Underwater image restoration method based on underwater polarization imaging and image layering

Abstract

The invention discloses an underwater image restoration method based on underwater polarization imaging and image layering, and belongs to the field of underwater image restoration, and the method comprises the steps: firstly, obtaining underwater polarization images of a target at three angles, and representing the underwater polarization images through a Stokes vector; dividing the underwater original image into a target layer, a scattering layer and a noise layer, and completing model reconstruction by combining an underwater polarization imaging model; thirdly, three-layer prior is introduced on the basis of the underwater polarization imaging model to obtain the value of a scattering layer, an area with the gradient being zero is recognized in the underwater image, the pixel point with the maximum brightness in the area is extracted, and the average value of the pixel points is calculated to serve as the estimated value of global background light; and finally substituting the values of the scattered light and the global background light obtained in the underwater polarization imaging model into the underwater polarization imaging model to restore an underwater image. According to the method, the underwater polarization imaging model and the image layering idea are combined, the polarization-based underwater imaging model is reconstructed, and finally a clear underwater image is restored.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater image restoration, and in particular to an underwater image restoration method based on underwater polarization imaging and image stratification. Background Art

[0002] In fields such as military exploration and marine archaeology, obtaining high-quality underwater images is crucial. The main challenges facing underwater imaging systems stem from the selective absorption of light by water and the multiple scattering effect caused by suspended particles. These physical processes lead to severe quality degradation of the acquired images. Degraded underwater images limit their application in high-level vision such as target segmentation, image recognition, and scene reconstruction. Traditional underwater image enhancement methods usually rely on physical models or image priors, but these methods have poor adaptability to different water environments and are prone to introducing color casts or artifacts. Moreover, the enhancement effect of this method depends on the accuracy of the prior assumptions. Once the assumptions are not true, the effect deteriorates.

[0003] Underwater polarization imaging technology, by capturing multidimensional polarization information, can effectively suppress backscatter noise caused by water, thereby enhancing the imaging contrast of underwater targets. Compared with traditional imaging methods, this technology exhibits unique advantages in complex water environments, improving image quality and clarity, particularly in low-visibility or highly turbid waters, significantly enhancing target discernibility. Currently, the main underwater polarization imaging technologies include polarization difference technology and Stokes vector-based methods. Prior underwater polarization imaging technologies often enhance image quality by introducing polarization angles. However, due to the complex scattering effects in water, AoP images are often subject to significant noise interference, which limits the accuracy of image restoration. Methods based on physical models often introduce physical priors, the accuracy of which affects the final restoration results. The main challenges facing underwater image restoration are: obtaining accurate prior information and effectively extracting polarization information. Summary of the Invention

[0004] The purpose of the present invention is to provide an underwater image restoration method based on underwater polarization imaging and image stratification. By introducing texture prior, smoothness prior and structure prior, the underwater image is divided into a scattering layer, a target layer and a noise layer. An underwater polarization reconstruction model guided by a tomographic model and polarization characteristics is established to realize the estimation of underwater scattered light.

[0005] To achieve the above objectives, the present invention provides an underwater image restoration method based on underwater polarization imaging and image layering, comprising the following steps:

[0006] Step 1: Underwater polarization image acquisition: Obtain underwater polarization images of the target at three angles: 0 degrees, 60 degrees, and 120 degrees, and use Stokes vector S = (I, Q, U, V) to represent I0, I 60 , I120 ;

[0007] Step 2: Establish underwater polarization imaging model: According to the Stokes vector, the underwater original image I is converted into I0, I 60 , I 120 Indicates that the underwater original image I is divided into the target layer, the scattering layer, and the noise layer, and the underwater polarization imaging model is combined to complete the reconstruction of the underwater polarization imaging model;

[0008] Step 3: Parameter estimation of underwater polarization imaging model: Based on the underwater polarization imaging model, a three-layer prior is introduced to obtain the value of the scattering layer. The area with zero gradient is identified in the underwater original image. The maximum brightness pixel point in the identified area is extracted. The average value of the extracted pixel point is calculated as the global background light G. ∞ estimated value of;

[0009] Step 4: Underwater image restoration: The scattered light G0 and G 60 , G 120 and global background light G ∞ The value of is substituted into the underwater polarization imaging model, and the underwater image is finally restored.

