Multi-domain interactive image rain removal method based on state space model

Abstract

The invention relates to the technical field of image processing, and discloses a multi-domain interactive image rain removal method based on a state space model, and the method comprises the steps: processing a raindrop image through a rain removal model, and obtaining a restoration image after raindrop removal; the rain removal model construction and training process comprises the following steps: carrying out feature extraction on an input raindrop image to obtain potential features; performing multi-domain interaction processing on the potential feature F0 by using a FreqSSM module, and integrating and interacting information of different domains; after down-sampling the raindrop image, using an attention module to extract rain streak information, and fusing the rain streak information with the trunk information flow output by the FreqSSM module to obtain a fusion feature; the fusion features are fused with the raindrop image after passing through a recovery module formed by a convolutional layer, and a final recovery image is obtained; according to the invention, accurate identification and removal of raindrops in the image are realized through hierarchical space and frequency information interaction, and the naturalness and accuracy of the rain removal effect are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular to a multi-domain interactive image deraining method based on a state space model. Background Art

[0002] Image deraining is an important research topic in the field of computer vision and image processing. Its goal is to restore clear scenes from images affected by raindrops. In practical applications, such as monitoring, autonomous driving, satellite remote sensing, etc., the acquired images often suffer from image quality degradation due to the influence of rain, which in turn affects the accuracy of image analysis and understanding. In order to solve this problem, researchers have proposed a variety of image deraining methods.

[0003] Early rain removal methods mainly rely on traditional image processing techniques, such as methods based on image statistical characteristics, which usually require certain prior knowledge of the morphology and distribution of raindrops. With the development of image processing technology, model-based methods have begun to emerge, which perform rain removal by establishing a physical model between raindrops and background. However, these traditional methods often require complex parameter adjustments and have limited effectiveness in dealing with complex scenes and atypical raindrop patterns.

[0004] In recent years, with the rise of deep learning technology, learning-based methods have made significant progress in the field of image deraining. Deep convolutional neural networks (CNNs) are widely used in image deraining tasks due to their powerful feature extraction capabilities. These learning-based methods usually train a network to learn deraining mapping directly from rainy images without the need for complex physical models and parameter adjustments. For example, some methods use attention mechanisms to enhance the network's ability to identify raindrop regions, while others improve deraining effects through multi-scale processing.

[0005] Although deep learning methods have achieved some success in image deraining, there are still some challenges and limitations. For example, existing deep deraining methods often focus on extracting local features and ignore the importance of global information. In addition, since raindrops have diverse shapes and their appearance in images is affected by many factors, such as the size, density, and direction of movement of raindrops, it is very difficult to design a universal deraining model that can adapt to various raindrop conditions. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a multi-domain interactive image deraining method based on a state-space model, which can effectively remove raindrops in an image while maintaining the details and quality of the image. The present invention realizes the accurate identification and removal of raindrops in an image through the interaction of hierarchical spatial and frequency information, thereby improving the naturalness and accuracy of the deraining effect.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A multi-domain interactive image deraining method based on a state space model processes a raindrop image through a rain removal model to obtain a restored image after removing raindrops. The construction and training process of the rain removal model includes the following steps:

[0009] Step 1: extract features from the input raindrop image to obtain the potential feature F0;

[0010] Step 2: Use the FreqSSM module to perform multi-domain interactive processing on the latent feature F0 and integrate the information of different domains;

[0011] The FreqSSM module consists of three branches: space branch, frequency band branch and Fourier branch. The space branch uses the state space model to process the potential features and extract the details and spatial correlation of the raindrop image. The frequency band branch uses discrete wavelet packet transform to decompose the potential features into different frequency sub-bands, and uses the frequency dimension sequence modeling method to rearrange the low-resolution features obtained after decomposition in the order from low frequency to high frequency, and scans them in the frequency dimension. The Fourier branch is responsible for global degradation modeling and converts the potential features to the frequency domain through fast Fourier transform.

