# Source-Free Domain Adaptation for Real-World Image Dehazing

Hu Yu  University of Science and Technology of China<EMAIL_ADDRESS>,  Jie Huang  University of Science and Technology of China
<EMAIL_ADDRESS>,  Yajing Liu  JD Logistics<EMAIL_ADDRESS>,  Qi
Zhu  University of Science and Technology of China<EMAIL_ADDRESS>,
Man Zhou  University of Science and Technology of China
<EMAIL_ADDRESS>and  Feng Zhao  University of Science and Technology
of China<EMAIL_ADDRESS>
(2022)

###### Abstract.

Deep learning-based source dehazing methods trained on synthetic datasets have
achieved remarkable performance but suffer from dramatic performance
degradation on real hazy images due to domain shift. Although certain Domain
Adaptation (DA) dehazing methods have been presented, they inevitably require
access to the source dataset to reduce the gap between the source synthetic
and target real domains. To address these issues, we present a novel Source-
Free Unsupervised Domain Adaptation (SFUDA) image dehazing paradigm, in which
only a well-trained source model and an unlabeled target real hazy dataset are
available. Specifically, we devise the Domain Representation Normalization
(DRN) module to make the representation of real hazy domain features match
that of the synthetic domain to bridge the gaps. With our plug-and-play DRN
module, unlabeled real hazy images can adapt existing well-trained source
networks. Besides, the unsupervised losses are applied to guide the learning
of the DRN module, which consists of frequency losses and physical prior
losses. Frequency losses provide structure and style constraints, while the
prior loss explores the inherent statistic property of haze-free images.
Equipped with our DRN module and unsupervised loss, existing source dehazing
models are able to dehaze unlabeled real hazy images. Extensive experiments on
multiple baselines demonstrate the validity and superiority of our method
visually and quantitatively.

Single image dehazing, source-free, domain adaptation, domain knowledge
disentangling

††journalyear: 2022††copyright: acmcopyright††conference: Proceedings of the
30th ACM International Conference on Multimedia; October 10–14, 2022; Lisboa,
Portugal††booktitle: Proceedings of the 30th ACM International Conference on
Multimedia (MM ’22), October 10–14, 2022, Lisboa, Portugal††price: 15.00††doi:
10.1145/3503161.3548410††isbn: 978-1-4503-9203-7/22/10††submissionid:
3090††ccs: Computing methodologies Scene understanding

##  1\. Introduction

Figure 1. (a) Source dehazing models that are trained on synthetic data
(_e.g._ MSBDN (Dong et al., 2020)). (b) Existing source-driven DA dehazing
methods. These methods design customized architecture and need both source
synthetic and target real hazy image during domain adaptation. (c) Our Source-
Free Unsupervised Domain Adaptation image dehazing paradigm. Our method works
with only target unpaired real hazy images available and can direct utilize
well trained source models with frozen parameters in a plug-and-play manner.

Haze is a common atmospheric phenomenon. Images captured in hazy environments
usually suffer from noticeable visual quality degradation in object appearance
and contrast, resulting in accuracy decreasing for subsequent visual analysis.
Thus, image dehazing has been a focus of research in the computational
photography and vision communities throughout the last decades.

As recognized, the hazing process can be represented by the physical
scattering model (McCartney, 1976), which is usually formulated as

(1) $\small I(x)=J(x)t(x)+A(1-t(x)),$

where $I(x)$ and $J(x)$ denote the hazy image and the clean image
respectively, $A$ is the global atmospheric light, and $t(x)$ is the
transmission map.

However, estimating the clean image from a single hazy input is an ill-posed
and challenging problem. Given a hazy image $I(x)$, conventional prior-based
dehazing algorithms attempt to estimate $t(x)$ and $A$ by constraining the
solution space using a variety of sharp image priors (Berman et al., 2016; He
et al., 2010; Fattal, 2014, 2008) and then restore the image via the
scattering model. However, these hand-crafted image priors are based on
specific observations, which may not be reliable for estimating the
transmission map in the physical scattering model.

Numerous convolutional neural networks (CNNs)-based systems have been
developed to estimate transmission maps (Cai et al., 2016; Ren et al., 2016;
Zhang and Patel, 2018) or yield clean images directly (Li et al., 2017, 2018a;
Ren et al., 2018; Liu et al., 2019a; Qu et al., 2019; Qin et al., 2020; Dong
et al., 2020; Wu et al., 2021), which achieve superior image dehazing
performance over classic prior-based algorithms. However, these approaches
require large quantities of paired hazy/clean images to train in a supervised
learning manner. In general, due to the impracticality of acquiring large
amounts of hazy-clean pairs in the real world, most dehazing models are
trained on hazy synthetic datasets. In this paper, we denote these synthetic
hazy dataset trained models as source models. However, source models often
suffer from degraded performance on real-world hazy images due to the domain
gap.

Recently, the above domain shift problem has drawn the attention of the image
dehazing community. Existing Domain-Adaptation (DA) dehazing methods (Li et
al., 2019b; Shao et al., 2020; Ye et al., 2022; Li et al., 2020a, 2021; Chen
et al., 2021; Liu et al., 2021b) achieve remarkable performance, but they have
two common drawbacks. First, they inevitably require full access to source
synthetic hazy datasets to reduce the gap between the source synthetic and
target real domains during model adaptation, which is cumbersome in practice
due to storage, privacy, and transmission constraints. Second, most of these
methods need to retrain source models with modification or use customized
architecture for domain adaptation, neglecting to direct utilize numerous
source models, which reduces the generality of their methods. In this paper,
we denote these DA dehazing methods as source-driven models.

To address these problems, we present a novel Source-Free Unsupervised Domain
Adaptation (SFUDA) image dehazing paradigm, where only a well-trained source
model and an unlabeled target real hazy dataset are available during model
adaptation. The overview of our method is shown in Fig. 1. Since the
representations of features across synthetic and real domains vary
significantly, our SFUDA achieves domain adaptation from the domain
representation perspective. Specifically, the DRN module is devised for making
the representation of real hazy image’s features match that of the synthetic
domain to adapt the source network. To implement this, the DRN module
disentangles the features of real hazy images into domain-invariant and
domain-variant parts. The domain-invariant part is obtained by Instance
Normalization (IN), while the domain-variant part is implicitly guided by the
feature statistics to make the features adapt to the source model. With IN
equipped in the feature space, it can normalize feature statistics for style
normalization (Huang and Belongie, 2017). The proposed DRN module can be
directly applied to existing dehazing models in a plug-and-play fashion.

