | 0.935 | 0.865
0.9 | 0.436 | 0.465 | 0.984 | 0.804 | 0.728
1.0 | 0.000 | 0.000 | 0.000 | 0.027 | 0.322
Table 2: We chose an IOU of 0.5 to generate a table and assess the performance of the model on various datasets. In this table, RT3 denotes clear data, RT4 represents noisy data, RT3+asinh and RT4+asinh indicate data subjected to asinh grayscale transformation, and RT4+restore+asinh is used for noisy images that underwent both image restoration and asinh transformation. Recall Data Precision | RT3 | RT4 | RT3+asinh | RT4+asinh | RT4+restore+asinh
---|---|---|---|---|---
0.0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000
0.1 | 0.995 | 0.639 | 1.000 | 1.000 | 1.000
0.2 | 0.992 | 0.334 | 1.000 | 1.000 | 0.998
0.3 | 0.974 | 0.270 | 1.000 | 1.000 | 0.997
0.4 | 0.913 | 0.255 | 1.000 | 0.999 | 0.990
0.5 | 0.816 | 0.255 | 1.000 | 0.997 | 0.978
0.6 | 0.642 | 0.251 | 0.999 | 0.992 | 0.949
0.7 | 0.226 | 0.080 | 0.998 | 0.948 | 0.862
0.8 | 0.000 | 0.000 | 0.997 | 0.822 | 0.706
0.9 | 0.000 | 0.000 | 0.981 | 0.024 | 0.477
1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000

Finally, we combine both the image restoration and gray scale transformation
algorithms to process noisy images and assess the performance of the detection
pipeline. The results serve as a reference for anticipating potential
scientific outputs of the CSST in the detection of strong lensing systems, as
depicted in Figure 9(9(c)). With an IOU of 0, the detection accuracy is 92.9%.
Although the improvement in mAP might not be dramatic, there is a noteworthy
increase in the recall rate when the IOU ranges between 0.2 and 1.0. This is
crucial since the initial maximum recall rate is 90%, indicating that at least
10% of strong lensing systems may go undetected regardless of parameter
adjustments. However, following image restoration, the recall rate reaches
100%, significantly reducing the number of undetectable targets. Hence, the
image restoration algorithm proves indispensable and justifies its integration
into the detection pipeline. The detection results demonstrate substantial
improvement with the pipeline. In practical scenarios, configuring the IOU
threshold to 0.5 yields a recall rate of 0.6 and a precision rate of 0.949.
Considering the vast number of galaxies and potential strong lensing systems
observable using the CSST, we have the potential to identify strong lensing
candidates. However, within this large pool, thorough verification by human
experts is necessary, posing a significant challenge. To address this, we are
exploring collaboration with citizen science projects to assist in obtaining
the final validated detection outcomes666https://nadc.china-vo.org/lensfinder,
which is inspired by the GalaxyZoo projects (Fortson et al., 2012).

###  5.4 Visual Analysis of Detection Results

It is crucial to examine the outcomes of the detection process and assess
potential issues and risks associated with deploying the detection algorithm.
We have evaluated four distinct scenarios and provide detailed discussions for
each of them below:
1\. Impact of Strong Lensing Systems with Large Size: Strong Lensing systems
often have different sizes. In the label creation step, we standardize the
bounding boxes to dimensions of $50\times 50$ pixels. This uniform size
facilitates efficient detection by the neural network while mitigating the
influence of background and noise. This approach generally proves effective
for most strong lensing systems. However, for certain instances with larger
spatial extents, their structures surpass these bounding boxes. This over-
extension disrupts their structural features and engenders information loss.
Consequently, our neural network encounters difficulty in accurately
pinpointing these extended gravitational lensing systems. As shown in the blue
box in the top-left corner of figure 10, the blue boxes represent the strong
lensing systems present in the labels, while the green boxes indicate the
correctly detected strong lensing systems. The strong lensing system on the
upper left is notably large. The bounding box with size of $50\times 50$ pixel
leads to a misplacement of the detection position at the center of the
bounding box for this extended object. This misalignment results in flawed
feature extraction by the model, yielding imprecise detection results.
Normally the strong lensing systems larger than $50\times 50$ pixels would
hard to be located accurately.