[0010] Preferably, in step 1, when a beam of incident light with a Stokes vector of S = (I, Q, U, V) passes through a polarizer with a polarization angle of θ, the mathematical expression of the polarized image intensity is derived based on the transformation relationship between the Stokes vector and the Mueller matrix:

[0011]

[0012] According to formula (1), when light with Stokes vector S = (I, Q, U, V) passes through a polarizer with the orientations of the polarizer at 0°, 60°, and 120°, the polarization image intensity at the three angles is expressed as:

[0013]

[0014] Preferably, in step 2,

[0015] According to formula (2), the underwater original image I is composed of I0, I 60 , I 120 Expressed as:

[0016]

[0017] The background scattered light is expressed as:

[0018]

[0019] The original underwater image is rewritten into the following three parts:

[0020]

[0021] Where T is the transmittance and N is the noise floor;

[0022] Combining formula (3) and formula (5), the reconstructed underwater image imaging model is obtained as follows:

[0023]

[0024] Preferably, in step 3, the image gradient is preserved by minimizing the texture prior term ||▽F-▽I||1, where ▽ represents the gradient operator and F represents the texture details in the target layer;

[0025] The texture prior is modified to ||W°(▽F-▽I)||, where ° represents element-wise multiplication and the weight matrix W ij The (i,j)th element of is given by:

[0026]

[0027] Among them, I ij represents the (i, j)th element of the underwater original image, θ is a non-negative parameter. When θ = 0, all gradients are retained with equal importance.

[0028] Preferably, the scattering layer G is assumed to be smooth in space and the smoothness of G is calculated using the second-order Laplace operator by minimizing To enhance the spatial smoothness of G, where Δ represents the Laplace operator;

[0029] Apply a low-pass filter to I to obtain I s , then minimize To satisfy the constraints;

[0030] After introducing prior knowledge, the original image is decomposed into three components: texture prior, smoothness prior, and structure prior. The following cost function is constructed and minimized:

[0031]

[0032] Among them, α, β, and γ are parameters that control the relative importance of different terms;

[0033] Each intensity value in F and G is positive and less than or equal to the intensity value at the same position in the underwater original image I. The optimization problem is reformulated as:

[0034] min F,G,N = J(F,G,N) (9);

[0035] In formula (9), 0≤(F,G)≤I, where ≤ represents the element inequality between the two matrices;

[0036] The semi-quadratic optimization technique is used for optimization. First, the auxiliary variable Q is introduced, and the ▽F-▽I term is deleted from the texture prior term. Based on the model in formula (5), G is replaced by IFG, and the optimization problem is rewritten as:

[0037]

[0038] The penalty method is used to replace the constrained optimization problem in formula (10). First, the penalty function P(Q, F, N, μ) is defined as:

[0039]

[0040] Where μ is the penalty parameter of the equality constraint, μ>0; then the solution to the original problem in formula (11) is obtained by minimizing its penalty function P(Q, F, N, μ):

[0041]

[0042] The alternating direction multiplier method (ADMM) is used for optimization. ADMM transforms the complex joint optimization problem into a series of analyzable subproblems and iteratively solves the following subproblems until convergence, ultimately obtaining the global optimal solution. The formula is as follows:

[0043]

[0044] Here, k represents the iteration index.