Additionally, the unsupervised frequency losses and physical prior losses are
applied to regularize the dehazing processing of unlabeled real hazy images.
Specifically, we explore the frequency property in our unsupervised setting.
It is worth noting that although source network fails to remove the haze of
real images, it well reconstructs the structural information. Therefore, we
introduce the phase structure loss between the intermediate stages and output
of the source network and the student network for structural consistency.
Besides, we find that the original real hazy image has an enhanced
illumination and color contrast after being processed by Contrast Limited
Adaptive Histogram Equalization (CLAHE). With this property, we introduce the
amplitude style loss to regularize the enhanced illumination contrast between
the output of CLAHE and the output of the student network. Moreover, we employ
the classical Dark Channel Prior (DCP) and Color Attenuation Prior (CAP) to
form prior loss to exploit the inherent statistic property of haze-free
images.

Existing source models that are equipped with our DRN module and unsupervised
losses gain generalization power and can dehaze unlabeled real hazy images. In
conclusion, the main contributions of this work are summarized as follows:

  * •

We propose a novel Source-Free Unsupervised Domain Adaptation (SFUDA) image
dehazing paradigm. To the best of our knowledge, this is the first attempt to
address the problem of source-free UDA for image dehazing. Our method can be
directly applied to existing dehazing models in a plug-and-play fashion, which
is more general in practical.

  * •

we propose the Domain Representation Normalization (DRN) module to regularize
representations of features in the real hazy domain to adapt to the frozen
source network.

  * •

To train the whole framework in an unsupervised manner, we leverage the
frequency property and physical priors to constrain the adaptation and
generate more natural images.

  * •

Extensive experiments on multiple baselines demonstrate the validity of our
method visually and quantitatively. In particular, our method outperforms the
state-of-the-art source-driven UDA approaches under a source-free setting.

##  2\. Related work

Figure 2. Overview of the proposed framework. The source network can be any
synthetic data pretrained model (e.g., MSBDN), while the student network is
built by inserting our DRN module into the intermediate stages of the source
model. Note that the parameters in the teacher network and student network’s
source model part are frozen.

###  2.1. Image dehazing

Recent years have witnessed significant advances in image processing (Yao et
al., 2019; Pan et al., 2022; Wang et al., 2021a), including single image
dehazing. Existing image dehazing methods can be roughly categorized into
physical-based methods and deep learning-based methods.

Physical-based. Physical-based methods depend on the physical model
(McCartney, 1976) and the handcraft priors from empirical observation, such as
dark channel prior (He et al., 2010), color line prior (Fattal, 2014), and
sparse gradient prior (Chen et al., 2016). However, the density of haze can be
affected by various factors, which makes the haze formation at individual
spatial locations space-variant. Therefore, the haze usually cannot be
accurately characterized by merely a single transmission map.

Deep learning-based. Different from the physical-based methods, deep learning-
based methods employ convolution neural networks and large-scale datasets to
learn the image prior (Cai et al., 2016; Li et al., 2017; Ren et al., 2016;
Zhang and Patel, 2018; Liu et al., 2018, 2019b) or directly learn hazy-to-
clear image translation (Ren et al., 2018; Liu et al., 2019a; Qu et al., 2019;
Dong and Pan, 2020; Deng et al., 2020; Hong et al., 2020; Dong et al., 2020;
Qin et al., 2020; Wu et al., 2021; Ye et al., 2021; Wang et al., 2021b; Zheng
et al., 2021). For example, MSBDN (Dong et al., 2020) proposes a boosted
decoder to progressively restore the haze-free images. Existing methods have
shown outstanding performances on image dehazing. However, they train on
paired synthetic data and generalize poorly on real-world data.

###  2.2. Domain adaptation dehazing

Recently, some domain adaptation dehazing methods (Li et al., 2019b; Shao et
al., 2020; Ye et al., 2022; Shyam et al., 2021; Li et al., 2020a, 2021; Chen
et al., 2021; Liu et al., 2021b) have been proposed to tackle domain shift
between synthetic and real domains. For example, Shao et al. (Shao et al.,
2020) developed a domain adaptation paradigm, which consists of a image
translation module and two dehazing modules and the image translation module
is used for data augmentation. Chen et al. (Chen et al., 2021) modified and
retrained an existing dehazing model with physical priors and fine-tune it on
both synthetic and real hazy images.

However, these existing techniques require the full access to source synthetic
hazy datasets during model adaptation, which limits their practical
application, due to the non-availability of source datasets in some cases.

###  2.3. Source-Free Unsupervised Domain Adaptation

Since labeled source data may not be available in some real-world scenarios
due to data privacy issues, Source-Free Unsupervised Domain Adaptation aims to
explore how to improve performance of an existing source model on the target
domain with only unlabeled target data available. Recently, this new domain
adaptation paradigm has been applied to different tasks (Liu et al., 2021a; Li
et al., 2020b; Chidlovskii et al., 2016; Huang et al., 2021; Ahmed et al.,
2021) for its high practical value and easy-to-use property. Different from
these techniques, we first attempt to introduce SFUDA to image dehazing tasks,
and innovatively address this problem from the domain representation
perspective. Our solution is general and can be directly applied to existing
source dehazing models.

##  3\. Method

###  3.1. Method Overview

Source dehazing models are trained on synthetic data, thus obtaining the
dehazing knowledge for the representation of synthetic domain. With this
property in mind, we design the DRN module from the domain representation
perspective to adapt to the source model. Besides, we design the unsupervised
loss to constrain the learning process. Our method makes the first attempt to
directly leverage the learned dehazing knowledge of existing source models,
providing a general solution for domain adaptation and works in a source-free
and plug-and-play manner.

