Underwater polarization imaging method and system based on Mueller matrix polarization analysis

Abstract

The invention discloses an underwater polarization imaging method and system based on Mueller matrix polarization analysis. The method comprises the following steps: shooting a plurality of polarization images of an underwater scene; according to the Fourier series simultaneous equation corresponding to each polarization image, calculating to obtain a Mueller matrix of the underwater scene; estimating the light intensity of backscattered light at the infinity; performing Clade decomposition on the Mueller matrix of the underwater scene to obtain an eigenvalue of the Mueller matrix, and calculating a polarization entropy and an overall purity index according to the eigenvalue; solving a low-rank part of the polarization entropy and the overall purity index by using robust principal component analysis based on an alternating direction multiplier method; according to the polarization entropy, the overall purity index and respective low-rank parts, a transmissivity graph is solved; and taking the first element of the Mueller matrix as the total light intensity of the underwater scene, substituting the total light intensity of the underwater scene, the backscattering light intensity at the infinity and the transmissivity graph into an underwater polarization imaging model for calculation, and performing histogram equalization to obtain an underwater restored image.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater polarization imaging, and specifically relates to an underwater polarization imaging method and system based on Mueller matrix polarization analysis. Background Art

[0002] Underwater imaging technology is widely used in underwater scientific research, underwater rescue and other fields. Among underwater imaging technologies, underwater polarization imaging technology starts from the dimension of polarization, uses the characteristic of partial polarization of backscattered light, establishes a physical model between total light intensity, target light and backscattered light to suppress backscattered light, and further processes it through imaging algorithms to overcome the influence of backscattered light on image quality, thus achieving clear underwater imaging.

[0003] At present, there are many ways to acquire images in underwater polarization imaging technology, including acquiring images in orthogonal polarization directions, Stokes vectors, and Mueller matrices. Among them, the Mueller matrix has attracted widespread attention by acquiring and utilizing more comprehensive polarization information, but most existing studies still use polarization parameters in traditional methods such as degree of polarization and polarization angle, and there is still room for improvement in the use of polarization information. In addition, imaging usually requires calculating the degree of polarization of the target and backscattered light, a process that brings about the difficulty of calculating differentiated degree of polarization. Summary of the invention

[0004] Purpose of the invention: In order to solve the problems of single polarization parameters and difficult calculation of differentiated polarization degree in the existing underwater polarization imaging technology based on the Mueller matrix, the present invention proposes an underwater polarization imaging method and system based on Mueller matrix polarization analysis. The method of the present invention uses more potential polarization parameters for polarization analysis, avoiding the calculation of differentiated polarization degree.

[0005] Technical solution: An underwater polarization imaging method based on Mueller matrix polarization analysis, comprising the following steps:

[0006] Step 1: In the Mueller matrix underwater polarization imaging system, take multiple polarization images of underwater scenes;

[0007] Step 2: Calculate the Mueller matrix of the underwater scene based on the Fourier series simultaneous equations corresponding to each polarization image;

[0008] Step 3: Estimate the backscattered light intensity at infinity based on the first element of the Mueller matrix of the underwater scene;

[0009] Step 4: Perform Claude decomposition on the Mueller matrix of the underwater scene to obtain its eigenvalues, and calculate the polarization entropy and overall purity index based on the eigenvalues;

[0010] Step 5: Use non-local mean filtering on the polarization entropy and the overall purity index, and use robust principal component analysis based on the alternating direction multiplier method to obtain the low-rank part of the polarization entropy and the overall purity index;

[0011] Step 6: Obtain a transmittance map according to the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index;

[0012] Step 7: Use the first element of the Mueller matrix as the total light intensity of the underwater scene, substitute the total light intensity of the underwater scene, the backscattered light intensity at infinity, and the transmittance map into the underwater polarization imaging model for calculation, and perform histogram equalization to obtain the underwater restored image.

[0013] Further, in step 3, the backscattered light intensity at infinity is estimated based on the first element of the Mueller matrix of the underwater scene, specifically including: for the first element of the Mueller matrix, after removing the 30% pixels with the highest brightness, calculating the average value of the 0.1% pixels with the highest brightness among the remaining pixels, and estimating the backscattered light intensity at infinity.