[0045] Preferably, the solution process of the above sub-problems is as follows:

[0046] In the initialization step, given F k The estimated value of Q is updated as:

[0047]

[0048] The objective function in formula (14) is composed of the norm term and adjacent terms, the subscript 1 in formula (14) is the norm term, for W / μ k > 0, the closed-form solution of the problem in formula (14) is obtained by the following formula:

[0049]

[0050] Where S B (A) represents the element-wise soft threshold operator, where [S B (A)] ij =sign(A ij )×max(|A ij |-B ij ,0);S B(A) represents the form of formula (15);

[0051] According to formula (15) and Q in formula (13) k+1 and N k , update F; the sub-problem in formula (13) is rewritten as:

[0052]

[0053] Assuming circular boundary conditions, the convolution matrices Δ and ▽ are diagonalized using the Fast Fourier Transform (FFT), where X k =IN k 、Y k =IN k -I s , F and F -1 are the forward and reverse FFT operators, F * (·) represents the complex conjugate, F(1) is Fourier transform of a function, ° represents component multiplication;

[0054] Given Q k+1 and F k+1 , solve the following optimization problem:

[0055]

[0056] The penalty parameter μ is updated as:

[0057] μ k+1 =min{ρμ k ,μ max} (20);

[0058] In formula (20), ρ>1 is the user parameter used to penalize constraint violations, μ max Represents the sequence {μ max}, dynamically select the parameter sequence according to the difficulty of minimizing the penalty function in each iteration, and adaptively adjust {μ max};

[0059] The optimization variables Q, F, N, and μ are iteratively updated until convergence, and the convergence rate of the kth iteration is defined as:

[0060]

[0061] and run the iterations until the stopping criterion, ξ, is met k <10 -1 ; Where H represents the number of rows of image pixels and W represents the number of columns of image pixels;

[0062] Finally, from formula (5) we get:

[0063] G = IFN (22).

[0064] Preferably, G ∞ The calculation formula is:

[0065]

[0066] Therefore, the present invention adopts the above-mentioned underwater image restoration method based on underwater polarization imaging and image layering, which has the following beneficial effects:

[0067] 1. This paper proposes an underwater image modeling method based on polarization tomography. It introduces texture prior, smoothness prior, and structure prior, divides underwater images into scattering layer, target layer, and noise layer, and establishes an underwater polarization reconstruction model guided by the tomography model and polarization characteristics. It realizes the estimation of underwater scattered light, improves the clarity of underwater scenes, has better detail restoration capabilities, and exhibits stable descattering performance under different environmental conditions.

[0068] 2. The method proposed in the present invention transforms the three-layer problem into an optimal solution problem. The original problem is divided into multiple sub-problems through the alternating multiplier method. The global convergence is achieved by alternately fixing other variables and optimizing individual variables in sequence to obtain the optimal solution. Finally, the underwater image is restored by combining the polarization underwater tomography model.

[0069] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0071] Figure 2 This is a 0-degree underwater polarization diagram of an embodiment of the present invention;

[0072] Figure 3 This is a 60-degree underwater polarization diagram of an embodiment of the present invention;

[0073] Figure 4 This is a 120-degree underwater polarization diagram of an embodiment of the present invention;

[0074] Figure 5 Figure 2 shows the underwater polarization imaging restoration results of an embodiment of the present invention ((a) original image, (b) target layer, (c) scattering layer, and (d) noise layer);

[0075] Figure 6 This is a flowchart of underwater polarization imaging restoration according to an embodiment of the present invention;

[0076] Figure 7These are the restoration results in different scenarios of the embodiments of the present invention ((a) original image; (b) Semi-UIR; (c) CWR; (d) UDCP; (e) Ancuti; (f) Peng; (g) the method of the present invention). DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solutions and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention are further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, where the same or similar numbers throughout represent the same or similar elements or elements with the same or similar functions.

[0078] It should be noted that the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or server that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products or devices.

[0079] Like reference numerals and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it does not require further definition or explanation in subsequent drawings.

[0080] In the description of the present invention, it should be noted that the terms "upper", "lower", "inside", "outside", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, or are the orientations or positional relationships in which the inventive product is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they should not be understood as limiting the present invention.