As shown in Fig. 2, our domain adaptation framework works in a teacher-student
mode. The teacher network can be any existing source dehazing models (_e.g._
FFA-Net (Qin et al., 2020), MSBDN (Dong et al., 2020), we choose MSBDN as the
source model by default), while the student network consists of our DRN module
and the source model. DRN module is expected to make the representation of
real data match the synthetic domain to adapt the frozen source network.
Besides, although the source network performs poorly on real hazy images, it
owns the ability to preserve the structure of images. Thus, we froze the
parameter of the source network during training so that the structure
information of the source network can provide supervision for the student
network. The parameter of the student network has two parts: the DRN module
part and the source network part. Only the parameter of the DRN module is
updated during back-propagation to keep the dehazing ability of the source
model on synthetic domain representation.

Figure 3. Examples of both real and synthetic hazy images after Instance
Normalization operation.

IN

###  3.2. Domain Representation Normalization Module

Existing normalization-based methods (Jia et al., 2019; Fan et al., 2021)
regularize the distribution by normalize it to the standard normal
distribution and then modulate it to another distribution with learned
statistics. After such $\sigma_{1}\frac{X-\mu}{\sigma}+\mu_{1}$ operation, the
distribution change from original $N\left(\mu,\sigma^{2}\right)$ to learned
$N\left(\mu_{1},\sigma_{1}^{2}\right)$, where $N\left(\mu,\sigma^{2}\right)$
denotes normal distribution with mean $\mu$ and standard deviation $\sigma$.
However, although such a strategy works well for high-level tasks,
normalization will inevitably induce the loss of the image discriminative
features (Jin et al., 2020; Pan et al., 2018) for image reconstruction.

Differently, for input real hazy domain feature $X(x)\in\mathbb{R}^{C\times
H\times W}$, where $C$, $H$ and $W$ represent channel dimension, height, and
width, respectively, our DRN module disentangles it into domain invariant
knowledge $DI$ and domain variant knowledge $DV$. We introduce Instance
normalization (IN) to get $DI$. IN performs style normalization by normalizing
feature statistics, which have been found to carry the style information of an
image (Huang and Belongie, 2017).

We show some hazy images after IN operation in Fig. 3. The synthetic and real
hazy images of the same scene are pulled closer in style after IN, which
demonstrates that IN property of excavating domain-invariant features fits
image dehazing task.

For the domain invariant part, $X(x)$ is first processed by IN to get $F(x)$,
formulated by:

(2) $\displaystyle{F}(x)=InstanceNorm(X)=\frac{X-\mu}{\sigma},$

where, $\mu\in\mathbb{R}^{C\times 1\times 1}$ and
$\sigma\in\mathbb{R}^{C\times 1\times 1}$ denote mean and standard deviation
of $X(x)$ along the channel dimension. $F(x)$ represents domain-invariant
features of standard normal distribution.

For the domain variant part, the residual between input $X(x)$ and domain
invariant part $F(x)$ are denoted as $Res(x)$, which can be regarded as domain
variant part. Besides, we also obtain the mean and standard deviation of
$X(x)$.

(3) $\small\mu=\frac{1}{m}\sum_{k\in
S_{i}}x_{k},\quad\sigma=\sqrt{\frac{1}{m}\sum_{k\in
S_{i}}\left(x_{k}-\mu_{i}\right)^{2}+\epsilon}$

with $\epsilon$ be a small constant for numerical stability. Unlike previous
methods, we implicitly incorporate $\mu$ and $\sigma$. Concretely, we first
expand $\mu$ and $\sigma$ along the spatial dimension to get the same size as
$Res(x)$. Afterwards, the expanded $\mu$, $\sigma$ and $Res(x)$ are
concatenated along the channel dimension to implicitly guide the learning of
$Res(x)$. The final domain variant knowledge $DV$ can be computed as:

(4) $\small DV=Conv(Cat\left(Res,\mu,\sigma\right)).$

Finally, we integrate domain invariant knowledge $DI$ with domain variant
knowledge $DV$ to get the final output $Y(x)$ of the DRN module. Our DRN
module keeps domain invariant knowledge $DI$ and modifies the domain variant
knowledge along with the loss constraints in Sec. 3.3, which make the
representation of output $Y(x)$ match the synthetic representation. To better
testify this, we show the feature visualization in Fig. 4. It is evident that
real hazy image features in our student network are more similar to the
synthetic domain representation than real hazy image features in the source
network.

Figure 4. Feature visualization on the effectiveness of our DRN module. The
second column is intermediate features.

demo

###  3.3. Training Losses

Figure 5. Visualization on the relationship between the haze degradation and
the characteristics of amplitude spectrum and phase spectrum in frequency
domain.

exchange

Our framework works in an unsupervised way. Therefore, it is critical to
design proper loss function as supervision to drive the DRN module learning.
Specifically, We explore the frequency property in our unsupervised setting
and innovatively introduce two frequency losses for keeping domain-invariant
structure and modulating domain-variant style. Besides, we select two
effective and well-grounded physical priors to provide us with the prior
knowledge of real images.

####  3.3.1. Frequency domain Losses

As is known, the illumination contrast of an image is represented by the
amplitude spectrum, while the structure information is represented by the
phase spectrum (Oppenheim and Lim, 1981; Skarbnik et al., 2009). Based on this
theory, we further conduct an amplitude and phase exchange experiment to
validate its applicability in our setting. As shown in Fig. 5, we exchange the
amplitude and phase of synthetic and real hazy images. The results demonstrate
that synthetic and real hazy images of the same scene have approximately the
same phase (structure) spectrum, while the style and haze degradation mainly
manifests in the amplitude spectrum.

Phase (Structure) Loss. The source dehazing network can not generalize well to
real hazy images, but they can still retain satisfactory structural
information, which is an important dehazing prior to unsupervised learning.
With this prior knowledge in mind, we design a Phase (Structure) Loss.

Concretely, we explore the information contained in the phase spectrum of both
intermediate features and output images from teacher to student to provide
structural constraints. The outputs of the teacher and student network are
denoted as $O_{t}$ and $O_{s}$. We first transform the output image to the
frequency domain by Fourier Transform.