[0012] In addition, after downsampling the raindrop image, the attention module is used to extract the rain streak information, which is bypassed and fused with the main information stream output by the FreqSSM module to obtain the fusion feature to enhance the image deraining effect;

[0013] Step 3, fusing the fused features with the raindrop image after passing through a restoration module composed of a convolutional layer to obtain a final restored image;

[0014] Step 4: Determine the loss function to optimize the deraining model. The total loss function includes spatial domain loss and frequency domain loss function, so that the deraining model can reduce the error at the pixel level and improve the quality of the restored image at the frequency level.

[0015] Furthermore, step one specifically includes:

[0016] The raindrop image is subjected to feature extraction through convolution operation to obtain the potential feature F0:

[0017] F0=Conv(I in );

[0018] Where Conv represents the convolution operation.

[0019] Furthermore, the FreqSSM module is used to perform multi-domain interactive processing on potential features and integrate information from different domains for interaction, specifically including:

[0020] The spatial branch is used to map the latent features F t Perform layer normalization to obtain the feature map F LN , and then processed by two parallel sub-branches; in the first sub-branch, the feature map F LN Through the activation function, in the second sub-branch, the feature map F LN After convolution, the feature map is processed using the Mamba scanning mechanism, and finally the outputs of the two parallel sub-branches are element-wise multiplied to obtain the output feature F of the spatial branch. spatial :

[0021] F LN =LN(F0);

[0022] F spatial =Mamba(conv 1×1 (F LN ))⊙S is not iLU(F LN );

[0023] In the formula, LN(·) represents layer normalization, conv 1×1 represents 1×1 convolution, ⊙ represents element-wise multiplication, SiLU(·) is the activation function; Mamba(·) represents the state space model, which can model sequence data through the selective scanning mechanism;

[0024] Frequency band branch: The feature map F LN Through k-layer discrete wavelet packet transform, it is decomposed into sub-bands of different frequencies, and the sub-bands are rearranged in order from low frequency to high frequency, processed by the frequency dimension sequence modeling method, and the obtained feature map is restored to the spatial domain through k-layer wavelet packet inverse transform to obtain the output feature F of the frequency band branch band :

[0025] F band =IDWT(FreqScan(DWT(F LN )))⊙SiLU(F LN );

[0026] In the formula, DWT represents wavelet packet transform, IDWT represents inverse wavelet packet transform, and FreqScan represents the frequency dimension sequence modeling method;

[0027] Fourier branch: Perform fast Fourier transform on the potential feature F0, and process the obtained amplitude spectrum and phase spectrum through the convolution layer respectively, and then convert the processed frequency domain features back to the spatial domain through inverse Fourier transform to obtain the output feature F of the Fourier branch fourier :

[0028]

[0029]

[0030]

[0031]

[0032] In the formula, represents the discrete Fourier transform, represents the inverse Fourier transform, ConvBlock(·) represents a 1×1 convolution and activation function sequence; represent the amplitude spectrum and phase spectrum respectively, F P represents the phase spectrum processed by the convolutional network, F A Represents the amplitude spectrum processed by the convolutional network;

[0033] Then, the output features of the spatial branch, frequency band branch, and Fourier branch of the FreqSSM module are concatenated, and the features are fused through the convolution layer to obtain the output of the FreqSSM module.

[0034] Furthermore, after downsampling the raindrop image, the attention module is used to extract rain streak information, and the rain streak information is bypassed and fused with the main information stream output by the FreqSSM module to obtain fusion features, which specifically include:

[0035] Downsample the raindrop image and use an attention module to identify the pattern and distribution of raindrops in the downsampled raindrop image and generate an attention map that highlights the most likely locations of raindrops in the downsampled raindrop image.

[0036] Fusion of the attention map with the backbone information flow: element-wise multiplication and summation.

[0037] M attn =Mamba(conv 1×1 (I in ));

[0038] F′=F⊙M atten +F;

[0039] Where Mamba(·) represents the state space model; M attn Indicates the intermediate variable; I in represents the input image; F represents the backbone information flow; F′ represents the backbone information flow of the fused attention map.

[0040] Furthermore, the fusion feature is fused with the raindrop image after passing through a restoration module composed of a convolutional layer to obtain a final restored image, specifically including:

[0041] The fused features are sent to multiple convolutional layers of the restoration module, and the convolutional layers of the restoration module contain activation functions; the fused features after the restoration module are jump-connected with the original raindrop image, and the final restored image I is obtained through the convolutional layer. restorsded .

