# Single Image Deraining via Feature-based Deep Convolutional Neural Network

Chaobing Zheng  School of Information
Science and Engineering,
Wuhan University of
Science and Technology,
Wuhan, China
<EMAIL_ADDRESS>Jun Jiang  School of Information
Science and Engineering,
Wuhan University of
Science and Technology,
Wuhan, China
<EMAIL_ADDRESS>Wenjian Ying  College of Weapon,
Naval University of Engineering,
Wuhan, China
<EMAIL_ADDRESS>Shiqian Wu  School of Information
Science and Engineering,
Wuhan University of
Science and Technology,
Wuhan, China
<EMAIL_ADDRESS>
###### Abstract

It is challenging to remove rain-steaks from a single rainy image because the
rain steaks are spatially varying in the rainy image. Although the CNN based
methods have reported promising performance recently, there are still some
defects, such as data dependency and insufficient interpretation. A single
image deraining algorithm based on the combination of data-driven and model-
based approaches is proposed. Firstly, an improved weighted guided image
filter (iWGIF) is used to extract high-frequency information and learn the
rain steaks to avoid interference from other information through the input
image. Then, transfering the input image and rain steaks from the image domain
to the feature domain adaptively to learn useful features for high-quality
image deraining. Finally, networks with attention mechanisms is used to
restore high-quality images from the latent features. Experiments show that
the proposed algorithm significantly outperforms state-of-the-art methods in
terms of both qualitative and quantitative measures.

###### Index Terms:

single image rain removal, weighted guided image filtering, data-driven,
model-based

††footnotetext:  * contributed equally, ${\dagger}$ corresponding author. This
work is supported by Nature Science Foundation of Hubei Province (Grant
No.2022CFB676)

##  I Introduction

As the most common severe weather condition, the impact of rain will reduce
the visual quality of images and seriously affect the performance of outdoor
visual system. Under rainy conditions, the rain steaks will not only produce a
fuzzy effect in the image, but also cause haze due to light scattering, low
visibility of the scene and occlusion of the background scene. The contrast
and color of the target in the image will be attenuated to varying degrees,
resulting in unclear expression of the background information (i.e. the target
image), which makes some video or image systems unable to work normally [1].
Therefore, it is necessary to eliminate the impact of rain on the image scene.
In fact, image rain removal has always been an important part of image
restoration and computer vision research, which is mainly used in video
surveillance, automatic driving and other fields.

Single image de-raining is more challenging than video-based de-raining
because there is less available information. It has attractted many
researchers’s attention to solve the problem of restoring rainy images. The
existing rain steaks removal methods for a single image can generally be
divided into two categories: model-based methods [2, 3, 4, 5] and data-driven
methods [6, 7, 8, 9, 10]. As we known, the model-based rain removal algorithm
is not robust enough, with excessive processing or retention of rain steaks,
and is not universal enough. Data-driven rain removal algorithm is very
popular. However, there are defects in data dependence and insufficient
interpretability.

A novel removal algorithm by combining data-driven and model-based approaches
is proposed in this paper. The proposed algorithm embeds deep learning into a
prior model, making full use of deep learning to enhance the robustness of the
algorithm. The priori model is used to enhance the interpretability of the
algorithm. The two algorithms are combined to complement each other [11, 24,
13]. Experimental results show that the proposed deraining algorithm
outperforms a few existing deraining algorithms. It also proves that the
algorithm combining deep learning and model-based can complement each other.

The rest of this paper is organized as below. The relevant works is proposed
in Section II. The proposed deraining algorithm is presented in Section III.
Experimental results are provided in Section IV to verify the proposed
algorithm. Finally, conclusion remarks are drawn in Section V

##  II Relevant Works

Rain removal has attracted many researchers’s attention to solve the problem
of restoring rain images. These methods fall into two categories: model-based
methods and data-driven methods.