Figure 10: The utilization of a fixed-size bounding box may affect detection
outcomes, especially when dealing with large-sized strong lensing systems.
Illustrated in this figure, the blue box denotes a specific strong lensing
object, but the bounding box only partially encloses it. As a result, the IOU
score becomes excessively low, hindering the accurate detection of this
particular strong lensing event.

2\. Impact of Strong Lensing Systems with Small Size or Low Signal-to-Noise
Ratio: Distinctive curved structures and the presence of multiple images are
features of strong lensing systems. However, the detection of these strong
lensing systems becomes particularly challenging when they are exceptionally
small or exhibit low signal-to-noise ratios. As illustrated in the left panel
of Figure 11(12(a)), the lens structure in the bottom right corner of the
image is extremely small, making it prone to identification as background or
other objects. In the right panel of Figure 11(12(b)), the strong lensing
system is heavily impacted by background noise, making it difficult for the
model to accurately recognize the objects. Both small- and low-signal-to-noise
ratio strong lensing systems could be categorized as targets with a low
signal-to-noise ratio, defined as
$SNR=TotalFlux\\_StrongLensing/Variance\\_Background$ (the ratio of total
photons within strong lensing systems to the variance of background noise).
Typically, identifying strong lensing systems in CSST observation data with a
signal-to-noise ratio less than 16 is considerably challenging, with 0.36% of
them being effectively undetected.

(a) (b)

Figure 11: The strong lensing system highlighted within the blue box in Figure
(a) exhibits dimensions of $16\times 17$ pixels and a signal-to-noise ratio
(SNR) of 15.88. However, due to its small size, our algorithm was unable to
detect it. The strong lensing system indicated by the blue box in Figure (b)
has dimensions of $25\times 25$ pixels and an SNR of 10.42. Despite its larger
size, its relatively low SNR prevented our algorithm from detecting it as
well.

3\. Impact of Bright Sources: Bright central galaxies and bright stars will
affect the detection efficiency. Light from the bright central galaxies will
make light from the strong lensing systems hard to recognize in multiple color
space defined by filters of the CSST, thus these targets will not be detected
in observation images. As shown in figure 12(12(a)), there is a strong lensing
system behind the galaxy, which are hard to be detected by our algorithm.
Meanwhile, several bright stars with similar colour are very likely to be
detected as strong lensing systems, which is probably caused by the
similaritiy between them and strong lensing systems. As shown in the right
panel of figure 12, the system in red colour stands for a false detection.
Detection of strong lensing system regardless of bright central galaxies is a
challenge for human beings. We can find that although our algorithm partly
solves this problem through looking into the image with more colours, there
are still gaps to fill. We need to further consider channel attention to
design some novel algorithms to solve this problem. However it should be
mentioned that the problems brought by bright stars may not be a problem,
since we can mask these targets before we start to detect strong lensing
systems.

(a) (b)

Figure 12: The presence of bright central galaxy light can pose challenges in
detecting strong lensing, as illustrated by the blue bounding box in Figure
(a). Figure (b) depicts several bright stars outlined with green bounding
boxes, which were detected as strong lensing systems. This could be attributed
to their visual similarity to actual strong lensing systems.

##  6 Detection of Strong Lensing Systems from Real observation Data

We evaluate the effectiveness of our pipeline using real observation data. Our
testing involves processing images obtained from the DESI Legacy Imaging
Surveys and media images from Euclid Early Release Observations using our
pipeline. The images from the DESI Legacy Imaging Surveys contain numerous
known strong lensing systems, providing an opportunity to assess the
performance of our method. Despite the lower gray scale levels in the media
images from Euclid, which is a space telescope with similar spatial
resolution, we can still make a preliminary estimation of the scientific
capabilities of the CSST in detecting strong lensing systems by using Euclid
images as a reference.

