An underwater polarized image restoration method based on physical and data double driving

Abstract

The application discloses a kind of underwater polarization image restoration methods based on physical and data double drive, belong to image processing technical field, including the following steps: S1, construct underwater polarization dataset by underwater imaging experiment platform;S2, according to the Stokes vector of underwater polarization image, establish target light model;S3, construct PCUNet network, and training is carried out.The application adopts the above-mentioned underwater polarization image restoration method based on physical and data double drive, for the problem of image noise amplification in calculation process, by constraint model and parameter merging, the target light model is further simplified.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an underwater polarization image restoration method based on both physical and data-driven approaches. Background Technology

[0002] Underwater optical imaging technology is a core technology supporting marine resource development and ecological protection, providing fundamental support for deep-sea exploration, environmental monitoring, and equipment development. However, due to the light absorption characteristics of water and the scattering effect of suspended objects, underwater images generally suffer from color cast and blurring, making it difficult for traditional imaging methods to accurately extract information, directly affecting underwater target identification and operational efficiency.

[0003] Underwater polarization imaging provides multi-dimensional polarization information. By utilizing the difference in polarization characteristics between background scattered light and target reflected light in the water, it can effectively suppress backscattering interference and improve the contrast of underwater targets, providing an effective way to improve the performance of underwater vision tasks. Existing methods improve underwater imaging by introducing the angle of polarization (AoP), but due to the influence of water scattering, AoP images suffer from significant noise interference, which limits the quality of image restoration. Furthermore, the increased model complexity restricts practical applications. Therefore, to achieve reliable underwater polarization imaging, it is necessary to focus on solving key problems such as the stability of parameter estimation under scattering interference, improving computational efficiency, and effectively extracting polarization information. Effectively solving these problems will directly affect the practical application of this technology in underwater exploration and other scenarios. Summary of the Invention

[0004] The purpose of this invention is to provide an underwater polarization image restoration method based on both physical and data-driven approaches to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, this invention provides an underwater polarization image restoration method based on both physical and data-driven approaches, comprising the following steps:

[0006] S1. Construct an underwater polarization dataset using an underwater imaging experimental platform;

[0007] S2. Establish the target light model based on the Stokes vector of the underwater polarization image;

[0008] S3. Construct the PCUNet network and train it.

[0009] Preferably, S1 includes:

[0010] S11. Construct an underwater imaging experimental platform;

[0011] S12. Select targets with different polarization characteristics as experimental objects and prepare suspensions. Adjust the concentration of the suspensions to simulate water environments with different degrees of attenuation.

[0012] S13. Use an underwater imaging experimental platform to obtain target polarization images at three angles: 0°, 60°, and 120° in water environments with different turbidity.

[0013] Preferably, the underwater imaging experimental platform includes an experimental container, an imaging module, a light source module, a water quality monitoring module, and a target. The inner wall of the experimental container is covered with a black matte plate, and water is placed inside the experimental container. The imaging module, the light source module, and the target sample are arranged sequentially inside the experimental container.

[0014] Preferably, the experimental container is a water tank; the imaging module is a color polarization camera, which is encapsulated in a waterproof sealed chamber and installed inside the experimental container; the light source module is a polarization-modulated white LED; and the water quality monitoring module is a dual-beam ratio turbidimeter.

[0015] Preferably, S2 includes:

[0016] S21. Based on the mathematical definitions of polarization degree DoP and polarization angle AoP, establish a right-angled triangle constraint model for polarization information;

[0017] S22. By using the right-angled triangle constraint model, AoP information is introduced into the underwater polarization imaging model to obtain an equation containing the target light S and to obtain the solution of S.

[0018] S23. Utilize angular relationships to perform model transformation and merge unknown parameters to obtain the final target light model.