Model-driven methods: Some priors have been employed to remove rain from
single images. They assume that rain-streaks $R$ are sparse and in similar
directions. They decompose the raining image $O$ into two layers, the rain-
free background scene $B$ and the rain-streaks layer $R$. Zhu et al. [5] first
detected rain-dominant regions and then the detected regions were utilized as
a guidance image to help separate rain-streaks $R$ from the background layer
$B$. Liu et al. [2] decomposed the rainy image into low-frequency and high-
frequency through low-pass filtering, captures the rain-free image details
from the high-frequency part, superimposes the rain-free image details on the
low-frequency part, and further alleviates the blurring caused by rain steaks
by using the dark channel prior algorithm, but the rain marks of the derainy
image is too obvious. Li et al. [3] proposed a rain removal method based on
the Gaussian mixture model, which achieved good results in many cases.
However, there are still rain line residues in the rain removal images and it
is difficult to accurately estimate the Gaussian mixture model. Due to the
effect of air resistance and wind, the shape and direction of movement of rain
are random during the falling. It is difficult for model-driven algorithms to
capture rules, so the effect of rain removal may be not ideal.

Data-driven methods: Data-driven based single image deraining algorithms were
popular. Fu et al. [8] learned the mapping relationship between rainy and
clean detail layers, and the predicted detail layer was added into a low-pass
filtered base layer for removing rain-streaks. Yang et al. [9] proposed a deep
recurrent dilated network to jointly detect and remove rain-streaks. Zhang et
al. [6] take the rain density into account and present a multi-task CNN for
joint rain density estimation and deraining. Later, they further improve their
work by propose a conditional generative adversarial network for rain-streaks
removal in [7]. Li et al. [10] introduced a novel multi-stage deep learning
based single image deraining algorithm. Different $\alpha$ values are assigned
to various rain-streak layers according to their properties at each stage, and
then a recurrent neural network was incorporated to preserve the useful
information in previous stages and benefit the residual prediction in later
stage. Data-driven relies on massive amounts of data and is superior to model-
driven algorithms in terms of performance. However, even data-driven methods
struggle to capture regularity due to the random nature of rainfall.

In this paper, a novel single-image rain removal method by combining data-
driven and model-based is designed. The proposed algorithm is based on an
observation that prior knowledge can assist data-driven better targeted
learning. Since both rain and noise are random, they exist in high frequency
components. The high-frequency part can be obtained by an edge-preserving
filter such as [21, 23], and the rain steak can be learned directly from the
high frequency information rather than the input image to avoid interference
from other information. Then, transforming the input image and rain steaks
image from the image domain to the feature domain, and adaptively inging the
useful features to remove rain [25]. Finally, networks with attention
mechanisms is used restore high-quality images from the latent features, which
will inevitably cause errors due to inaccurate model. Experimental results
validate the prior is indeed very helpful for the single image deraining. The
proposed algorithm is useful for autonomous navigation in raining
conditions.inging

Figure 1: The proposed framework for single-image rain removal. $I$ is a rainy
image, $B$ is a restored image, and $B_{T}$ is the ground truth image of $B$.

##  III The Proposed Deraining Algorithm

###  III-A Framework of The Proposed Algorithm

The widely used rainy image model is expressed as [4]:

$I(p)=B(p)+S(p)\\\ $ (1)

where $I$ is a rainy image with rain-streaks; $B$ is the background layer; $S$
is the rain-streak layer; and $p$ is a pixel. Single image deraining is to
restore the image $B$ from the rainy image $I$. However, removing rain from a
single image is an ill posed problem. Especially, when the structure and
direction of the object are similar to the rain steaks, even though the DCNN
has a strong learning ability, it is also difficult to remove the rain steaks
and maintain the details at the same time.

A new single image rain-streaks removal algorithm is proposed in this paper is
by combining data-driven and model-based method. As shown in Fig. 1, based on
the model of $I(p)=B(p)+S(p)$, and the prior knowledge that rain steaks exist
in high-frequency information, due to the disadvantage of DCNN for learning
high-frequency information, directly using the rainy image to learn rain
steaks is not ideal. Therefore, an improved weighted guided image filter
(iWGIF) is adopted to obtain high frequency components which mainly contain
noise, rain-streaks, etc. A Rain-streaks Extract Net is proposed to obtain
rain steaks. Due to the limitation of prior knowledge, the high-frequency
information obtained cannot include all rain steaks, the learned rain steaks
may have inaccurate information, which needs further enhancement. Therefore,
converting the rainy image and rain steaks from the image domain to the
feature domain can reduce the interference of noise and other useless
information, make full use of effective information, and improve the network
training efficiency. Through the feature extraction network, the rainy image
and rain steaks are converted from the image domain to the feature domain, and
obtain the derain feature, as shown in Eq. 2.