[0081] In the description of the present invention, it should also be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," and "connected" should be understood broadly. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0082] Example

[0083] like Figure 1 As shown, the underwater image restoration method based on underwater polarization imaging and image stratification described in the present invention includes the following steps:

[0084] Step 1: Acquisition of underwater polarization images: Figure 2 、 Figure 3 、 Figure 4 As shown in the figure, underwater polarization images of the target at three angles of 0 degree, 60 degree and 120 degree are obtained, and Stokes vector S = (I, Q, U, V) is used to represent I0, I 60 , I 120 .

[0085] In underwater optical imaging, both scattered light and total light intensity exhibit partial polarization characteristics, which can be fully described by the Stokes vector. When a beam of incident light with a Stokes vector of S = (I, Q, U, V) passes through a polarizer with a polarization angle of θ, the mathematical expression for the polarized image intensity is derived based on the transformation relationship between the Stokes vector and the Mueller matrix:

[0086]

[0087] According to formula (1), when light with Stokes vector S = (I, Q, U, V) passes through a polarizer with the orientations of the polarizer at 0°, 60°, and 120°, the polarization image intensity at the three angles is expressed as:

[0088]

[0089] Step 2: Establish underwater polarization imaging model: According to the Stokes vector, the underwater original image I is converted into I0, I 60 , I 120 It means that the underwater original image I is divided into target layer, scattering layer and noise layer, and the underwater polarization imaging model is combined to complete the reconstruction of the underwater polarization imaging model.

[0090] According to formula (2), the underwater original image I is composed of I0, I 60 , I 120 It is expressed as follows:

[0091]

[0092] Background scattered light can also be expressed by formula (4):

[0093]

[0094] Noise often occurs in underwater images, so the original underwater image is rewritten into the following three parts:

[0095]

[0096] Where T is the transmittance and N is the noise floor.

[0097] Combining formula (3) and formula (5), the reconstructed underwater image imaging model is obtained as follows:

[0098]

[0099] Step 3: Parameter estimation of underwater polarization imaging model: Based on the underwater polarization imaging model, a three-layer prior is introduced to obtain the value of the scattering layer. The area with zero gradient is identified in the underwater original image. The maximum brightness pixel point in the identified area is extracted. The average value of the extracted pixel point is calculated as the global background light G. ∞ estimated value.

[0100] ① Scattered light estimation

[0101] The texture details F in the target layer should be similar to the texture details in the input underwater original image I. To enforce this constraint, the image gradient is preserved by minimizing the texture prior term ||▽F-▽I||1, where ▽ represents the gradient operator.

[0102] norm is used for texture prior because it is more robust and effectively preserves the texture similarity between F and I. In addition, weak details and strong details in I should have equal influence on the texture. Regions with low gradient magnitude should be retained more, while regions with strong magnitude should be retained less. To this end, in order to balance the overall magnitude, the texture prior term is modified to ||W°(▽F-▽I)||, where ° represents element-wise multiplication, and the weighting matrix W ij The (i,j)th element of is given by:

[0103]

[0104] Among them, I ij represents the (i, j)th element of the underwater original image. θ is a non-negative parameter. When θ = 0, all gradients are retained with equal importance. As θ increases, the texture prior better preserves local details in areas with low gradient magnitudes.

[0105] The multiple scattering effect in underwater scenes makes the scattered light in the captured image smooth in space. Therefore, assuming that the scattering layer G is also smooth in space, the second-order Laplacian operator is used to calculate the smoothness of G by minimizing To enhance the spatial smoothness of G, where Δ represents the Laplace operator.

[0106] While the texture layer F contains image details, the scattering layer G encodes large-scale variations corresponding to the underlying structure in the input image. Therefore, in addition to the smoothness constraint, G should also preserve the underlying structure in the input image. The low-frequency components of the image can preserve these underlying structures. Therefore, we first apply a low-pass filter to I to obtain I s , then minimize to satisfy the constraints.

[0107] After introducing prior knowledge, the original image is decomposed into three components: texture prior, smoothness prior, and structure prior. In addition, the energy of the noise component must be suppressed as much as possible. To achieve these goals simultaneously, the following cost function is constructed and minimized:

[0108]

[0109] Among them, α, β, and γ are parameters that control the relative importance of different items. This embodiment discusses the impact of these parameters on the scatter removal performance in experiments and evaluations.