(5)
$\small{F}(x)(u,v)=\sum_{h=0}^{H-1}\sum_{w=0}^{W-1}x(h,w)e^{-j2\pi\left(\frac{h}{H}u+\frac{w}{W}v\right)}.$

The frequency-domain feature $F(x)$ is denoted as $F(x)=R(x)+jI(x)$, where
$R(x)$ and $I(x)$ represent the real and imaginary part of $F(x)$. Then the
real and imaginary parts are converted to amplitude and phase spectrums, which
can be formulated as:

(6)
$\small\begin{array}[]{l}{A}(x)(u,v)=\left[R^{2}(x)(u,v)+I^{2}(x)(u,v)\right]^{1/2},\\\
{P}(x)(u,v)=\arctan\left[\frac{I(x)(u,v)}{R(x)(u,v)}\right],\end{array}$

where $A(x)$ is the amplitude spectrum, $P(x)$ is the phase spectrum. The
phase spectrums of teacher and student network outputs are denoted as
$P_{t}(x)$ and $P_{s}(x)$. Then the Phase (Structure) Loss are formulated as:

(7)
$\small{L}_{Pha}=\frac{2}{UV}\sum_{u=0}^{U/2-1}\sum_{v=0}^{V-1}\left\|\left|P_{t}\right|_{u,v}-|P_{s}|_{u,v}\right\|_{1}.$

Note, in our implementation, the summation for $u$ is only performed up to
$U/2-1$, since $50\%$ of all frequency components are redundant. Moreover,
this phase loss is also applied to intermediate features in the same way.

Amplitude (Style) Loss. Contrast Limited Adaptive Histogram Equalization
(CLAHE) (Pizer et al., 1987; Reza, 2004) is a classical digital image
processing technology for improving image contrast and it is also applied to
image dehazing. However, it is inadvisable to directly apply CLAHE-enhanced
images as supervision since CLAHE inevitably introduces bottom noise and
brings inherent flaws into our network. To address this problem, we leverage
the mentioned frequency property that the illumination contrast of an image is
represented by the amplitude spectrum and design the Amplitude (Style) Loss to
utilize CLAHE-enhanced illumination and contrast.

Specifically, the amplitude spectrum of student network output $O_{s}(x)$ is
denoted as $A_{s}(x)$ and the amplitude spectrum of CLAHE-enhanced real hazy
image is denoted as $A_{CLAHE}(x)$. Then the Amplitude (Style) Loss is
formulated as:

(8)
$\small{L}_{Amp}=\frac{2}{UV}\sum_{u=0}^{U/2-1}\sum_{v=0}^{V-1}\left\|\left|A_{s}\right|_{u,v}-|A_{CLAHE}|_{u,v}\right\|_{1}.$

####  3.3.2. Physical Prior Losses

Various handcraft priors, such as dark channel prior (He et al., 2010), color
line prior (Fattal, 2014), color attenuation prior (Zhu et al., 2014), sparse
gradient prior (Chen et al., 2016), maximum reflectance prior (Zhang et al.,
2017), and non-local prior (Berman et al., 2016), are drawn from empirical
observation and reflect inherent statistic property of haze-free images. From
these priors, we select two effective and well-grounded ones to provide us
with the prior knowledge of real images. Additionally, unlike (Chen et al.,
2021; Liu et al., 2021b), we employ these prior losses with only output images
available.

Dark Channel Prior (DCP) Loss. Dark Channel Prior (DCP) (He et al., 2010) is
the most famous and effective prior for image dehazing. DCP is a statistical
property of outdoor haze-free images: most patches in these images should
contain pixels that are dark in at least one color channel. We formulate DCP
as a loss function as in (Li et al., 2020a).

(9)
$\small{L}_{DCP}=\left\|\min_{c\in\\{r,g,b\\}}\left(F^{c}(y)\right)\right\|_{p},$

where $F^{c}(\cdot)$ is the c-th color channel of $y$, and $y$ is a local
patch of the student network output $O_{s}(x)$. With this dark channel loss,
our student network incorporates the statistical properties from the recovered
clean images, avoiding an explicit ground truth on the recovered image.

Color attenuation prior (CAP) Loss. Color attenuation prior (CAP) (Zhu et al.,
2014, 2015) can be explained as, in a haze-free region, the difference between
the brightness and the saturation is close to zero. In concrete
implementation, the difference between the value and saturation in the
predicted $O_{s}(x)$ should be minimized as small as possible. We formulate
CAP as a loss function as in (Li et al., 2021).

(10)
$\small{L}_{CAP}=\left\|V\left(O_{s}(x)\right)-S\left(O_{s}(x)\right)\right\|_{p},$

where $V\left(O_{s}(x)\right)$ and $S\left(O_{s}(x)\right)$ respectively
denotes the brightness and saturation of $O_{s}(x)$.

Total Loss. The final loss function used in our method can be defined as:

(11)
$\small{L}=\lambda_{p}{L}_{Pha}+\lambda_{a}{L}_{Amp}+\lambda_{d}{L}_{DCP}+\lambda_{c}{L}_{CAP},$

where $\lambda_{p}$, $\lambda_{a}$, $\lambda_{d}$ and $\lambda_{c}$ are weight
factors.

Figure 6. Visual comparison of source baseline and DA dehazing results on
labeled real hazy dataset I-Haze.

##  4\. Experiments

###  4.1. Experiment Setup

Datasets. We select Unannotated Real Hazy Images (URHI) from RESIDE dataset
(Li et al., 2018b) for domain adaptation training. For evaluating the
effectiveness of our method, we test on two real-world datasets, RTTS (Li et
al., 2018b) and I-Haze (Ancuti et al., 2018). RTTS is a subset of RESIDE
dataset (Li et al., 2018b), consisting of $4322$ real unlabeled outdoor hazy
images. I-Haze contains 30 paired real indoor hazy images.

Metrics. We employ two widely used metrics, the Peak Signal to Noise Ratio
(PSNR) and the Structural Similarity Index (SSIM), to quantitatively assess
the results on the labeled I-Haze dataset. Besides, we utilize two well-known
no-reference image quality assessment indicators: BRISQUE (Mittal et al.,
2012a) and NIQE (Mittal et al., 2012b) to assess the results on the unlabeled
RTTS dataset.

Figure 7. Visual comparison of DA dehazing results on unlabeled real hazy
dataset RTTS.