$F(I(p))=F(B(p))+F(S(p))\\\ $ (2)

where $F(\cdot)$ represents the feature extraction function btained through
feature extraction network. Finally, DeRain Enhance Branch (DERB) is used for
image enhancement and restoration. The combination of prior knowledge and deep
learning enhances the robustness and physical interpretability of the
algorithm.

Figure 2:  Recursive residual group (RRG), Feature Extract Net and Rain-sreaks
Extract Net, each RRG contains multiple dual attention blocks (DAB). Each DAB
contains spatial and channel attention modules.

###  III-B Improved Weighted Guided Image Filtering [24]

In this subsection, an iWGIF is provided by using the edge-aware weighting in
[21] to improve the WAGIF in [23]. The objective is to reduce the sensitivity
of the WAGIF with respect to the regularization parameter [24].

Let $I$ be an image to be processing and $G$ be a guidance image. Let
$\Omega_{\zeta}(p)$ be a square window centered at the pixel $p$ of a radius
$\zeta$. Same as the GIF, WGIF, GGIF and WAGIF, $I(p)$ is assumed to be a
linear transform of the guidance image $G(p)$ in the window
$\Omega_{\zeta}(p^{\prime})$:

$I(p)=a_{p^{\prime}}G(p)+b_{p^{\prime}},\forall
p\in\Omega_{\zeta}(p^{\prime}),$ (3)

where $a_{p^{\prime}}$ and $b_{p^{\prime}}$ are two constants in the window
$\Omega_{\zeta}(p^{\prime})$.

It should be pointed out that the guidance image $G$ and the image to be
processed $I$ can be the same. The optimal values of $a_{p^{\prime}}$ and
$b_{p^{\prime}}$ are derived by minimizing a cost function
$E(a_{p^{\prime}},b_{p^{\prime}})$ which is defined as

$\displaystyle\sum_{p\in\Omega_{\zeta}(p^{\prime})}[\Gamma^{G}_{p^{\prime}}(a_{p^{\prime}}G(p)+b_{p^{\prime}}-I(p))^{2}+\lambda
a_{p^{\prime}}^{2}],$ (4)

where $\lambda$ is a regularization parameter which can be used to penalize a
large $a_{p^{\prime}}$.

Similarly to the WGIF, the edge-aware weighting $\Gamma^{G}_{p^{\prime}}$ is
defined by using local variances of $3\times 3$ windows of all pixels as
follows:

$\displaystyle\Gamma^{G}_{p^{\prime}}=\frac{1}{M}\sum_{p=1}^{N}\frac{\sigma^{2}_{G,1}(p^{\prime})+\varepsilon}{\sigma^{2}_{G,1}(p)+\varepsilon},$
(5)

where $M$ is the total number of pixels in the image $I$, and $\varepsilon$ is
a small constant. Certainly, there are many different methods to compute the
edge-ware weighting [21]. Different edge-aware weighting could be selected for
different applications.

By solving the optimization problem (4), the optimal values of
$a_{p^{\prime}}$ and $b_{p^{\prime}}$ are computed as

$\displaystyle a_{p^{\prime}}$
$\displaystyle=\frac{\Gamma^{G}_{p^{\prime}}\mbox{cov}_{I,G,\zeta}(p^{\prime})}{\Gamma^{G}_{p^{\prime}}\sigma^{2}_{G,\zeta}(p^{\prime})+\lambda},$
(6) $\displaystyle b_{p^{\prime}}$
$\displaystyle=\mu_{I,\zeta}(p^{\prime})-a_{p^{\prime}}\mu_{G,\zeta}(p^{\prime}),$
(7)

where the operation $\odot$ is the element-by-element product of two matrices.
$\mbox{cov}_{I,G,\zeta}(p^{\prime})$ is

$\displaystyle\mbox{cov}_{I,G,\zeta}(p^{\prime})=\mu_{G\odot
I,\zeta}(p^{\prime})-\mu_{G,\zeta}(p^{\prime})\mu_{I,\zeta}(p^{\prime}),$ (8)

and $\mu_{G,\zeta}(p^{\prime})$, $\mu_{I,\zeta}(p^{\prime})$, and $\mu_{G\odot
I,\zeta}(p^{\prime})$ are the mean values of $G$, $I$ and $G\odot I$ in the
window $\Omega_{\zeta}(p^{\prime})$, respectively.