[0019] Preferably, S21 includes:

[0020] The polarization state of an underwater polarization image is represented by Stokes vectors I, Q, and U. The formulas for Stokes vectors I, Q, and U are as follows:

[0021]

[0022] Among them, I0, I 60 and I 120 Images representing polarization angles of 0°, 60°, and 120°, respectively;

[0023] The expressions for obtaining the polarization angle θ and degree of polarization P using the Stokes vector are as follows:

[0024]

[0025] Where AoP represents the polarization angle and DoP represents the degree of polarization;

[0026] Based on the definitions of θ and P, we derive:

[0027] (PI) 2 =Q 2+U 2 ;

[0028]

[0029] Based on the properties of right triangles, a right triangle constraint model for polarization information is constructed as follows:

[0030]

[0031] Preferably, S22 includes:

[0032] We obtain two equations that include the polarization degree DoP and polarization angle AoP of the background light and the target light, respectively:

[0033]

[0034] Among them, Q B and U B The Stokes vector representing the background light, P B and θ B Q represents the degree of polarization and polarization angle of the background light, respectively. S and U S P represents the Stokes vector of the target light. S and θ S Indicates the degree of polarization and polarization angle of the target light;

[0035] Based on the above formula, we get:

[0036]

[0037] Preferably, S23 includes:

[0038] The model of the target light S is simplified using the sum of trigonometric functions and the formula for angles as follows:

[0039]

[0040] Among them, P S θ B and θ S All are unknown parameters, θ I Indicates the polarization angle of underwater image I;

[0041] All unknown parameters in the target light model are merged into a single parameter S. dif This further simplifies the model to:

[0042] S = PIS dif ;

[0043] S dif The expression is as follows:

[0044]

[0045] Preferably, S3 includes:

[0046] S31. Construct a PCUNet network based on the U-shaped ConvNeXt architecture; the PCUNet network includes an encoder, an intermediate layer, and a decoder;

[0047] S32. During model optimization, a composite loss function containing multiple loss functions is used for parameter updates; the loss function combination includes L1 loss, SSIM loss, and perceptual loss.

[0048] S33. Train the network using an underwater polarization dataset.

[0049] Preferably, in step S32, the formula for the L1 loss function is as follows:

[0050]

[0051] Where L1 represents L1 loss, and N is the number of pixels. The network outputs the calculated result, where S is the corresponding label image in the clean water environment;

[0052] The SSIM loss function is expressed as follows:

[0053]

[0054] in, express The SSIM value between L and S, L SSIM Indicates SSIM loss. and μ S for and the mean of S, and σ S for and the standard deviation of S, for The covariance of S, C1 and C2 are small constants introduced for stability;

[0055] The formula for the perceptual loss function is as follows:

[0056]

[0057] Among them, L Perceptual φ() represents the perceptual loss, and φ() represents the output from the start layer to the conv2_1 layer in VGG16.

[0058] By weighting and combining the L1 loss, SSIM loss, and perception loss, we obtain the composite loss function as follows:

[0059] Ltotal =L1+λ1L SSIM +λ2L Perceptual ;

[0060] Among them, L total Let λ1 represent the total loss of the composite loss, and λ2 represent the weight ratios of the SSIM loss and the perception loss in the total loss, respectively. λ1 = L1 / L SSIM λ2=L1 / L Perceptual .

[0061] Therefore, the underwater polarization image restoration method based on both physical and data-driven approaches described above has the following advantages:

[0062] (1) To address the problem of polarization information utilization, a target light model based on polarization right-angled triangle constraint is proposed. Through theoretical derivation, AoP information is effectively integrated into the underwater polarization imaging model, while simplifying model parameters to reduce computational complexity. To improve image restoration quality, a PCUNet network structure is designed, which improves the utilization rate of underwater polarization information through feature extraction and recombination mechanisms. Combined with the guidance of the physical model, the task of underwater polarization image sharpening is achieved.

[0063] (2) The PCUNet network not only achieves effective extraction of polarization features, but also further enhances image quality through feature recombination.

[0064] (3) In order to make full use of polarization information, this invention establishes a constraint model of a right triangle of polarization information based on the mathematical definitions of DoP and AoP, and establishes a new underwater polarization imaging model by combining the Stokes vector with DoP and AoP through geometric properties, and obtains the solution of the target light; in order to address the problem of image noise amplification during the calculation process, the target light model is further simplified by merging the constraint model and parameters.

[0065] (4) Polarization imaging technology can capture multi-dimensional polarization information features during underwater imaging, providing effective support for target feature reconstruction. This invention constructs a PCUNet neural network architecture, which realizes the deep extraction and reconstruction optimization of image features. In order to improve the physical interpretability of the algorithm model, the established target light model and polarization feature parameters are integrated into the PCUNet framework to form a polarization image restoration method driven by physical data, which effectively improves the imaging quality of targets in underwater turbid environments.