###  6.1 Detection of Strong Lensing Systems from DESI Legacy Imaging Surveys

We use the following steps to test the performance of our pipeline with images
from the DESI Legacy Imaging Surveys:

  * •

We have collected images from the DESI Legacy Imaging Surveys DR9 (Huang et
al., 2020) that contain 5060 known strong lensing systems. Due to hardware
limitations, we have resized these larger images to dimensions of $1000\times
1000$ pixels, resulting in a dataset of 12667 images. In this dataset, we also
split the data into the training set and the validation set in a 7:3 ratio.

  * •

Given the random distribution of strong lensing systems in actual data, our
model is designed to identify such systems regardless of their placement. This
means that no matter where the strong lensing systems is situated within the
image, our model should be adept at detection. Consequently, when generating
training data, we deliberately shuffle the positions of strong lensing systems
to simulate different scenarios. With the above steps, we have obtained the
training data.

  * •

We begin by choosing the detection neural network that has been trained using
CSST simulation data as the initial weights. Subsequently, we employ the
specified training data discussed earlier to fine-tune this neural network.
With the learning rate set at 0.001, we have train the neural network over 100
epochs.

  * •

After training, the neural network becomes capable of identifying strong
lensing systems from images obtained from the DESI Legacy Imaging Surveys. To
assess its performance, we utilize the entire set of 5060 images to evaluate
the effectiveness of our pipeline, aiming to ascertain its ability to detect
recognized strong lensing systems and also discover previously known strong
lensing systems.

####  6.1.1 Detection Pipeline Test with Known Strong Lensing Systems

For detection of known strong lensing systems, we have set the confusion
matrix with confidence score threshold of 0, 0.5 and 0.9 in figure 13. When
the threshold is set to 0, the recall rate of the model is 84.3%, indicating
that the model is able to capture a certain proportion of true strong lensing
systems. At this threshold, the precision is 97.54%, meaning that 97.54% of
the samples detected by the model are indeed true strong lensing systems, with
only about 2.5% being false positives. As the threshold increases, the number
of false positives gradually decreases, indicating a continuous improvement in
the precision of the model. Particularly, at a threshold of 0.5, there are
only one false positives, and the precision reaches 99.97%. This demonstrates
that the detection ability and accuracy of the model significantly improve at
higher thresholds. At a threshold of 0.9, there are no false positives,
resulting in a precision of 100%. This further confirms that our pipeline has
good performance in processing real observation data.

(a) (b) (c)

Figure 13: Figures (a), (b), and (c) depict the confusion matrix of our
detection algorithm using confidence score threshold values of 0, 0.5, and 0.9
on the simulated data. As demonstrated in these figures, our algorithm
performs well in detecting strong lensing systems, especially considering the
significant influence of bright central galaxies and low signal-to-noise
ratios on many of these systems. Additionally, it is important to highlight
that we can achieve a satisfactory balance of precision and recall rates for
further analysis by selecting a confidence score threshold of 0.5.

It is worth noting that the low false positive rate implies that when applying
the model to large-scale sky survey data for detecting galaxy-scale lensings,
there will not be a significant number of falsely reported strong lensing
cases. This is a crucial property as reducing false alarms can save valuable
time and resources in research, while enhancing the overall credibility of the
study. These results provide crucial metrics for evaluating the performance of
the model in identifying strong lensing systems in real data. It is evident
that by adjusting the threshold, we can control the accuracy and recall rate
of the detection results. Depending on specific requirements, we can choose a
higher threshold (such as 0.9) to reduce false positives or lower the
threshold to improve the recall rate.