Implementation Details. We use ADAM as the optimizer with $\beta_{1}=0.9$, and
$\beta_{2}=0.999$, and the initial learning rate is set to $1\times 10^{-4}$.
The learning rate is adjusted by the cosine annealing strategy (He et al.,
2019). The training epoch, batch and patch sizes are set to $10$, $6$, and
$256\times 256$, respectively. The trade-off weights in loss function are set
to $\lambda_{p}=1$, $\lambda_{a}=1$, $\lambda_{d}=10^{-3}$, and
$\lambda_{c}=10^{-3}$.

Table 1. Quantitative comparisons with state-of-the-art (SOTA) DA methods on two real-world dehazing datasets. $\downarrow$ denotes lower is better, while $\uparrow$ means higher is better.  | Method | I-HAZE (Ancuti et al., 2018) | RTTS (Li et al., 2018b)
---|---|---|---
PSNR$\uparrow$ | SSIM$\uparrow$ | BRISQUE$\downarrow$ | NIQE$\downarrow$
| Hazy | - | - | 36.703 | 5.209
Baseline | MSBDN (Dong et al., 2020) | 16.623 | 0.780 | 32.575 | 4.865
DA | DAD (Shao et al., 2020) | 12.076 | 0.750 | 34.423 | 5.367
DA | DMT (Liu et al., 2021b) | 12.902 | 0.521 | 31.594 | 4.963
DA | PSD (Chen et al., 2021) | 14.575 | 0.781 | 28.011 | 4.494
DA | Ours | 17.602 | 0.802 | 27.330 | 4.326

###  4.2. Comparison with State-of-the-art Methods

We compare the performance of our SFUDA with three SOTA DA dehazing methods:
DAD (Shao et al., 2020), PSD (Chen et al., 2021), and DMT-Net (Liu et al.,
2021b). Amounts of experiments are conducted on two real-world hazy datasets.

####  4.2.1. Comparison on labeled I-Haze Dataset

Visual Quality. As shown in Fig. 6, Compared with the ground truths, it is
evident that the results of MSBDN, DAD, and DMT not only fail to remove the
dense haze but also suffer from color shift. Moreover, the severe color
distortion problem of PSD is clearly exposed under ground-truth haze-free
images. Compared with all these methods, our method generates the highest-
fidelity dehazed results.

Quantitatively results. Table 1 compares the quantitative results of different
methods on the I-Haze dataset, which indicates our source-free method achieves
the best performance with 17.602dB PSNR and 0.802 SSIM. What’s more, different
from outdoor datasets URHI and RTTS, I-Haze is an indoor dataset and its
representation is far away from that of the training dataset URHI than the
RTTS dataset, which is shown in the supplementary material. Consequently, our
best performance on the I-Haze dataset strongly proves the generalization
ability of our method.

####  4.2.2. Comparison on unlabeled RTTS Datasets

Visual Quality. As shown in Fig. 7, the source baseline model MSBDN remains
haze residual, especially in distant areas. The dehazing results of DAD and
DMT are dark in some regions. PSD tends to produce visually satisfactory
images, but it over amplifies color contrast by direct use of CLAHE prior,
thus seems to be unnatural. In contrast, our SFUDA generates high-quality
haze-free images with more natural color, clearer architecture, and finer
details.

No-Reference Image Quality Assessment. For quantitative comparison of the
unlabeled dataset, we employ two well-known no-reference image quality
assessment indicators: BRISQUE (Mittal et al., 2012a) and NIQE (Mittal et al.,
2012b). As shown in table 1, our method largely outperforms baseline MSBDN.
Besides, it also surpasses the source-driven DA methods DAD, DMT, and PSD.

Task-Driven Evaluation. The performance of high-level computer vision tasks
such as object detection and scene understanding is considerably influenced by
input images captured in hazy scenes (Li et al., 2019a; VidalMata et al.,
2020; Yang et al., 2020). Thus, image dehazing task can be used as a
preprocessing step for these high-level tasks. Inversely, the performance of
these downstream tasks can also be used to evaluate the effectiveness of image
dehazing algorithms. To this end, we testify our method and other SOTA
dehazing methods on the RTTS dataset with object detection task. We show the
detection result of a representative image sampled from RTTS in Figure 8. It
is evident that the detection performance of our method surpasses the baseline
MSBDN and DA dehazing methods DAD and DMT-Net. Besides, it achieves comparable
results compared to PSD.

Table 2. Quantitative comparisons with baseline methods and their vanilla direct fine-tuning on two real-world dehazing datasets. “ft” represents fine-tuned baseline. Method | RTTS (Li et al., 2018b) | I-HAZE (Ancuti et al., 2018)
---|---|---
BRISQUE$\downarrow$ | NIQE$\downarrow$ | PSNR$\uparrow$ | SSIM$\uparrow$
FFA-Net | 59.145 | 8.212 | 10.105 | 0.552
FFA-Net (ft) | 42.145 | 7.393 | 12.151 | 0.638
Ours (FFA-Net) | 29.311 | 6.191 | 13.404 | 0.718
MSBDN | 32.575 | 4.865 | 16.623 | 0.780
MSBDN (ft) | 30.210 | 4.659 | 17.180 | 0.781
Ours (MSBDN) | 27.330 | 4.326 | 17.602 | 0.802
Figure 8. Detection results of SOTA DA methods on an representative image
sampled from RTTS dataset. Figure 9. Visual comparison with baselines and
their fine-tuned (ft) models on labeled real hazy dataset I-Haze.

###  4.3. Comparison with fine-tuned source models

In order to compare more fairly with existing source baseline methods and
further prove the superiority of our method, we compare with two state-of-the-
art source baselines methods: FFA-Net (Qin et al., 2020) and MSBDN (Dong et
al., 2020) and their fine-tuned ones. Note that these source models are fine-
tuned in the same setting as our method for fair comparison. The quantitative
comparison results are presented in Table 2. It is obvious that applying our
method to these baseline methods is much more effective than vanilla direct
fine-tuning. Not that our method improves performance with negligible
additional parameters (MSBDN 31.35M, Ours(MSBDN) 31.93M).

Besides, we present the visual comparison in Fig. 9, vanilla direct fine-
tuning ones still fails to remove the haze and suffer from color shift
problem. In contrast, our method on these baselines generates natural and
visually desirable results.