[0110] In addition to minimizing J(F, G, N) in formula (8), the target layer F and the scattering layer G should also satisfy further constraints. First, each intensity value in F and G should be positive and less than or equal to the intensity value at the same position in the underwater original image I. Therefore, the optimization problem can be reformulated as:

[0111] min F,G,N = J(F,G,N) (9);

[0112] In formula (9), 0≤(F,G)≤I, where ≤ represents an element inequality between two matrices.

[0113] Since the cost function in formula (8) is regularized, and the semi-quadratic optimization technique is used to solve the optimization problem. First, the auxiliary variable Q is introduced, and the ▽F-▽I term is deleted from the texture prior term. Based on the model in formula (5), G is replaced by IFG, and the optimization problem is rewritten as:

[0114]

[0115] The penalty method is used to replace the constrained optimization problem in formula (10) to solve a series of unconstrained sub-problems. First, the penalty function P(Q, F, N, μ) is defined as:

[0116]

[0117] Where μ is the penalty parameter of the equality constraint, μ>0; as μ increases, the violation of the constraint will be punished more severely, thus forcing the constraint to be satisfied. Then, by minimizing its penalty function P(Q,F,N,μ), the solution of the original problem in formula (11) is obtained, where the value of μ is large enough:

[0118]

[0119] Since the joint optimization problem of the three variables in formula (12) is difficult to solve directly in practical applications, the alternating direction multiplier method (ADMM) is used for efficient optimization. The core idea of ​​this method is to decompose the original problem into multiple independent sub-optimization tasks, and achieve global convergence by alternately fixing other variables and optimizing individual variables in sequence. ADMM transforms the complex joint optimization problem into a series of analyzable sub-problems and iteratively solves the following sub-problem sequence until convergence, ultimately obtaining the global optimal solution, as shown in the following formula:

[0120]

[0121]

[0122] Here, k represents the iteration index.

[0123] The solution process of each sub-problem will be explained in detail below.

[0124] In the initialization step, given F k The estimated value of Q is updated as:

[0125]

[0126] The objective function in formula (14) is composed of the norm term and adjacent terms, for W / μ k > 0, the closed-form solution of the problem in formula (14) is obtained by the following formula:

[0127]

[0128] Where S B (A) represents the element-wise soft threshold operator, where [S B (A)] ij =sign(A ij )×max(|A ij |-B ij ,0);

[0129] According to formula (15) and Q in formula (13) k+1 and N k , update F; the sub-problem in formula (13) is rewritten as:

[0130]

[0131] Assuming circular boundary conditions, the convolution matrices Δ and ▽ are diagonalized using the Fast Fourier Transform (FFT), where X k =IN k 、Y k =IN k -I s , F and F -1 are the forward and reverse FFT operators, F * (·) represents the complex conjugate, F(1) is The Fourier transform of the function, in addition, ° represents the component multiplication. Since most of the terms can be calculated in advance, the Fourier domain calculation in formula (18) is significantly faster than directly solving (16), which involves the inversion of a large matrix.

[0132] Given Q k+1 and F k+1 , solve the following optimization problem:

[0133]

[0134]

[0135] The penalty parameter μ is updated as:

[0136] μ k+1 =min{ρμ k ,μ max} (20);

[0137] In formula (20), ρ>1 is the user parameter used to penalize constraint violations, μ max Represents the sequence {μ max}, and dynamically selects the parameter sequence according to the difficulty of minimizing the penalty function in each iteration, thereby achieving adaptive adjustment of {μ max} to achieve better convergence. However, it is found through experiments that the simple update in formula (20) can achieve good convergence.

[0138] The optimization variables Q, F, N, and μ are iteratively updated until convergence, and the convergence rate of the kth iteration is defined as:

[0139]

[0140] and run the iterations until the stopping criterion, ξ, is met k <10 -1 ; Where H represents the number of rows of image pixels and W represents the number of columns of image pixels.