####  6.1.2 Detection Pipeline Test For Discovery of New Strong Lensing
Systems

While testing the performance of our algorithm on data from the DESI Legacy
Imaging Survey DR9, we have identified several new strong lensing candidates.
With a detection threshold set at 0.5, we have applied the pipeline to process
the images illustrated in Figure 14. The dataset also comprises 5060 images,
each with dimensions of $1000\times 1000$ pixels, covering an area of 241.207
$deg^{2}$. Following the procedures outlined in Section 3 and Section 4, these
images are processed. The PSF-Net was trained using CSST images blurred by the
Moffat model with variable FWHM values ranging from 2.0 to 8.0 pixels. After
preprocessing and gray scale transformation, the neural network discussed in
Section 6.1.1 is utilized for further image processing. The comprehensive task
of processing all these images takes 72 hours and results in the
identification of additional candidates beyond the known 5060 instances of
strong gravitational lensings. In Appendix A, we provide the celestial
coordinates of some these newly identified strong lensing candidates. These
findings indicate that the majority of them exhibit arc-like structures or
multiple images, emphasizing the need for further follow-up observations. To
facilitate such endeavors, we have included a complete table of strong lensing
systems in this paper, providing users with a comprehensive resource for
undertaking subsequent observations.

Figure 14: The images selected for detecting strong lensing systems follow the
distribution outlined in Huang et al. (2020). It is important to highlight
that only a small subset of these images is utilized in this paper. Further
elaboration on this issue will be provided in our future papers.

###  6.2 Detection of Strong Lensing Systems from Media Images from Euclid
Early Data Release

Euclid, a spaceborne telescope developed and operated by the European Space
Agency, boasts a 1.2-meter aperture and a spatial resolution of 0.2
arcseconds. Given that the Euclid observes across the visible (550 nm) to
near-infrared (900 nm) band and shares a spatial resolution similar to that of
the CSST, its images can effectively assess the performance of our pipeline.
To evaluate our algorithm, we utilize the media images released by Euclid on
November 7, 2023. For testing purposes, we exclude the Horsehead Nebula
because of its complex background, which could introduce additional errors
into the detection algorithm. As these media images have already undergone
processing by pipelines developed by Professor Jean-Charles Cuillandre, we
directly apply our algorithm to detect strong lensing systems without the need
for additional data preprocessing. However, given that the media images are
tiff files, which have relatively low gray scale levels and are composed of
data from both visible and near-infrared bands, the algorithm may make errors
since it was trained on simulated CSST data covering the near-ultraviolet to
visible band. We extract stamp images with dimensions of $200\times 200$
pixels from the original images and set the confidence threshold for detection
at 0.5. To ensure a complete detection of strong lensing systems, we also
check the results by eyes.

In total, our algorithm identified 67 strong lensing system candidates, which
we categorize into three groups: strong lensing systems with high quality,
strong lensing systems with moderate quality, and false positive results. The
Appendix B shows 15 candidates for high quality strong lensing systems,
confirming the effectiveness of our method in detecting strong lensing
systems. Additionally, there are 22 strong lensing system candidates with
moderate quality, indicating that the completeness and purity of our algorithm
can be adjusted by varying the confidence level. However, 30 of the detection
results are false positives, mostly attributed to spiral galaxies and spikes
generated by the diffraction of the spider. Given that the CSST employs a
Three-Mirror Anastigmat system, which does not introduce diffraction arms, we
anticipate that these false positives will not pose a serious problem.
However, the lack of spiral galaxies with fine details remains a challenge for
our algorithm. To address this, we plan to perform high-fidelity simulations
to obtain data for further training of the neural network.

##  7 Conclusions

Traditional methods for searching for strong lensing systems are known for
being time-consuming and labor-intensive. As we look ahead to upcoming sky
survey projects, such as the CSST, the development of highly efficient
detection algorithms becomes paramount. In response to these urgent needs,
this study has developed a comprehensive pipeline. The process begins with the
generation of mock observation images based on a catalog of strong lensing
systems and other celestial objects, which serve as prior information.
Subsequently, a neural network based on the Swin-Transformer architecture is
trained using either simulated images or real observation images containing
verified strong lensing systems. Through training, the neural network becomes
adept at identifying strong lensing systems within observation images. To
enhance the detection ablity of the algorithm, we introduce additional image
preprocessing steps. These steps involve various operations, including
grayscale transformation and image restoration, applied to the original
astronomical image data.