[0066] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0067] Figure 1 This is a flowchart of an underwater polarization image restoration method based on dual physical and data-driven approaches according to an embodiment of the present invention;

[0068] Figure 2 This is a schematic diagram of the polarization information triangle constraint according to an embodiment of the present invention;

[0069] Figure 3 This is a diagram of the PCUNet network structure according to an embodiment of the present invention;

[0070] Figure 4 This is a comparison chart of experimental results from an embodiment of the present invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0072] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0073] Example

[0074] like Figure 1 As shown, this invention provides an underwater polarization image restoration method based on both physical and data-driven approaches, comprising the following steps:

[0075] S1. Construct an underwater polarization dataset.

[0076] Specifically, step S1 includes:

[0077] S11. Construct an underwater imaging experimental platform. The platform includes an experimental container, an imaging module, a light source module, a water quality monitoring module, and a target. The inner wall of the experimental container is covered with a matte black panel to eliminate external stray light interference. Water is placed inside the container. The imaging module, light source module, and target are sequentially arranged within the container. In this embodiment, the experimental container is a water tank with dimensions of 100cm × 50cm × 50cm. The imaging module uses a color polarization camera with a resolution of 2592 × 1944. This device is encapsulated in a waterproof sealed chamber and installed inside the experimental container, capable of simultaneously acquiring JPG format images at three polarization angles of 0°, 60°, and 120°. The light source module uses a polarization-modulated white LED with a color temperature of 6500-7500K. The water quality monitoring module is equipped with a dual-beam ratio turbidimeter conforming to the HJ1075-2019 standard to record water turbidity data under conditions where different amounts of turbid liquid have been added.

[0078] S12. Targets with different polarization characteristics were selected as experimental subjects, and a suspension was prepared by mixing milk and sodium copper chlorophyll. The concentration of the mixture was adjusted to simulate water environments with different degrees of attenuation. Polarization characteristics include polarization, color, and texture.

[0079] S13. Use an underwater polarization imaging platform to obtain target polarization images at three angles: 0°, 60°, and 120° in water environments with different turbidity.

[0080] S2. Establish the target light model.

[0081] Specifically, step S2 includes:

[0082] S21. Based on the mathematical definitions of polarization degree DoP and polarization angle AoP, establish a right-angled triangle constraint model for polarization information.

[0083] Specifically, step S21 includes:

[0084] The polarization state of an underwater polarization image can be represented by Stokes vectors I, Q, and U:

[0085]

[0086] Among them, I0, I 60 and I 120 Images representing polarization angles of 0°, 60°, and 120°, respectively.

[0087] The polarization angle θ and the degree of polarization P can be calculated from the Stokes vector using the following formula:

[0088]

[0089] Based on the definitions of θ and P, we derive:

[0090] (PI) 2 =Q 2 +U 2 ;

[0091]

[0092] By the definition of a right triangle, the Stokes vectors θ and P satisfy the constraints of a right triangle with legs Q and U, hypotenuse PI, and an angle of 2θ between Q and PI, as shown below. Figure 2 As shown.

[0093] Using the properties of right triangles, we can obtain the following relationship between the Stokes vector and θ and P, thus obtaining the right triangle constraint model for polarization information as follows:

[0094]

[0095] S22. By using the right-angled triangle constraint model, AoP information is introduced into the underwater polarization imaging model to obtain an equation containing the target light S and to solve for S.

[0096] In this embodiment, step S22 includes:

[0097] We obtain two equations that include the polarization degree DoP and polarization angle AoP of the background light and the target light, respectively:

[0098]

[0099] Among them, Q B and U B The Stokes vector representing the background light, P B and θ B Q represents the degree of polarization and polarization angle of the background light, respectively. S and U S P represents the Stokes vector of the target light. S and θ S Indicates the degree of polarization and polarization angle of the target light;

[0100] Based on the above formula, we get:

[0101]

[0102] S23. Utilize angular relationships to perform model transformation and merge unknown parameters to obtain the final target light model.