Table 3. Ablation study of our method on I-Haze dataset. Label | DRN | Str | Sty | DCP | CAP | PSNR (dB) | SSIM
---|---|---|---|---|---|---|---
a | $\times$ | ✓ | ✓ | ✓ | ✓ | 17.180 | 0.781
b | ✓ | $\times$ | ✓ | ✓ | ✓ | 17.124 | 0.781
c | ✓ | ✓ | $\times$ | ✓ | ✓ | 16.752 | 0.780
d | ✓ | ✓ | ✓ | $\times$ | ✓ | 17.548 | 0.794
e | ✓ | ✓ | ✓ | ✓ | $\times$ | 17.564 | 0.796
f | ✓ | ✓ | ✓ | ✓ | ✓ | 17.602 | 0.802

###  4.4. Ablation Studies

In this section, we perform ablation study experiments to evaluate the
effectiveness of major components of our method. Specifically, we denote our
frequency structure loss, frequency style loss, physical DCP loss, and
physical CAP loss as ”Str”, ”Sty”, ”DCP”, and ”CAP”, respectively. Different
models are denoted as follows: (a) without DRN module; (b) without structure
loss; (c) without style loss; (d) without DCP loss; (e) without CAP loss; (f)
our method. Table 3 summarizes the PSNR and SSIM results of our method under
the above settings. It is obvious that our designed DRN module, Style loss,
and Structure loss are of greater importance. We further verify the
rationality of the DRN module in the supplementary material.

##  5\. Conclusion

In this paper, we present a novel Source-Free Unsupervised Domain Adaptation
image dehazing paradigm, in which only a well-trained source model and an
unlabeled target real hazy dataset are available. Our SFUDA achieves domain
adaptation from the domain representation perspective and can be directly
applied to existing dehazing models in a plug-and-play fashion. Specifically,
we devise a Domain Representation Normalization(DRN) module to make the
representation of real hazy data match the synthetic hazy domain. Besides, we
leverage the frequency property and physical prior knowledge to form
unsupervised losses. Extensive experiments validate that the proposed method
achieves SOTA domain adaptation performances in a source-free and easy-to-use
way.

###### Acknowledgements.

This work was supported by the JKW Research Funds under Grant
20-163-14-LZ-001-004-01. We acknowledge the support of GPU cluster built by
MCC Lab of Information Science and Technology Institution, USTC.