[0042] Furthermore, the spatial domain loss evaluates the quality of the restored image by calculating the pixel-level difference between the restored image and the annotated rain-free image. Specifically, the spatial domain loss adopts the mean absolute error;

[0043] The frequency domain loss includes the loss calculated for the amplitude spectrum and the phase spectrum after Fourier transformation respectively;

[0044] The total loss function L total is the sum of spatial domain loss and frequency domain loss:

[0045] L spa =||Y out -X gt ||1;

[0046]

[0047]

[0048] L total =L spa +αL amp +βL pha ;

[0049] Among them, L spa represents the spatial domain loss, L amp Indicates the amplitude loss, L pha represents the frequency domain phase loss, α and β are weight parameters; ‖·‖1 represents the 1-norm.

[0050] Compared with the prior art, the beneficial technical effects of the present invention are:

[0051] The present invention realizes accurate recognition and removal of raindrops in images through hierarchical interaction of spatial and frequency information, thereby improving the naturalness and accuracy of the rain removal effect. This hierarchical processing not only enhances the model's ability to recognize raindrop details, but also effectively removes the visual interference caused by raindrops while maintaining the original details of the image. The multi-scale degradation prior attention map is used to enable the model to more accurately identify and process raindrops in the image. This attention mechanism enables the model to dynamically adjust the processing strategy according to the degradation of the image, thereby achieving excellent rain removal effects under different degradation levels.

[0052] The present invention proposes an innovative FreqMamba structure, which effectively enhances the perception of global image degradation from the perspective of frequency by combining the Mamba model and frequency analysis. This structure not only improves the deraining effect, but also provides a new perspective and method for the field of image processing by introducing a new frequency dimension. At the same time, the loss function design of the present invention takes into account the information in the spatial domain and the frequency domain, so that the model can be fully optimized during the training process, thereby achieving an efficient deraining effect. The design of this loss function helps the model to better learn how to distinguish and process raindrops, and how to maintain the naturalness and visual effects of the image while removing raindrops. It has shown excellent performance and generalization ability on multiple data sets, and can effectively process complex raindrop patterns and images under different weather conditions. This means that the method of the present invention not only performs well on specific data sets, but also can adapt to changing environments and conditions, and has a wide range of applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of the method in the present invention;

[0054] Figure 2 It is a structural diagram of the rain removal model proposed in the present invention;

[0055] Figure 3 Schematic diagram of the principle of frequency dimension sequence modeling proposed in the present invention. DETAILED DESCRIPTION

[0056] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0057] like Figure 1 As shown, the present invention proposes an image deraining method based on the combination of frequency and spatial domains. The method combines the Mamba model with frequency analysis to improve the modeling capabilities of global degradation and local details in image deraining tasks. The specific implementation process includes the following modules: frequency band Mamba module, spatial Mamba module and Fourier modeling module. These three modules are organically combined to form a frequency state space model (Frequency State Space Model, FreqSSM) module, which realizes the effective processing of rain degradation from the frequency dimension and the spatial dimension, and finally optimizes the overall performance through multi-scale degradation prior.

[0058] Next, the FreqSSM module, which is the core part of the present invention, is described.

[0059] like Figure 2As shown in Figure 1, the spatial Mamba module is used to capture local details and degradation information in the image. In the spatial domain, the rainfall phenomenon of the image often manifests as blur or occlusion in the local area, so the capture of these local information is crucial for the image deraining task. The spatial Mamba module scans the image pixel by pixel (spatial domain scanning) and uses its selective scanning mechanism to finely process local details. Its basic workflow is as follows: Figure 2 As shown in the spatial branch of , the input potential features are first extracted through the convolution layer, and then the extracted features are processed by the spatial Mamba module. The specific calculation formula is:

[0060] F spatial =Mamba(W1(F LN ))⊙SiLU(F LN );

[0061] Where W1 represents a 1×1 convolution, Mamba(·) is the 2D scanning process of the Mamba model, SiLU is the activation function, and ⊙ represents the element-wise dot product. Spatial Mamba can help the model identify and repair local degraded areas in the image by effectively modeling the long-distance dependencies between local areas in the image.