Instead of using the averaging method in [19, 21], an optimal based method is
adopted to compute the final value of $I(p)$ as

$\min_{I(p)}\\{\sum_{p^{\prime}\in\Omega_{\zeta}(p)}W_{p^{\prime}}(I(p)-a_{p^{\prime}}G(p)-b_{p^{\prime}})^{2}\\},$
(9)

where $W_{p^{\prime}}$ is a weighting factor and it is given as [23]

$\displaystyle W_{p^{\prime}}$
$\displaystyle=\exp^{-\frac{1}{|\Omega_{\zeta}(p^{\prime})|}{\displaystyle\sum_{p\in\Omega_{\zeta}(p^{\prime})}}\frac{(a_{p^{\prime}}G(p)+b_{p^{\prime}}-I(p))^{2}}{\eta}}+0.001,$
(10)

$\eta$ is a small positive constant, and $|\Omega_{\zeta}(p^{\prime})|$ is the
cardinality of the set $\Omega_{\zeta}(p^{\prime})$.

The optimal solution is computed as

$I^{*}(p)=\bar{a}_{p}^{W}G(p)+\bar{b}_{p}^{W},$ (11)

where $\bar{a}_{p}$ and $\bar{b}_{p}$ are computed as

$\displaystyle\bar{a}_{p}^{W}$
$\displaystyle=\frac{1}{W^{sum}_{p}}\sum_{p^{\prime}\in\Omega_{\zeta}(p)}W_{p^{\prime}}a_{p^{\prime}},$
(12) $\displaystyle\bar{b}_{p}^{W}$
$\displaystyle=\frac{1}{W^{sum}_{p}}\sum_{p^{\prime}\in\Omega_{\zeta}(p)}W_{p^{\prime}}b_{p^{\prime}},$
(13)

and $W_{p}^{sum}$ is

$\displaystyle W_{p}^{sum}$
$\displaystyle=\sum_{p^{\prime}\in\Omega_{\zeta}(p)}W_{p^{\prime}}.$ (14)

It can be easily derived that

$\displaystyle\frac{1}{|\Omega_{\zeta}(p^{\prime})|}\sum_{p\in\Omega_{\zeta}(p^{\prime})}(a_{p^{\prime}}G(p)+b_{p^{\prime}}-I(p))^{2}$
$\displaystyle=$ $\displaystyle
a_{p^{\prime}}^{2}\sigma_{G,\zeta}^{2}(p^{\prime})-2a_{p^{\prime}}\mbox{cov}_{I,G,\zeta}(p^{\prime})+\sigma_{I,\zeta}^{2}(p^{\prime})$
$\displaystyle=$
$\displaystyle\sigma_{I,\zeta}^{2}(p^{\prime})-a_{p^{\prime}}^{2}(\sigma_{G,\zeta}^{2}(p^{\prime})+\frac{2\lambda}{\Gamma_{p^{\prime}}^{G}}).$
(15)

Therefore, same as the GIF in [19], WGIF in [21] and WAGIF in [23], the
complexity of the iWGIF is $O(M)$ for an image with $M$ pixels.

The iWGIF is adopted to decompose the rainy image $I$ into base layer and
detail laye, the guidance image $G$ is the same as the rainy image $I$. The
detail layer mainly contains high-frequency information, and most rain steaks
are in the detail layer. Using the detail layer to learn the rain is more
direct, avoiding other interference, and improving the learning efficiency of
the network.

###  III-C Feature-based deep convolutional neural network

Due to the limited modeling ability of prior knowledge, high-frequency
information cannot cover all raindrops. In addition, DCNN is not good at
obtaining high-frequency information, the learned rain steaks have incorrect
information, it is necessary to enhance de-rainy image. A feature extract
network is proposed, which transforms the rainy image and rain steaks from the
image domain to the feature domain to adaptively learn useful features for
high-quality image deraining, and enhances the efficiency of the network. Fig.
1 and 2 summarizes the pipeline of our algorithm. To make efficient use of
useful features, the CNN used in the proposed framework is on top of the
DeNoiseNet in [20], which achieves outstanding performance in denoising. The
recursive residual group (RRG) in DeNoiseNet is shown in Fig. 2. The RRG
contains Dual Attention Blocks (DAB) and each DAB performs both spatial and
channel attention operations. The feature extract network contains two RRGs
and one $3*3$ convolution, which can suppress the less useful features and
only allow the propagation of more informative ones. The rain-streaks extract
network contains two $3*3$ convolution and two RRGs, which can pay more
attention to the learning of rain steaks under the effect of attention
mechanism.