## References

  * (1)
  * Ahmed et al. (2021) Sk Miraj Ahmed, Dripta S Raychaudhuri, Sujoy Paul, Samet Oymak, and Amit K Roy-Chowdhury. 2021\.  Unsupervised multi-source domain adaptation without access to source data. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 10103–10112.
  * Ancuti et al. (2018) Cosmin Ancuti, Codruta O Ancuti, Radu Timofte, and Christophe De Vleeschouwer. 2018.  I-HAZE: a dehazing benchmark with real hazy and haze-free indoor images. In _International Conference on Advanced Concepts for Intelligent Vision Systems_. Springer, 620–631.
  * Berman et al. (2016) Dana Berman, Shai Avidan, et al. 2016\.  Non-local image dehazing. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 1674–1682.
  * Cai et al. (2016) Bolun Cai, Xiangmin Xu, Kui Jia, Chunmei Qing, and Dacheng Tao. 2016.  Dehazenet: An end-to-end system for single image haze removal.  _IEEE Transactions on Image Processing_ 25, 11 (2016), 5187–5198.
  * Chen et al. (2016) Chen Chen, Minh N Do, and Jue Wang. 2016.  Robust image and video dehazing with visual artifact suppression via gradient residual minimization. In _Proceedings of the European Conference on Computer Vision (ECCV)_. Springer, 576–591.
  * Chen et al. (2021) Zeyuan Chen, Yangchao Wang, Yang Yang, and Dong Liu. 2021\.  PSD: Principled synthetic-to-real dehazing guided by physical priors. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 7180–7189.
  * Chidlovskii et al. (2016) Boris Chidlovskii, Stephane Clinchant, and Gabriela Csurka. 2016.  Domain adaptation in the absence of source domain data. In _Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining_. 451–460.
  * Deng et al. (2020) Qili Deng, Ziling Huang, Chung-Chi Tsai, and Chia-Wen Lin. 2020\.  Hardgan: A haze-aware representation distillation gan for single image dehazing. In _Proceedings of the European Conference on Computer Vision (ECCV)_. Springer, 722–738.
  * Dong et al. (2020) Hang Dong, Jinshan Pan, Lei Xiang, Zhe Hu, Xinyi Zhang, Fei Wang, and Ming-Hsuan Yang. 2020\.  Multi-scale boosted dehazing network with dense feature fusion. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 2157–2167.
  * Dong and Pan (2020) Jiangxin Dong and Jinshan Pan. 2020.  Physics-based feature dehazing networks. In _Proceedings of the European Conference on Computer Vision (ECCV)_. Springer, 188–204.
  * Fan et al. (2021) Xinjie Fan, Qifei Wang, Junjie Ke, Feng Yang, Boqing Gong, and Mingyuan Zhou. 2021\.  Adversarially adaptive normalization for single domain generalization. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 8208–8217.
  * Fattal (2008) Raanan Fattal. 2008\.  Single image dehazing.  _ACM Transactions on Graphics (TOG)_ 27, 3 (2008), 1–9.
  * Fattal (2014) Raanan Fattal. 2014\.  Dehazing using color-lines.  _ACM Transactions on Graphics (TOG)_ 34, 1 (2014), 1–14.
  * He et al. (2010) Kaiming He, Jian Sun, and Xiaoou Tang. 2010.  Single image haze removal using dark channel prior.  _IEEE Transactions on Pattern Analysis and Machine Intelligence_ 33, 12 (2010), 2341–2353.
  * He et al. (2019) Tong He, Zhi Zhang, Hang Zhang, Zhongyue Zhang, Junyuan Xie, and Mu Li. 2019\.  Bag of tricks for image classification with convolutional neural networks. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 558–567.
  * Hong et al. (2020) Ming Hong, Yuan Xie, Cuihua Li, and Yanyun Qu. 2020\.  Distilling image dehazing with heterogeneous task imitation. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 3462–3471.
  * Huang et al. (2021) Jiaxing Huang, Dayan Guan, Aoran Xiao, and Shijian Lu. 2021\.  Model adaptation: Historical contrastive learning for unsupervised domain adaptation without source data.  _Advances in Neural Information Processing Systems_ 34 (2021).
  * Huang and Belongie (2017) Xun Huang and Serge Belongie. 2017.  Arbitrary style transfer in real-time with adaptive instance normalization. In _Proceedings of the IEEE International Conference on Computer Vision_. 1501–1510.
  * Jia et al. (2019) Songhao Jia, Ding-Jie Chen, and Hwann-Tzong Chen. 2019\.  Instance-level meta normalization. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 4865–4873.
  * Jin et al. (2020) Xin Jin, Cuiling Lan, Wenjun Zeng, Zhibo Chen, and Li Zhang. 2020.  Style normalization and restitution for generalizable person re-identification. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 3143–3152.
  * Li et al. (2021) Boyun Li, Yuanbiao Gou, Shuhang Gu, Jerry Zitao Liu, Joey Tianyi Zhou, and Xi Peng. 2021\.  You only look yourself: Unsupervised and untrained single image dehazing neural network.  _International Journal of Computer Vision_ 129, 5 (2021), 1754–1767.
  * Li et al. (2020a) Boyun Li, Yuanbiao Gou, Jerry Zitao Liu, Hongyuan Zhu, Joey Tianyi Zhou, and Xi Peng. 2020a.  Zero-shot image dehazing.  _IEEE Transactions on Image Processing_ 29 (2020), 8457–8466.
  * Li et al. (2017) Boyi Li, Xiulian Peng, Zhangyang Wang, Jizheng Xu, and Dan Feng. 2017.  Aod-net: All-in-one dehazing network. In _Proceedings of the IEEE International Conference on Computer Vision_. 4770–4778.
  * Li et al. (2018b) Boyi Li, Wenqi Ren, Dengpan Fu, Dacheng Tao, Dan Feng, Wenjun Zeng, and Zhangyang Wang. 2018b.  Benchmarking single-image dehazing and beyond.  _IEEE Transactions on Image Processing_ 28, 1 (2018), 492–505.
  * Li et al. (2019b) Lerenhan Li, Yunlong Dong, Wenqi Ren, Jinshan Pan, Changxin Gao, Nong Sang, and Ming-Hsuan Yang. 2019b.  Semi-supervised image dehazing.  _IEEE Transactions on Image Processing_ 29 (2019), 2766–2779.
  * Li et al. (2020b) Rui Li, Qianfen Jiao, Wenming Cao, Hau-San Wong, and Si Wu. 2020b.  Model adaptation: Unsupervised domain adaptation without source data. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 9641–9650.
  * Li et al. (2018a) Runde Li, Jinshan Pan, Zechao Li, and Jinhui Tang. 2018a.  Single image dehazing via conditional generative adversarial network. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_. 8202–8211.
  * Li et al. (2019a) Siyuan Li, Iago Breno Araujo, Wenqi Ren, Zhangyang Wang, Eric K Tokuda, Roberto Hirata Junior, Roberto Cesar-Junior, Jiawan Zhang, Xiaojie Guo, and Xiaochun Cao. 2019a.  Single image deraining: A comprehensive benchmark analysis. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 3838–3847.
  * Liu et al. (2018) Risheng Liu, Xin Fan, Minjun Hou, Zhiying Jiang, Zhongxuan Luo, and Lei Zhang. 2018\.  Learning aggregated transmission propagation networks for haze removal and beyond.  _IEEE Transactions on Neural Networks and Learning Systems_ 30, 10 (2018), 2973–2986.
  * Liu et al. (2019a) Xiaohong Liu, Yongrui Ma, Zhihao Shi, and Jun Chen. 2019a.  Griddehazenet: Attention-based multi-scale network for image dehazing. In _Proceedings of the IEEE/CVF International Conference on Computer Vision_. 7314–7323.
  * Liu et al. (2019b) Yang Liu, Jinshan Pan, Jimmy Ren, and Zhixun Su. 2019b.  Learning deep priors for image dehazing. In _Proceedings of the IEEE/CVF International Conference on Computer Vision_. 2492–2500.