[0014] Furthermore, in step 4, the Mueller matrix of the underwater scene is subjected to Claude decomposition to obtain its eigenvalues, and polarization entropy and overall purity index are calculated based on the eigenvalues. The specific operations include:

[0015] The Pauli matrix σ is used to calculate the covariance matrix H(M) of the Mueller matrix of the underwater scene:

[0016]

[0017] In the formula, m ij is the element in the Mueller matrix, σ i represents the ith Pauli matrix, σ j represents the jth Pauli matrix;

[0018] Find the eigenvalue λ of the covariance matrix H(M) 1～4 And arrange the eigenvalues ​​in descending order to achieve the Claude decomposition of the Mueller matrix;

[0019] According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the polarization entropy S(H), expressed as:

[0020]

[0021] In the formula, λ i is the eigenvalue of the covariance matrix H(M);

[0022] According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the overall purity index PI, expressed as:

[0023]

[0024] In the formula, P1, P2, and P3 are polarization purity indicators, and the expression is:

[0025]

[0026] In the formula, m 11 Represents the first element of the Mueller matrix.

[0027] Furthermore, in step 5, the low-rank part of the polarization entropy and the overall purity index is obtained by using the robust principal component analysis based on the alternating direction multiplier method, which is expressed as:

[0028] [S(H) Low ,S(H) S ]=RobustPCA(S(H),λ,μ,tol,N max )

[0029] [PI Low ,PI S ]=RobustPCA(PI,λ,μ,tol,N max )

[0030] In the formula, S(H) Low 、S(H) S are the low-rank and sparse parts of the polarization entropy S(H), respectively; PI Low ,PI S are the low-rank and sparse parts of the overall purity index PI, respectively; RobustPCA(·) represents robust principal component analysis, λ is the regularization parameter, μ is the augmented Lagrangian parameter, tol is the reconstruction error tolerance, N max is the maximum number of iterations.

[0031] Further, in step 6, the transmittance graph is obtained according to the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index, which is expressed as:

[0032]

[0033] Where t(x) is the transmittance diagram and γ is the nonlinear adjustment factor.

[0034] Further, in step 7, the first element of the Mueller matrix is ​​used as the total light intensity of the underwater scene, the total light intensity of the underwater scene, the backscattered light intensity at infinity and the transmittance map are substituted into the underwater polarization imaging model for calculation, and histogram equalization is performed to obtain the underwater restored image. The specific operations include:

[0035] The first element m of the Mueller matrix 11As the total light intensity of the underwater scene, the total light intensity of the underwater scene m 11 , the backscattered light intensity A at infinity ∞ Substitute the transmittance map t(x) into the following formula to obtain the underwater target restoration image L(x):

[0036]

[0037] The underwater target restoration image L(x) is processed by histogram equalization to generate the final image.

[0038] The present invention discloses an underwater polarization imaging system based on Mueller matrix polarization analysis, comprising:

[0039] A polarization image acquisition module, used to capture multiple polarization images of underwater scenes in a Mueller matrix underwater polarization imaging system;

[0040] A Mueller matrix calculation module is used to calculate the Mueller matrix of the underwater scene according to the Fourier series simultaneous equations corresponding to each polarization image;

[0041] A backscattered light intensity estimation module at infinity, used to estimate the backscattered light intensity at infinity according to the first element of the Mueller matrix of the underwater scene;

[0042] A polarization entropy and overall purity index calculation module is used to perform Claude decomposition on the Mueller matrix of the underwater scene, obtain its eigenvalue, and calculate the polarization entropy and overall purity index based on the eigenvalue;

[0043] A low-rank part obtaining module is used to apply non-local mean filtering to the polarization entropy and the overall purity index, and to obtain the low-rank part of the polarization entropy and the overall purity index using robust principal component analysis based on the alternating direction multiplier method;

[0044] A transmittance map obtaining module, used for obtaining a transmittance map according to the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index;

[0045] The underwater restored image output module is used to take the first element of the Mueller matrix as the total light intensity of the underwater scene, substitute the total light intensity of the underwater scene, the backscattered light intensity at infinity and the transmittance map into the underwater polarization imaging model for calculation, and perform histogram equalization to obtain the underwater restored image.