[0062] like Figure 2 As shown in the frequency band branch, the frequency band Mamba module decomposes the input features into multiple frequency sub-bands by using wavelet packet transform (WPT). Wavelet packet transform is a multi-resolution technology widely used in signal analysis, which can decompose the image into low-frequency components and high-frequency components at different frequency levels so as to scan and process the image in different frequency ranges. Specifically, the input feature I is transformed into four sub-bands through wavelet packet transform, namely I LL ,I LH ,I HL ,I HH , they represent the low-frequency and high-frequency components in different directions, and the expression formula is as follows:

[0063] I LL ,I LH ,I HL ,I HH =DWT(I);

[0064] Among them, I LL is the low-frequency component of the input feature, I LH ,I HL ,I HHDWT(·) represents the discrete wavelet packet transform, which captures the detailed changes of the image in different frequencies and directions. By scanning these frequency sub-bands one by one, the detailed information in the frequency dimension can be effectively extracted. It is worth noting that in the frequency band Mamba module, the present invention adopts a local scanning strategy such as Figure 3 As shown, this ensures that frequency information is processed sequentially from low frequency to high frequency.

[0065] F band =IDWT(FreqScan(DWT(F LN )))⊙SiLU(F LN );

[0066] Wherein, DWT represents wavelet packet transform, IDWT represents inverse wavelet packet transform, and FreqScan represents the frequency dimension sequence modeling method proposed in the present invention, such as Figure 3 shown.

[0067] After the frequency band Mamba module is processed, all frequency subbands are returned to the original spatial domain through inverse wavelet transform (IDWT), so that the model can use information from both the frequency domain and the spatial domain. This frequency band scanning method not only improves the model's ability to capture frequency details, but also provides a solid foundation for subsequent global modeling and local detail restoration.

[0068] like Figure 2 As shown in the Fourier branch of , the Fourier modeling module is an important part of the present invention and is mainly used to process the global degradation information in the image. As a classic frequency analysis tool, Fourier transform can transform the image from the spatial domain to the frequency domain, making it easier to analyze the global statistical characteristics of the image. In the present invention, the Fourier modeling module converts the input features into frequency domain representations, including amplitude spectrum and phase spectrum, through fast Fourier transform (FFT):

[0069]

[0070]

[0071] Here, A(F0) and P(F0) represent the amplitude spectrum and phase spectrum, respectively, which represent the amplitude and phase information of the image in the frequency domain. The Fourier modeling module enhances the modeling ability of the global degradation pattern by convolution processing the amplitude spectrum and phase spectrum, and converts the processed frequency information back to the spatial domain through inverse Fourier transform (iFFT). The specific operation is shown in the formula:

[0072]

[0073]

[0074]

[0075]

[0076] In the formula, represents discrete Fourier transform, represents the inverse Fourier transform, and ConvBlock(·) represents a 1×1 convolution and activation function sequence.

[0077] Through the Fourier modeling module, the model can effectively separate and process global degradation phenomena in the image, especially the impact of rain on the entire image. Since rain degradation is usually more significant in the amplitude spectrum, Fourier transform can help the model better understand and remove this degradation information.

[0078] In order to further improve the deraining effect of the model, the present invention introduces a multi-scale degradation prior attention map. Figure 2 As shown in the figure, the degradation prior is generated by processing images at different scales, which can help the model better identify and locate the rain area in the image. In specific operations, the Mamba model performs a 2D scan on the input multi-scale image to generate an attention map corresponding to the rain area. The generated attention map will be element-wise multiplied with the image features of the same scale to enhance the weight of the rain area, and finally added to the original feature map to improve the model's ability to identify the rain area. By introducing multi-scale degradation priors, the model can more accurately handle rain degradation phenomena at different scales, thereby improving the overall performance of the deraining task.

[0079] M attn =Mamba(conv 1×1 (I in ));

[0080] F=F⊙M atten +F;

[0081] Where Mamba(·) represents a new state space model mentioned above.

[0082] Finally, the feature map processed by the FreqSSM module is sent to the recovery block composed of multiple convolutional layers for further feature extraction and enhancement. These convolutional layers contain activation functions to increase nonlinearity and improve the expressiveness of the model. The present invention jump-connects the fused feature map with the original raindrop image, and performs the final image restoration processing through the convolutional layer to obtain a clear image after rain removal.