  * Liu et al. (2021a) Yuang Liu, Wei Zhang, and Jun Wang. 2021a.  Source-free domain adaptation for semantic segmentation. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 1215–1224.
  * Liu et al. (2021b) Ye Liu, Lei Zhu, Shunda Pei, Huazhu Fu, Jing Qin, Qing Zhang, Liang Wan, and Wei Feng. 2021b.  From Synthetic to Real: Image Dehazing Collaborating with Unlabeled Real Data. In _Proceedings of the 29th ACM International Conference on Multimedia_. 50–58.
  * McCartney (1976) Earl J McCartney. 1976\.  Optics of the atmosphere: scattering by molecules and particles.  _New York_ (1976).
  * Mittal et al. (2012a) Anish Mittal, Anush Krishna Moorthy, and Alan Conrad Bovik. 2012a.  No-reference image quality assessment in the spatial domain.  _IEEE Transactions on Image Processing_ 21, 12 (2012), 4695–4708.
  * Mittal et al. (2012b) Anish Mittal, Rajiv Soundararajan, and Alan C Bovik. 2012b.  Making a “completely blind” image quality analyzer.  _IEEE Signal Processing Letters_ 20, 3 (2012), 209–212.
  * Oppenheim and Lim (1981) Alan V Oppenheim and Jae S Lim. 1981.  The importance of phase in signals.  _Proc. IEEE_ 69, 5 (1981), 529–541.
  * Pan et al. (2018) Xingang Pan, Ping Luo, Jianping Shi, and Xiaoou Tang. 2018\.  Two at once: Enhancing learning and generalization capacities via ibn-net. In _Proceedings of the European Conference on Computer Vision (ECCV)_. 464–479.
  * Pan et al. (2022) Zhihong Pan, Baopu Li, Dongliang He, Mingde Yao, Wenhao Wu, Tianwei Lin, Xin Li, and Errui Ding. 2022\.  Towards Bidirectional Arbitrary Image Rescaling: Joint Optimization and Cycle Idempotence. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 17389–17398.
  * Pizer et al. (1987) Stephen M Pizer, E Philip Amburn, John D Austin, Robert Cromartie, Ari Geselowitz, Trey Greer, Bart ter Haar Romeny, John B Zimmerman, and Karel Zuiderveld. 1987.  Adaptive histogram equalization and its variations.  _Computer Vision, Graphics, and Image Processing_ 39, 3 (1987), 355–368.
  * Qin et al. (2020) Xu Qin, Zhilin Wang, Yuanchao Bai, Xiaodong Xie, and Huizhu Jia. 2020.  FFA-Net: Feature fusion attention network for single image dehazing. In _Proceedings of the AAAI Conference on Artificial Intelligence_ , Vol. 34. 11908–11915.
  * Qu et al. (2019) Yanyun Qu, Yizi Chen, Jingying Huang, and Yuan Xie. 2019\.  Enhanced pix2pix dehazing network. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 8160–8168.
  * Ren et al. (2016) Wenqi Ren, Si Liu, Hua Zhang, Jinshan Pan, Xiaochun Cao, and Ming-Hsuan Yang. 2016\.  Single image dehazing via multi-scale convolutional neural networks. In _Proceedings of the European Conference on Computer Vision (ECCV)_. Springer, 154–169.
  * Ren et al. (2018) Wenqi Ren, Lin Ma, Jiawei Zhang, Jinshan Pan, Xiaochun Cao, Wei Liu, and Ming-Hsuan Yang. 2018.  Gated fusion network for single image dehazing. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_. 3253–3261.
  * Reza (2004) Ali M Reza. 2004\.  Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement.  _Journal of Signal Processing Systems for Signal Image and Video Technology_ 38, 1 (2004), 35–44.
  * Shao et al. (2020) Yuanjie Shao, Lerenhan Li, Wenqi Ren, Changxin Gao, and Nong Sang. 2020.  Domain adaptation for image dehazing. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 2808–2817.
  * Shyam et al. (2021) Pranjay Shyam, Kuk-Jin Yoon, and Kyung-Soo Kim. 2021\.  Towards domain invariant single image dehazing.  _arXiv preprint arXiv:2101.10449_ (2021).
  * Skarbnik et al. (2009) Nikolay Skarbnik, Yehoshua Y Zeevi, and Chen Sagiv. 2009\.  _The importance of phase in image processing_.  Technion-Israel Institute of Technology, Faculty of Electrical Engineering.
  * VidalMata et al. (2020) Rosaura G VidalMata, Sreya Banerjee, Brandon RichardWebster, Michael Albright, Pedro Davalos, Scott McCloskey, Ben Miller, Asong Tambo, Sushobhan Ghosh, Sudarshan Nagesh, et al. 2020\.  Bridging the gap between computational photography and visual recognition.  _IEEE Transactions on Pattern Analysis and Machine Intelligence_ 43, 12 (2020), 4272–4290.
  * Wang et al. (2021b) Chao Wang, Hao-Zhen Shen, Fan Fan, Ming-Wen Shao, Chuan-Sheng Yang, Jian-Cheng Luo, and Liang-Jian Deng. 2021b.  EAA-Net: A novel edge assisted attention network for single image dehazing.  _Knowledge-Based Systems_ 228 (2021), 107279.
  * Wang et al. (2021a) Menglu Wang, Xueyang Fu, Zepei Sun, and Zheng-Jun Zha. 2021a.  JPEG artifacts removal via compression quality ranker-guided networks. In _Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence_. 566–572.
  * Wu et al. (2021) Haiyan Wu, Yanyun Qu, Shaohui Lin, Jian Zhou, Ruizhi Qiao, Zhizhong Zhang, Yuan Xie, and Lizhuang Ma. 2021\.  Contrastive Learning for Compact Single Image Dehazing. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 10551–10560.
  * Yang et al. (2020) Wenhan Yang, Ye Yuan, Wenqi Ren, Jiaying Liu, Walter J Scheirer, Zhangyang Wang, Taiheng Zhang, Qiaoyong Zhong, Di Xie, Shiliang Pu, et al. 2020\.  Advancing image understanding in poor visibility environments: A collective benchmark study.  _IEEE Transactions on Image Processing_ 29 (2020), 5737–5752.
  * Yao et al. (2019) Mingde Yao, Zhiwei Xiong, Lizhi Wang, Dong Liu, and Xuejin Chen. 2019.  Spectral-depth imaging with deep learning based reconstruction.  _Optics Express_ 27, 26 (2019), 38312–38325.
  * Ye et al. (2021) Tian Ye, Mingchao Jiang, Yunchen Zhang, Liang Chen, Erkang Chen, Pen Chen, and Zhiyong Lu. 2021.  Perceiving and Modeling Density is All You Need for Image Dehazing.  _arXiv preprint arXiv:2111.09733_ (2021).
  * Ye et al. (2022) Tian Ye, Yun Liu, Yunchen Zhang, Sixiang Chen, and Erkang Chen. 2022.  Mutual Learning for Domain Adaptation: Self-distillation Image Dehazing Network with Sample-cycle.  _arXiv preprint arXiv:2203.09430_ (2022).
  * Zhang and Patel (2018) He Zhang and Vishal M Patel. 2018.  Densely connected pyramid dehazing network. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_. 3194–3203.
  * Zhang et al. (2017) Jing Zhang, Yang Cao, Shuai Fang, Yu Kang, and Chang Wen Chen. 2017.  Fast haze removal for nighttime image using maximum reflectance prior. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_. 7418–7426.
  * Zheng et al. (2021) Zhuoran Zheng, Wenqi Ren, Xiaochun Cao, Xiaobin Hu, Tao Wang, Fenglong Song, and Xiuyi Jia. 2021.  Ultra-high-definition image dehazing via multi-guided bilateral learning. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_. IEEE, 16180–16189.
  * Zhu et al. (2014) Qingsong Zhu, Jiaming Mai, and Ling Shao. 2014.  Single Image Dehazing Using Color Attenuation Prior.. In _British Machine Vision Conference(BMVC)_. Citeseer.
  * Zhu et al. (2015) Qingsong Zhu, Jiaming Mai, and Ling Shao. 2015.  A fast single image haze removal algorithm using color attenuation prior.  _IEEE Transactions on Image Processing_ 24, 11 (2015), 3522–3533.