To restore high-quality images from the latent features $F(I(p))-F(S(p))$,
deRain enhance branch (DERB) is adopted. The DERB contains four RRGs and one
$3*3$ convolution. By using the DERB, further feature extraction and recovery,
the experiment also proves the importance of DERB.

Loss functions play an important role in training the CNN from $N$ pairs of
images $\\{(I,B_{T})\\}$. Here, $I$ is a rainy image and $B_{T}$ is a rain-
free image. To better regularize the network, we apply an $L1$ loss functions.
The loss function is given as:

$L_{r}=\frac{1}{N}\sum_{p}|B_{T}-B|,$ (16)

##  IV Experiments

In this section, we first introduce the details of the implementation, then
evaluate the effectiveness of the proposed method on the existing deraining
datasets, compare the proposed deraining method with several state-of-the-art
single-image deraining methods. Finally, ablation experiments are designed to
prove the contribution of each module. The details are as follows:

###  IV-A Implementation Details

To verify the proposed derain method, we conduct the comparison and analysis
experiments on synthetic rain image Rain100L [14], Rain100H [14] and Rain1400
[15], and use SSIM and PSNR to evaluate the performance.

Each RRG contains two DAB. The number of RRG of SERB is set as four. We
randomly crop a $128*128$ patch from each input during training. The proposed
network is trained using the proposed loss functions and Adam optimizer with
${{\beta}_{1}}=0.9$ and ${{\beta}_{2}}=0.99$. We set the batch size to $8$.
The learning rate is initially set to $2*10^{-4}$ and then decreased using a
cosine annealing schedule. All the experiments are implemented using PyTorch
on NVIDIA GP100 GPUs.

###  IV-B Comparison with Existing Algorithms

The proposed algorithm is compared with five state-of-the-art deraining
algorithms in [14], [15], [16], [17], [18] on synthetic rainy dataset. These
algorithms were published at top conferences in computer vision. As shown in
Fig. 3, the algorithms in [18, 17] and the proposed algorithm can be adopted
to reduce rain-streaks better than the algorithms in [14, 15, 16]. There are
still visible artifact in the restored images by the algorithm in [18, 17], as
shown in the red box. The [15] also uses high-frequency information to learn
rain steaks. However, DCNN is not good at learning high-frequency information,
and there are obvious traces.

Figure 3: Comparison of different deraining algorithms on synthetic rainy
images. From left to right, the rainy images and the restored images by [14],
[15], [16], [17], [18] and the proposed method, respectively.

Besides the subjective evaluation, the objective quality metrics including the
SSIM and PSNR are adopted to further compare the proposed algorithm with those
in [14], [15], [16], [17], [18]. The average SSIM and PSNR are shown in Tables
I-III. The proposed algorithm can achieve higher PSNR and SSIM than others.