[0083] In order to ensure the effectiveness of the FreqMamba model in the image deraining task, this paper designs a loss function based on L1 norm and frequency analysis to guide the training of the model. The loss function is used to measure the pixel-level difference between the derained image and the rain-free image in the spatial and frequency domains, thereby adjusting the parameters of the model.

[0084] During the training process, the present invention uses the Adam optimizer, and its initial learning rate is set to 0.0003, which is reduced to 0.000006 by cosine annealing. The entire training process is completed on NVIDIA GeForce RTX 3090 and implemented using the deep learning framework PyTorch. In order to prevent overfitting, data enhancement techniques are used during the training process, including random cropping, horizontal flipping, and brightness adjustment, to improve the generalization ability of the model.

[0085] The training and testing of the FreqMamba model uses the Rain100H, Rain100L, Test2800, and Test1200 datasets, which are designed for image deraining tasks. This dataset contains a large number of rainy day images and their corresponding rain-free images for supervised learning.

[0086] Rain100L: Contains a simple rainfall mode, suitable for light rainfall scenes.

[0087] Rain100H: contains more complex rainfall patterns and dense rain occlusions, which is more challenging and suitable for verifying the generalization ability of the model.

[0088] Test1200: Contains 1,200 test images with rain noise, covering a variety of scenes and rainfall conditions of different intensities, and is used to test the model's rain removal effect under various conditions.

[0089] Test2800: This dataset contains 2,800 test images with more complex rain interference. It is more challenging and suitable for verifying the robustness and accuracy of the model in complex rainy environments.

[0090] By training and testing on the Rain100H, Rain100L, Test1200, and Test2800 datasets, the FreqMamba model is able to demonstrate its comprehensive performance in different rain scenarios, ensuring the high efficiency of the rain removal effect and its wide application applicability.

[0091] The complementary combination of frequency domain and spatial domain through the above modules greatly improves the deraining effect of the model, so that the final generated image achieves the best performance in both visual and quantitative evaluation. By combining the advantages of frequency analysis and Mamba model, the present invention provides an innovative and effective solution for image deraining, greatly improves the deraining effect, and provides a new direction for future research in related fields.

[0092] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

[0093] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A multi-domain interactive image deraining method based on a state space model, characterized in that: The raindrop image is processed by the rain removal model to obtain a restored image after the raindrops are removed; the construction and training process of the rain removal model includes the following steps: Step 1: extract features from the input raindrop image to obtain the potential feature F0; Step 2: Use the FreqSSM module to perform multi-domain interactive processing on the latent feature F0 and integrate the information of different domains; The FreqSSM module consists of three branches: space branch, frequency band branch and Fourier branch. The space branch uses the state space model to process the potential features and extract the details and spatial correlation of the raindrop image. The frequency band branch uses discrete wavelet packet transform to decompose the potential features into different frequency sub-bands, and uses the frequency dimension sequence modeling method to rearrange the low-resolution features obtained after decomposition in the order from low frequency to high frequency, and scans them in the frequency dimension. The Fourier branch is responsible for global degradation modeling and converts the potential features to the frequency domain through fast Fourier transform. In addition, after downsampling the raindrop image, the attention module is used to extract the rain streak information, which is bypassed and fused with the main information stream output by the FreqSSM module to obtain the fusion feature to enhance the image deraining effect; Step 3, fusing the fused features with the raindrop image after passing through a restoration module composed of a convolutional layer to obtain a final restored image; Step 4: Determine the loss function to optimize the deraining model. The total loss function includes spatial domain loss and frequency domain loss function, so that the deraining model can reduce the error at the pixel level and improve the quality of the restored image at the frequency level.

2. According to the state space model based multi-domain interactive image deraining method of claim 1, it is characterized in that: Step 1 specifically includes: The raindrop image is subjected to feature extraction through convolution operation to obtain the potential feature F0: F0=Conv(I in ); Where Conv represents the convolution operation.