[0103] In this embodiment, step S23 includes:

[0104] To reduce excessive computational errors and simplify the model, the final model of the target light S can be obtained using the sum-of-angle formulas of trigonometric functions. The unknown parameters include P. S θ B and θ S .

[0105]

[0106] Where, θ I Indicates the polarization angle of underwater image I;

[0107] Even with computational simplifications, the model incorporating polarization angle information still contains multiple unknown parameters. Therefore, all unknown parameters in the model are merged into a single parameter S. dif This further simplifies the model to:

[0108] S = PIS dif ;

[0109] S dif The expression is as follows:

[0110]

[0111] It can be seen that S dif It is an intermediate physical quantity in which the numerator contains information on light intensity and background light polarization angle, and the denominator contains information on target light polarization and background light polarization angle.

[0112] S3. Construct a PCUNet network based on the U-shaped ConvNeXt architecture and train it.

[0113] In this embodiment, step S3 includes:

[0114] S31. Given the powerful capabilities of neural networks in feature extraction and feature recombination, constructing a system such as... Figure 3 The U-shaped PCUNet network based on the ConvNeXt v2 Block shown consists of an encoder, intermediate layers, and a decoder. The encoder input receives a 9-channel feature tensor as initial data, and the decoder inputs a 3-channel feature tensor corresponding to the polarization information PI, ultimately outputting a 3-channel underwater reconstruction image.

[0115] The overall architecture of the PCUNet network is based on U-Net and the ConvUNeXt bottleneck structure. The encoder consists of multiple downsampling blocks, with the basic convolutional module being ConvNeXt v2Block. The first layer uses a Down(4x)-CB×N structure, and subsequent downsampling blocks use an LN-Down(2x)-CB×N structure for multi-scale feature extraction. Here, N represents the number of CB blocks, set to [3,3,9,3] in the encoder stage. The connection between the encoder and decoder uses an intermediate layer composed of Conv1(1×1)-CB×N to fuse image features; this intermediate layer has only one CB block. The decoder consists of multiple upsampling blocks. The first upsampling block uses a Conv(1×1)-LN-Up(2x)-Conv(1×1)-CB×N structure, and subsequent upsampling blocks use an LN-Up(2 / 4x)-Conv(1×1)-CB×N configuration. The decoder stage always has only one CB block. Corresponding to the first layer of the encoder is the output layer at the end of the network, which is upsampled by 4 times. This layer, while receiving the output features from the previous layer, integrates the initial input data and polarization imaging physical model parameters through residual connections, enhancing the feature reconstruction capability. To improve network performance, a CGA module containing spatial attention, channel attention, and pixel attention mechanisms is embedded in the skip connections. Skip connections effectively improve the stability and consistency of the network, while the CGA module further enhances the network's ability to capture diverse features, thereby improving the reconstruction effect.

[0116] The network's first-layer input consists of a 9-channel tensor composed of color polarization images at three angles: 0°, 60°, and 120°. In the output layer, polarization information (PI) is incorporated into the network's processing based on skip connections, ultimately guiding the network to output a 3-channel color reconstructed image. Table 1 shows the input and output variations of tensors in each module of the PCUNet network on the main branch. Here, C×H×W represents the number of channels, height, and width of the tensor.

[0117] Table 1. Changes in the Input and Output Shapes of Network Modules

[0118]

[0119] S32. To improve the network's predictive ability, a composite loss function containing multiple loss functions is used for parameter updates during model optimization, thereby guiding the network's learning. The loss function combination includes L1 loss, SSIM loss, and perceptual loss.

[0120] Compared to MSE loss, L1 loss avoids getting trapped in local optima and penalizes large error values ​​less during gradient descent, thus improving the stability and effectiveness of optimization. The formula for the L1 loss function is as follows:

[0121]

[0122] Where L1 represents L1 loss, also known as mean absolute error, and N is the number of pixels. The result calculated by the network outputs S, where S is the corresponding label image in the clean water environment and also the target light image.