TABLE I: SSIM and PSNR Of Different Algorithms for Rain100L | [14] | [15] | [16] | [17] | [18] | Ours
---|---|---|---|---|---|---
SSIM | 0.965 | 0.948 | 0.952 | 0.984 | 0.98 | 0.984
PSNR | 34.32 | 32.94 | 32.15 | 38.58 | 38.21 | 38.43
TABLE II: SSIM and PSNR Of Different Algorithms for Rain100H | [14] | [15] | [16] | [17] | [18] | Ours
---|---|---|---|---|---|---
SSIM | 0.786 | 0.751 | 0.760 | 0.886 | 0.855 | 0.903
PSNR | 24.37 | 24.56 | 21.79 | 28.81 | 27.62 | 29.53
TABLE III: SSIM and PSNR Of Different Algorithms for Rain1400 | [14] | [15] | [16] | [17] | [18] | Ours
---|---|---|---|---|---|---
SSIM | 0.876 | 0.864 | 0.877 | 0.909 | 0.908 | 0.912
PSNR | 28.37 | 28.19 | 28.21 | 30.59 | 30.6 | 31.04
TABLE IV: Ablation study on key components of the proposed exposure interpolation framework on Rain100H ($\uparrow$: larger is better) Case | iWGIF | Feature Extract Net | DERB |  SSIM ($\uparrow$) |  PSNR ($\uparrow$)
---|---|---|---|---|---
1 | N | Y | Y | 0.885 | 28.64
2 | Y | N | Y | 0.885 | 28.58
3 | Y | Y | N | 0.802 | 25.22
4 | Y | Y | Y | 0.903 | 29.53
Figure 4: (a) and (c) Comparisons of PSNR between the modes with and without
the iWGIF and Feature Net for Rain100H. (b) and (d) Comparisons of SSIM
between the modes with and without the iWGIF and Feature Net for Rain100H.

###  IV-C Ablation Study

Key components of the proposed framework are: 1) iWGIF, 2) DERB, 3) Feature
Extract Net. Their performances are evaluated in this subsection. As
illustrated in Table IV, the mode with the iWGIF is more stable than the mode
without iWGIF, and can achieve higher PSNR and SSIM values in different
epoches. It also proves the performance of feature extraction network as shown
in Fig. 4. The feature extraction network can adaptively use useful features
for image enhancement and improve network training efficiency. The results
with and without EDRB are shown in Fig. 5, the DERB can avoid the inaccuracy
of modeling and further enhance the latent features.

Figure 5: Comparison of results with and without DERB.

##  V Conclusion Remarks and Discussions

A novel single image deraining algorithm by combinating data-driven and model-
based methods is proposed in this paper. By using high-frequency information
extracted by iWGIF to learn rain steaks, the training efficiency of CNN is
improved. Combined with the rain removal model, the input image and rain
steaks are converted from the image domain to the feature domain, which can
use the useful information adaptively. Finally, the latent features are
enhanced and restored through the network with dual attention mechanism.
Experimental results show that the proposed algorithm could outperform several
existing single image de-raining algorithms.

For other low-level visual processing tasks such as dehazing and illumination
enhancement, the prior knowledge can also be incorporated into data-driven
approaches. Besides the prior knowledge, it is also important to combine
model-based and data-driven methods for the low-level visual processing. The
proposed algorithm can also be applied to study autonomous navigation in
raining conditions. All these problems will be studied in our future research.