We rigorously assess the performance of the model using a comprehensive set of
evaluation metrics. This assessment encompasses simulated data and real
observed data, as well as grayscale transformation applied to the data. When
the noise in the data had a significant impact, we introduced an image
restoration algorithm, combined with gray scale transformation, to enhance the
completeness of the detection. When applied to simulated CSST observation
data, our method demonstrates a detection accuracy rate of 98.6% and a recall
rate of 99.79%. Given the remarkable observation capabilities of the CSST, we
are optimistic about its potential to identify undiscovered strong lensing
systems. Moreover, we extend the application of our pipeline to some images
from the Euclid observation data, where it successfully identifies 37 strong
lensing system candidates.

Moving forward, our strategic roadmap involves refining the data structure to
align the proportion of strong lens data more closely with real situations.
This crucial adjustment is anticipated to improve the precision of the
detection capabilities of the model. In response to false detection results
stemming from small lens/source structures and bright stars, we will enhance
the data simulation algorithms by involving HST observations and hydrodynamic
simulations to generate training sets adhering more rigorously to real
observations, which is particularly important for the reliability of applying
our framework to space-borne imaging surveys, such as CSST, Euclid, and
Roman777https://roman.gsfc.nasa.gov/. Furthermore, the images from the DESI
Legacy Survey DR9 that we have been using are limited, and only several images
from Euclid telescopes are used. In the future, our plan involves searching
for strong lensing systems from the DESI Legacy Survey DR 10, with the goal of
identifying an increased number of strong gravitational lensing system
candidates. Expanding our strategy, we plan to undertake joint training
utilizing real observation data obtained from different telescopes. This
concerted approach seeks to increase the accuracy and recall rate. This
comprehensive plan not only promises more scientific outcomes for ongoing
initiatives such as the CSST main survey or the data from Euclid but also
holds the potential to significantly advance our capacity to discover other
celestial objects, ranging from nebulae and galaxies to strong lensing
systems.

## Acknowledgments

This paper used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, the Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho
de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Científico e Tecnológico and the Ministério da Ciência,
Tecnologia e Inovacão, the Deutsche Forschungsgemeinschaft, and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Enérgeticas, Medioambientales y Tecnológicas-Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de
Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-
Maximilians Universität München and the associated Excellence Cluster
Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, the Ohio State University, the
OzDES Membership Consortium the University of Pennsylvania, the University of
Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the
University of Sussex, and Texas A&M University.

This paper used public media images from Euclid. Euclid is a European mission,
built and operated by ESA, with contributions from NASA. The Euclid Consortium
– consisting of more than 2000 scientists from 300 institutes in 13 European
countries, the US, Canada and Japan – is responsible for providing the
scientific instruments and scientific data analysis. ESA selected Thales
Alenia Space as prime contractor for the construction of the satellite and its
service module, with Airbus Defence and Space chosen to develop the payload
module, including the telescope. NASA provided the detectors of the Near-
Infrared Spectrometer and Photometer, NISP. Euclid is a medium-class mission
in ESA’s Cosmic Vision Programme.

This work is supported by the National Natural Science Foundation of China
(NFSC) with funding numbers 12173027, 12303105, 12173062, 12120101003,
12373010, and National Key Research and Development Program with funding
number of 2023YFF0725300. We acknowledge the science research grants from the
China Manned Space Project with NO. CMS-CSST-2021-A01, CMS-CSST-2021-A02 and
science research grants from the Square Kilometre Array (SKA) Project with NO.
2020SKA0110102.

## Data Availability

Data resources are supported by China National Astronomical Data Center (NADC)
and Chinese Virtual Observatory (China-VO). This work is supported by
Astronomical Big Data Joint Research Center, co-founded by National
Astronomical Observatories, Chinese Academy of Sciences and Alibaba Cloud. The
code and data used in this paper can be found at the PaperData Repository
powered by the China-VO team.

##  Appendix A Catalog of All Newly Discovered Strong Lensing System
Candidates

In this section, we have presented an overview of all strong lensing system
candidates in figure 15, complete with their positions and images. As
illustrated in the figure, it is noteworthy that while the majority of strong
lensing systems have been initially identified by scientists, our method has
managed to discover additional candidates. Many of these candidates exhibit
challenges such as low signal-to-noise ratios or interference from the intense
illumination from nearby bright central galaxies, factors that might have
rendered them elusive in earlier detection attempts.