[0141] Finally, from formula (5) we get:

[0142] G = IFN (22).

[0143] The present invention identifies the areas with zero gradient in the underwater image, extracts the maximum brightness pixels in these areas, and finally calculates the average value of these pixels as the background light G ∞ The corresponding calculation formula is:

[0144]

[0145] Step 4: Underwater image restoration: The scattered light G0 and G 60 , G 120 and global background light G ∞ The value of is substituted into the underwater polarization imaging model, and the underwater image is finally restored. The underwater polarization imaging restoration result is as follows: Figure 5 As shown in the flowchart of underwater polarization imaging algorithm, Figure 6 shown.

[0146] In order to evaluate the effectiveness of this method, different underwater scenes were selected from the dataset for verification. The restoration results in different scenes are shown in the figure below. Figure 7 shown.

[0147] In objective evaluation, four metrics were used to quantitatively assess the underwater image restoration algorithm: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Perceptual Color Image Quality Index (PCQI), and Underwater Color Image Quality Evaluation (UCIQE). Table 1 shows this.

[0148] Table 1 Evaluation table of indicators for restoration results of different methods on polarization datasets

[0149] Way PSNR SSIM PCQI UCIQE Semi-UIR 8.6675 0.2057 0.9982 26.8664 CWR 8.4651 0.2402 0.9980 23.4843 UDCP 11.4997 0.2223 0.9984 21.9558 Ancuti 8.3913 0.2475 0.9981 28.9003 Peng 7.4665 0.0970 0.9978 26.8596 OURS 12.3831 0.3056 0.9985 22.3402

[0150] Experimental results show that the descattering method based on polarization tomography proposed in this invention can significantly improve the clarity of underwater scenes, has good detail restoration capability, and exhibits stable descattering performance under different environmental conditions.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An underwater image restoration method based on underwater polarization imaging and image layering, characterized by: The following steps are involved: Step 1: Underwater polarization image acquisition: Obtain underwater polarization images of the target at three angles: 0 degrees, 60 degrees, and 120 degrees, and use Stokes vector S = (I, Q, U, V) to represent I0, I 60 , I 120 ; Step 2: Establish underwater polarization imaging model: According to the Stokes vector, the underwater original image I is converted into I0, I 60 , I 120 Indicates that the underwater original image I is divided into target layer, scattering layer, and noise layer, and the underwater polarization imaging model is combined to complete the reconstruction of the underwater polarization imaging model; Step 3: Parameter estimation of underwater polarization imaging model: Based on the underwater polarization imaging model, a three-layer prior is introduced to obtain the value of the scattering layer. The area with zero gradient is identified in the underwater original image. The maximum brightness pixel point in the identified area is extracted. The average value of the extracted pixel point is calculated as the global background light G. ∞ estimated value of; Step 4: Underwater image restoration: The scattered light G0 and G 60 , G 120 and global background light G ∞ The value of is substituted into the underwater polarization imaging model, and the underwater image is finally restored.

2. The underwater image restoration method based on underwater polarization imaging and image layering according to claim 1, characterized in that: In step 1, when a beam of incident light with a Stokes vector of S = (I, Q, U, V) passes through a polarizer with a polarization angle of θ, the mathematical expression for the polarized image intensity is derived based on the transformation relationship between the Stokes vector and the Mueller matrix: According to formula (1), when light with Stokes vector S = (I, Q, U, V) passes through a polarizer with the orientations of the polarizer at 0°, 60°, and 120°, the polarization image intensity at the three angles is expressed as:

3. The underwater image restoration method based on underwater polarization imaging and image layering according to claim 2, characterized in that: In step 2, According to formula (2), the underwater original image I is composed of I0, I 60 , I 120 Expressed as: The background scattered light is expressed as: The original underwater image is rewritten into the following three parts: Where T is the transmittance and N is the noise floor; Combining formula (3) and formula (5), the reconstructed underwater image imaging model is obtained as follows:

4. The underwater image restoration method based on underwater polarization imaging and image layering according to claim 3, characterized in that: In step 3, the image gradient is preserved by minimizing the texture prior term ||▽F-▽I||1, where ▽ represents the gradient operator and F represents the texture details in the target layer; The texture prior is modified to ||W°(▽F-▽I)||, where ° represents element-wise multiplication and the weight matrix W ij The (i,j)th element of is given by: Among them, I ij represents the (i, j)th element of the underwater original image, θ is a non-negative parameter. When θ = 0, all gradients are retained with equal importance.