3. The multi-domain interactive image deraining method based on state space model according to claim 1, characterized in that: The FreqSSM module is used to perform multi-domain interactive processing on potential features and integrate information from different domains, specifically including: The spatial branch performs layer normalization on the potential feature F0 to obtain the feature map F LN , and then processed by two parallel sub-branches; in the first sub-branch, the feature map F LN Through the activation function, in the second sub-branch, the feature map F LN After convolution, the feature map is processed using the Mamba scanning mechanism, and finally the outputs of the two parallel sub-branches are element-wise multiplied to obtain the output feature F of the spatial branch. spatial : F LN =LN(F0); F spatial =Mamba(conv 1×1 (F LN ))⊙SiLU(F LN ); In the formula, LN(·) represents layer normalization, conv 1×1 represents 1×1 convolution, ⊙ represents element-wise multiplication, SiLU(·) is the activation function; Mamba(·) represents the state space model, which can model sequence data through the selective scanning mechanism; Frequency band branch: The feature map F LN Through k-layer discrete wavelet packet transform, it is decomposed into sub-bands of different frequencies, and the sub-bands are rearranged in order from low frequency to high frequency, processed by the frequency dimension sequence modeling method, and the obtained feature map is restored to the spatial domain through k-layer wavelet packet inverse transform to obtain the output feature F of the frequency band branch band : F band =IDWT(FreqScan(DWT(F LN )))⊙SiLU(F LN ); In the formula, DWT represents wavelet packet transform, IDWT represents inverse wavelet packet transform, and FreqScan represents the frequency dimension sequence modeling method; Fourier branch: Perform fast Fourier transform on the potential feature F0, and process the obtained amplitude spectrum and phase spectrum through the convolution layer respectively, and then convert the processed frequency domain features back to the spatial domain through inverse Fourier transform to obtain the output feature F of the Fourier branch fourier : In the formula, represents the discrete Fourier transform, represents the inverse Fourier transform, ConvBlock(·) represents a 1×1 convolution and activation function sequence; represent the amplitude spectrum and phase spectrum respectively, F P represents the phase spectrum processed by the convolutional network, F A Represents the amplitude spectrum processed by the convolutional network; Then, the output features of the spatial branch, frequency band branch, and Fourier branch of the FreqSSM module are concatenated, and the features are fused through the convolution layer to obtain the output of the FreqSSM module.

4. The multi-domain interactive image deraining method based on state space model according to claim 1, characterized in that: After downsampling the raindrop image, the attention module is used to extract the rain streak information, and the rain streak information is bypassed and fused with the main information stream output by the FreqSSM module to obtain the fusion feature, which specifically includes: Downsample the raindrop image and use an attention module to identify the pattern and distribution of raindrops in the downsampled raindrop image and generate an attention map that highlights the most likely locations of raindrops in the downsampled raindrop image. Fusion of the attention map with the backbone information flow: element-wise multiplication and summation. M attn =Mamba(conv 1×1 (I in )); F′=F⊙M atten +F; Where Mamba(·) represents the state space model; M attn Indicates the intermediate variable; I in represents the input image; F represents the backbone information flow; F′ represents the backbone information flow of the fused attention map.

5. The multi-domain interactive image deraining method based on state space model according to claim 1, characterized in that: The step of fusing the fused features with the raindrop image after passing through a restoration module composed of a convolutional layer to obtain a final restored image specifically includes: The fused features are sent to multiple convolutional layers of the restoration module, and the convolutional layers of the restoration module contain activation functions; the fused features after the restoration module are jump-connected with the original raindrop image, and the final restored image I is obtained through the convolutional layer. restorsded .

6. The multi-domain interactive image deraining method based on state space model according to claim 1, characterized in that: The spatial domain loss evaluates the quality of the restored image by calculating the pixel-level difference between the restored image and the labeled rain-free image. Specifically, the spatial domain loss adopts the mean absolute error; The frequency domain loss includes the loss calculated for the amplitude spectrum and the phase spectrum after Fourier transformation respectively; The total loss function l total is the sum of spatial domain loss and frequency domain loss: L spa =||Y out -X gt ||1; L total =L spa +αL amp +βL pha ; Among them, L spa represents the spatial domain loss, L amp represents the amplitude loss, l pha represents the frequency domain phase loss, α and β are weight parameters; ‖·‖1 represents the 1-norm.

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