Figure 15: The figure demonstrates several detection candidates obtained from real observation data by our method. It can be observed that our model accurately detects and identifies strong lensing systems at arbitrary positions in the image. Table 3: Strong lensing system candidates obtained from some images obtained by the DESI Legacy Survey DR9. In this table, we show the RA, Dec and confidence of detection results returned by our algorithm. Name | RA | Dec | Confidence
---|---|---|---
DESI-3.7326+1.6078 | 3.7326 | 1.6078 | 0.65
DESI-15.2178-46.3197 | 15.2178 | -46.3197 | 0.59
DESI-19.6827-61.9314 | 19.6827 | -61.9314 | 0.08
DESI-20.4523-18.132 | 20.4523 | -18.132 | 1.00
DESI-21.3413-15.4198 | 21.3413 | -15.4198 | 0.99
DESI-37.2950-17.2694 | 37.2950 | -17.2694 | 0.83
DESI-38.1692-49.2411 | 38.1692 | -49.2411 | 0.89
DESI-45.0621-39.7797 | 45.0621 | -39.7797 | 0.05
DESI-50.324-22.2528 | 50.324 | -22.2528 | 0.53
DESI-57.0827-36.0632 | 57.0827 | -36.0632 | 0.99
DESI-65.0649-65.2484 | 65.0649 | -65.2484 | 0.58
DESI-65.6016-61.3769 | 65.6016 | -61.3769 | 0.97
DESI-65.7486-4.1514 | 65.7486 | -4.1514 | 0.57
DESI-65.7605-4.1592 | 65.7605 | -4.1592 | 0.58
DESI-73.516-51.3344 | 73.516 | -51.3344 | 0.96
DESI-75.4883-41.3736 | 75.4883 | -41.3736 | 1.00
DESI-80.3946-44.7907 | 80.3946 | -44.7907 | 0.97
DESI-81.2582-26.4191 | 81.2582 | -26.4191 | 0.05
DESI-84.1911-45.3239 | 84.1911 | -45.3239 | 0.81
DESI-87.4004-23.927 | 87.4004 | -23.927 | 0.78
DESI-92.3782-59.4316 | 92.3782 | -59.4316 | 0.09
DESI-128.1441+11.584 | 128.1441 | 11.584 | 0.53
DESI-220.3862-0.9106 | 220.3862 | -0.9106 | 0.82
DESI-355.2487-39.8141 | 355.2487 | -39.8141 | 0.11

##  Appendix B Catalog of Detected Strong Lensing System Candidates from
Euclid Early Released observation Images

On 7 November 2023, the European Space Agency released five public images
888https://www.esa.int/Science_Exploration/Space_Science/Euclid/Euclid_s_first_images_the_dazzling_edge_of_darkness.
We have chosen four of them to evaluate the performance of our algorithm,
excluding images of the Horse Head Nebula because of their complex background.
Using the deep neural network with weights trained on CSST simulation data, we
directly detect strong lensing systems in these images. Subsequently, we
visually inspect and classify the results into strong lensing systems with
high quality, those with moderate qualities, and false positives. All strong
lensing systems with high quality and some with moderate quality are shown in
Figure 16. The figure illustrates that our method effectively identifies
strong lensing systems. Additionally, we show several typical false detection
results in Figure 16. These false positives are primarily caused by
diffraction spikes and spiral galaxies, which share structural similarities
with arcs in strong lensing systems and are not included in the training data.

ıin 1,…,25

Figure 16: The above figure shows the results of our method in identifying
strong lensing systems in Euclid media images. We have individually examined
and categorized all these images based on their morphology, classifying them
into strong lensing systems of varying quality. The top three rows exhibit
high-quality instances of strong lensing systems, whereas the fourth row
displays strong lensing systems of moderate quality. The fifth row reveals
some false positive detection results. The coordinates of these identified
targets in different Euclid media images are highlighted in red color.

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