[0123] SSIM loss effectively captures the structural information of an image, focusing on preserving image brightness, contrast, and structure. Introducing SSIM loss helps improve the visual quality of the restored image, ensuring perceptual consistency between the restored result and the original image. The formula for the SSIM loss function is as follows:

[0124]

[0125] in, express The SSIM value between L and S. SSIM is a structural similarity index, a commonly used and classic metric for measuring the similarity between two images. SSIM Indicates SSIM loss. and μ S for and the mean of S, and σ S for and the standard deviation of S, for The covariance of S, C1 and C2 are small constants introduced for stability.

[0126] To further improve the perceptual quality of the image, a perceptual loss is introduced. This loss function uses the output of the conv2_1 layer in the VGG16 network as a shallow feature extractor and calculates the L1 loss between the restored image and the reference image in the shallow feature space. This approach allows the network to focus more on preserving the high-level semantic information and detailed features of the image. The formula for the perceptual loss function is as follows:

[0127]

[0128] Among them, L Perceptual φ() represents the perceptual loss, and φ() represents the output from the start layer to the conv2_1 layer in VGG16.

[0129] Ultimately, the network was trained using a weighted combined loss, integrating the advantages of L1 loss, SSIM loss, and perceptual loss. The weight parameters adjusted the contribution of each loss to the optimization objective, thus achieving a good balance between restoration accuracy and perceptual quality. The resulting composite loss function is expressed as follows:

[0130] L total=L1+λ1L SSIM +λ2L Perceptual ;

[0131] Among them, L total Let λ1 represent the total loss of the composite loss, and λ2 represent the weight ratios of the SSIM loss and the perception loss in the total loss, respectively. λ1 = L1 / L SSIM λ2=L1 / L Perceptual Since the L1 loss, SSIM loss, and perceptual loss have different scales, this dynamic adjustment method aligns the scales of the SSIM loss and perceptual loss to the same level as the L1 loss, ensuring stability during training and the effectiveness of the loss function.

[0132] S33. Train the network using an underwater polarization dataset.

[0133] The network training set contains 160 sets of polarization image samples. Each set of images is pre-processed and cropped to a fixed size of 512×512 pixels with a cropping stride of 512 pixels. The network model adopts a multi-channel input structure, using a 9-channel tensor composed of images from three polarization angles as input, and outputting a 3-channel tensor result after processing. The training process was completed on an Nvidia RTX A6000 graphics card using the PyTorch framework, for a total of 200 epochs. The optimizer used was Adamw, with an initial learning rate of 0.0005, and cosine annealing was used to adjust the learning rate. The batch size was set to 16.

[0134] Reference Figure 4 To evaluate the effectiveness of this invention, the performance of PCUNet, the image enhancement method CLAHE, the imaging model-based method UDCP, two underwater polarization imaging methods APD and UDPLC, and two deep learning methods Semi-UIR and CWR on SSIM, PSNR, PCQI, LPIPS, UIQM, and UCIQE metrics was assessed using an underwater polarization dataset. The results are shown in Table 2.

[0135] Table 2 Evaluation Indicators of Experimental Results

[0136]

[0137] Comparative experimental results with other methods show that the present invention not only outperforms other methods in polarization information processing performance, but also demonstrates competitive advantages in edge detail preservation and contrast enhancement, providing a new methodological path and potential technological development direction for underwater polarization imaging technology.

[0138] Therefore, the present invention adopts the above-mentioned underwater polarization image restoration method based on physical and data dual-drive, establishes a polarization information right triangle constraint model through the physical definition of polarization information, introduces AoP into the underwater polarization imaging model, and combines DoP and AoP to realize the physical modeling of target light.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for underwater polarization image restoration based on dual physical and data-driven approaches, characterized in that, Includes the following steps: S1. Construct an underwater polarization dataset using an underwater imaging experimental platform; S2. Establish the target light model based on the Stokes vector of the underwater polarization image; S3. Construct the PCUNet network and train it; S2 includes: S21. Based on the mathematical definitions of polarization degree DoP and polarization angle AoP, establish a right-angled triangle constraint model for polarization information; S22. By using the right-angled triangle constraint model, AoP information is introduced into the underwater polarization imaging model to obtain an equation containing the target light S and to obtain the solution of S. S23. Use the angular relationship to perform model transformation and merge the unknown parameters to obtain the final target light model; S21 includes: The polarization state of an underwater polarization image is represented by Stokes vectors I, Q, and U. The formulas for Stokes vectors I, Q, and U are as follows: Among them, I0, I 60 and I 120 Images representing polarization angles of 0°, 60°, and 120°, respectively; The expressions for obtaining the polarization angle θ and degree of polarization P using the Stokes vector are as follows: Where AoP represents the polarization angle and DoP represents the degree of polarization; Based on the definitions of θ and P, we derive: PI) 2 *Q 2 +U 2 ; Based on the properties of right triangles, a right triangle constraint model for polarization information is constructed as follows:

2. The underwater polarization image restoration method based on dual physical and data-driven approaches according to claim 1, characterized in that, S1 includes: S11. Construct an underwater imaging experimental platform; S12. Select targets with different polarization characteristics as experimental objects and prepare suspensions. Adjust the concentration of the suspensions to simulate water environments with different degrees of decay. S13. Use an underwater imaging experimental platform to obtain target polarization images at three angles: 0°, 60°, and 120° in water environments with different turbidity.

3. The underwater polarization image restoration method based on dual physical and data driving as described in claim 2, characterized in that: The underwater imaging experimental platform includes an experimental container, an imaging module, a light source module, a water quality monitoring module, and a target. The inner wall of the experimental container is covered with a matte black plate, and water is placed inside the experimental container. The imaging module, the light source module, and the target sample are arranged sequentially inside the experimental container.

4. The underwater polarization image restoration method based on dual physical and data driving as described in claim 3, characterized in that: The experimental container is a water tank; the imaging module uses a color polarization camera, which is encapsulated in a waterproof sealed chamber and installed inside the experimental container; the light source module uses a polarization-modulated white LED; and the water quality monitoring module uses a dual-beam ratio turbidimeter.

5. The underwater polarization image restoration method based on dual physical and data driving as described in claim 2, characterized in that, S22 includes: We obtain two equations that include the polarization degree DoP and polarization angle AoP of the background light and the target light, respectively: Among them, Q B and U B The Stokes vector representing the background light, P B and θ B Q represents the degree of polarization and polarization angle of the background light, respectively. S and U S P represents the Stokes vector of the target light. S and θ S Indicates the degree of polarization and polarization angle of the target light; Based on the above formula, we get:

6. The underwater polarization image restoration method based on dual physical and data driving as described in claim 5, characterized in that, S23 includes: The model of the target light S is simplified using the sum of trigonometric functions and the formula for angles as follows: Among them, P S θ B and θ S All are unknown parameters, θ I Indicates the polarization angle of underwater image I; All unknown parameters in the target light model are merged into a single parameter S. dif This further simplifies the model to: S=PIS dif ; S dif The expression is as follows:

7. The underwater polarization image restoration method based on dual physical and data driving as described in claim 6, characterized in that, S3 includes: S31. Construct a PCUNet network based on the U-shaped ConvNeXt architecture; the PCUNet network includes an encoder, an intermediate layer, and a decoder; S32. During model optimization, a composite loss function containing multiple loss functions is used for parameter updates; the loss function combination includes L1 loss, SSIM loss, and perceptual loss. S33. Train the network using an underwater polarization dataset.

8. The underwater polarization image restoration method based on dual physical and data driving as described in claim 7, characterized in that, In S32, the formula for the L1 loss function is as follows: Where L1 represents L1 loss, and N is the number of pixels. The network outputs the calculated result, where S is the corresponding label image in the clean water environment; The SSIM loss function is expressed as follows: in, express The SSIM value between L and S, L SSIM Indicates SSIM loss, and μ S for and the mean of S, and σ S for and the standard deviation of S, for The covariance of S, C1 and C2 are small constants introduced for stability; The formula for the perceptual loss function is as follows: Among them, L Perceptual φ() represents the perceptual loss, and φ() represents the output from the start layer to the conv2_1 layer in VGG16. By weighting and combining the L1 loss, SSIM loss, and perception loss, we obtain the composite loss function as follows: L total =L1+λ1L SSIM +λ2L Perceptual ; Among them, L total Let λ1 represent the total loss of the composite loss, and λ2 represent the weight ratios of the SSIM loss and the perception loss in the total loss, respectively. λ1 = L1 / L SSIM λ2=L1 / L Perceptual .

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