## References

  * [1] C. B. Zheng, Z. G. Li, Y. W. Li and S. Q. Wu, Non-Local Single Image DE-Raining Without Decomposition, IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 1425-1429, 2021.
  * [2] J. C. Liu, S. H. Teng, and Z. Y. Li, Removing Rain from Single Image Based on Details Preservation and Background Enhancement, IEEE 2nd International Conference on Information Communication and Signal Processing, pp. 322-326, 2019.
  * [3] Y. Li, R. T. Tan, X. Guo, J. Lu and M. S. Brown, Rain Streak Removal Using Layer Priors, IEEE Conference on Computer Vision and Pattern Recognition, pp. 2736-2744, 2016.
  * [4] L.W. Kang, C. W. Lin, and Y. H. Fu, Automatic single-image-based rain streaks removal via image decomposition, IEEE Trans. on Image Processing , vol. 21, no. 4, pp. 1742-1755, Apr. 2012.
  * [5] L. Zhu, C. W. Fu, D. Lischinski, and P. A. Heng, Joint bi-layer optimization for single-image rain streak removal, IEEE International Conference on Computer Vision, pp. 2545–2553, 2017.
  * [6] H. Zhang and V. M. Patel, Density-aware single image deraining using a multi-stream dense network, IEEE Conference on Computer Vision and Pattern Recognition, pp. 695–704, 2018.
  * [7] H. Zhang, V. Sindagi, and V. M. Patel, Image deraining using a conditional generative adversarial network, IEEE Trans. on Circuits and Systems for Video Technology , vol. 30, no. 11, pp. 3943 - 3956, Nov. 2020.
  * [8] X. Fu, J. Huang, X. Ding, Y. Liao, and J. Paisley, Clearing the skies: a deep network architecture for single-image rain removal, IEEE Trans. on Image Processing, vol. 26, no. 6, pp. 2944-2956, Jun. 2017.
  * [9] W. Yang, R. T. Tan, J. Feng, J. Liu, Z. Guo, and S. Yan, Deep joint rain detection and removal from a single image, IEEE Conference on Computer Vision and Pattern Recognition, pp. 1357-1366, 2017.
  * [10] X. Li, J. Wu, Z. Lin, H. Liu, and H. Zha, Recurrent squeeze-andexcitation context aggregation net for single image deraining, ECCV, pp. 262–277, 2018.
  * [11] C. B. Zheng, Z. G. Li, Y. Yang, and S. Q. Wu,  “Single image brightening via multi-scale exposure fusion with hybrid learning,”  IEEE Trans. on Circuits and Systems for Video Technology, vol. 31, no. 4, pp. 1425-1435, Apr., vol. 31, no. 4, pp. 1425-1435, Apr. 2021.
  * [12] Z. Li, C. Zheng, H. Shu and S. Wu, Dual-Scale Single Image Dehazing via Neural Augmentation, IEEE Transactions on Image Processing, vol. 31, pp. 6213-6223, 2022.
  * [13] C. Zheng, W. Jia, S. Wu and Z. Li, Neural Augmented Exposure Interpolation for Two Large-Exposure-Ratio Images, IEEE Transactions on Consumer Electronics, vol. 69, no. 1, pp. 87-97, Feb. 2023.
  * [14] W. Yang, R. T. Tan, J. Feng, J. Liu, Z. Guo, and S. Yan, Deep joint rain detection and removal from a single image, IEEE Conference on Computer Vision and Pattern Recognition, pp. 1685-1694, 2017.
  * [15] X.Y. Fu, J. B. Huang, D. L. Zeng, Y. Huang, X. H. Ding, and J. W. Paisley, Removing rain from single image via a deep detail network, IEEE Conference on Computer Vision and Pattern Recognition, pp. 1715-1723, 2017.
  * [16] X.Y. Fu, B. R. Liang, Y. Huang, X. H. Ding, and J. Paisley, Lightweight Pyramid Networks for Image Deraining, IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 6, pp. 1794-1807, June. 2020.
  * [17] H. Wang, Q. Xie. Wang, Q. Zhao, and D. Y. Meng, A Model-Driven Deep Neural Network for Single Image Rain Removal, IEEE Conference on Computer Vision and Pattern Recognition, pp. 3100-3109, 2020.
  * [18] H. Wang, Z. S. Yue, Q. Xie, Q. Zhao, Y,F, Zheng, and D. Y. Meng, From Rain Generation to Rain Removal, IEEE Conference on Computer Vision and Pattern Recognition, pp. 14791-14801, 2021.
  * [19] K. He, J. Sun, and X. Tang, Guided image filtering, IEEE Trans. on Pattern Analyis and Machine Intelligence, vol. 35, no. 6, pp. 1397-1409, Jun. 2013.
  * [20] S. Zamir, A. Arora, S. Khan, M. Hayat, F. S. Khan, M. Yang, and L. Shao, CycleISP: real image restoration via improved data synthesis, IEEE Conference on Computer Vision and Pattern Recognition, 2020.
  * [21] Z. G. Li, J. H. Zheng, Z. J. Zhu, W. Yao, and S. Q. Wu, Weighted guided image filtering, IEEE Trans. on Image Processing. vol. 24, no.1, pp. 120-129, Jan. 2015.
  * [22] W. Wang, Z. G. Li, S. Q. Wu, and L. C. Zeng, Haze image decolorization with color contrast restoration, IEEE Trans. on Image Processing, vol. 28, no. 12, pp. 1776 - 1787, Dec. 2019.
  * [23] B. Chen and S. Q. Wu, Weighted aggregation for guided image filtering, Signal, Image and Video Processing, pp. 1-8, Oct. 2019.
  * [24] Z. G. Li, J. H. Zheng, and J. Senthilnath,  “ Simultaneously smoothing and sharpening using iWGIF”,  in 2022 IEEE International Conference on Image Processing, pp. 861-865, France, Oct 2022.
  * [25] J. Dong, S. Roth and B. Schiele, DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 12, pp. 9960-9976, 2022.