5. The underwater image restoration method based on underwater polarization imaging and image layering according to claim 4, characterized in that: Assuming that the scattering layer G is smooth in space, the second-order Laplace operator is used to calculate the smoothness of G by minimizing To enhance the spatial smoothness of G, where Δ represents the Laplace operator; Apply a low-pass filter to I to obtain I s , then minimize To satisfy the constraints; After introducing prior knowledge, the original image is decomposed into three components: texture prior, smoothness prior, and structure prior. The following cost function is constructed and minimized: Among them, α, β, and γ are parameters that control the relative importance of different terms; Each intensity value in F and G is positive and less than or equal to the intensity value at the same position in the underwater original image I. The optimization problem is reformulated as: life F,G,N =J(F,G,N) (9); In formula (9), 0≤(F,G)≤I, where ≤ represents the element inequality between the two matrices; The semi-quadratic optimization technique is used for optimization. First, the auxiliary variable Q is introduced, and the ▽F-▽I term is deleted from the texture prior term. Based on the model in formula (5), G is replaced by IFG, and the optimization problem is rewritten as: The penalty method is used to replace the constrained optimization problem in formula (10). First, the penalty function P(Q, F, N, μ) is defined as: Where μ is the penalty parameter of the equality constraint, μ>0; then the solution to the original problem in formula (11) is obtained by minimizing its penalty function P(Q, F, N, μ): The alternating direction multiplier method (ADMM) is used for optimization. ADMM transforms the complex joint optimization problem into a series of analyzable subproblems and iteratively solves the following subproblems until convergence, ultimately obtaining the global optimal solution. The formula is as follows: Here, k represents the iteration index.

6. The underwater image restoration method based on underwater polarization imaging and image layering according to claim 5, characterized in that: The solution process of the above sub-problems is as follows: In the initialization step, given F k The estimated value of Q is updated as: The objective function in formula (14) is composed of the norm term and adjacent terms, the subscript 1 in formula (14) is the norm term, for W / μ k > 0, the closed-form solution of the problem in formula (14) is obtained by the following formula: Where S B (A) represents the element-wise soft threshold operator, where [S B (A)] ij =sign(A ij )×max(|A ij |-B ij ,0);S B (A) represents the form of formula (15); According to formula (15) and Q in formula (13) k+1 and N k , update F; the sub-problem in formula (13) is rewritten as: Assuming circular boundary conditions, the convolution matrices Δ and ▽ are diagonalized using the Fast Fourier Transform (FFT), where X k =IN k 、Y k =IN k -I s , F and F -1 are the forward and reverse FFT operators, F * (·) represents the complex conjugate, F(1) is Fourier transform of a function, ° represents component multiplication; Given Q k+1 and F k+1 , solve the following optimization problem: The penalty parameter μ is updated as: m k+1 =min{ρμ k ,m max } (20); In formula (20), ρ>1 is the user parameter used to penalize constraint violations, μ max Represents the sequence {μ max }, dynamically select the parameter sequence according to the difficulty of minimizing the penalty function in each iteration, and adaptively adjust {μ max }; The optimization variables Q, F, N, and μ are iteratively updated until convergence, and the convergence rate of the kth iteration is defined as: and run the iterations until the stopping criterion, ξ, is met k <10 -1 ; Where H represents the number of rows of image pixels and W represents the number of columns of image pixels; Finally, from formula (5) we get: G = IFN(22).

7. The underwater image restoration method based on underwater polarization imaging and image layering according to claim 6, characterized in that: G ∞ The calculation formula is:

Images