[0046] Furthermore, the Mueller matrix of the underwater scene is subjected to Claude decomposition to obtain its eigenvalues, and polarization entropy and overall purity index are calculated based on the eigenvalues. Specifically, the operations include:

[0047] The Pauli matrix σ is used to calculate the covariance matrix H(M) of the Mueller matrix of the underwater scene:

[0048]

[0049] In the formula, m ij is the element in the Mueller matrix, σ i represents the ith Pauli matrix, σ j represents the jth Pauli matrix;

[0050] Find the eigenvalue λ of the covariance matrix H(M) 1～4 And arrange the eigenvalues ​​in descending order to achieve the Claude decomposition of the Mueller matrix;

[0051] According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the polarization entropy S(H), expressed as:

[0052]

[0053] In the formula, λ i is the eigenvalue of the covariance matrix H(M);

[0054] According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the overall purity index PI, expressed as:

[0055]

[0056] In the formula, P1, P2, and P3 are polarization purity indicators, and the expression is:

[0057]

[0058] In the formula, m 11 represents the first element of the Mueller matrix;

[0059] The robust principal component analysis based on the alternating direction multiplier method is used to obtain the low-rank part of the polarization entropy and the overall purity index, which is expressed as:

[0060] [S(H) Low ,S(H) S ]=RobustPCA(S(H),λ,μ,tol,N max )

[0061] [PI Low ,PI S ]=RobustPCA(PI,λ,μ,tol,N max )

[0062] In the formula, S(H) Low 、S(H) S are the low-rank and sparse parts of the polarization entropy S(H), respectively; PI Low ,PI Sare the low-rank and sparse parts of the overall purity index PI, respectively; RobustPCA(·) represents robust principal component analysis, λ is the regularization parameter, μ is the augmented Lagrangian parameter, tol is the reconstruction error tolerance, N max is the maximum number of iterations.

[0063] Furthermore, the transmittance graph is obtained based on the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index, which is expressed as:

[0064]

[0065] Where t(x) is the transmittance diagram and γ is the nonlinear adjustment factor.

[0066] Further, in step 7, the first element of the Mueller matrix is ​​used as the total light intensity of the underwater scene, the total light intensity of the underwater scene, the backscattered light intensity at infinity and the transmittance map are substituted into the underwater polarization imaging model for calculation, and histogram equalization is performed to obtain the underwater restored image. The specific operations include:

[0067] The first element m of the Mueller matrix 11 As the total light intensity of the underwater scene, the total light intensity of the underwater scene m 11 , the backscattered light intensity A at infinity ∞ Substitute the transmittance map t(x) into the following formula to obtain the underwater target restoration image L(x):

[0068]

[0069] The underwater target restoration image L(x) is processed by histogram equalization to generate the final image.

[0070] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0071] (1) The method of the present invention introduces the Mueller matrix, which can provide richer polarization information and has broad application potential;

[0072] (2) The method of the present invention introduces polarization entropy and overall purity index. These two polarization parameters are different from the degree of polarization and polarization angle in traditional methods, and perform better than the degree of polarization in some image evaluation indicators.

[0073] (3) The method of the present invention introduces the use of robust principal component analysis, which is used to obtain the low-rank part of the polarization entropy and the overall purity index, so as to better analyze and utilize the polarization characteristics of the backscattered light;

[0074] (4) The method of the present invention reconstructs the transmittance map, making full use of polarization entropy and overall purity index, which can more accurately reflect the polarization characteristics of different regions in the image and improve evaluation indicators such as image contrast and average gradient. By comprehensively considering the polarization information and the optical properties of the image itself, it can better cope with complex imaging environments, thereby improving the visual effect and analysis accuracy of the image. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 A flow chart of an underwater polarization imaging method based on Mueller matrix polarization analysis proposed by the present invention;

[0076] Figure 2 A schematic diagram of the Mueller matrix underwater polarization imaging system proposed in the present invention;

[0077] Figure 3 This is an example diagram of the Mueller matrix image proposed in the present invention, and the example is a complex polarization target of a 38.0NTU turbid water body;

[0078] Figure 4 The transmittance proposed by the present invention Figure 3 Dimensional example diagram, the example is a complex polarization target of 38.0NTU turbid water;

[0079] Figure 5 This is a diagram showing the effect of high and low concentration experiments using the method of the present invention, wherein: Figure 5 (a) is the total light intensity image underwater at low concentration. Figure 5 (b) is a diagram showing the effect of the method of the present invention at low concentrations. Figure 5 (c) is the total light intensity image under high concentration. Figure 5 (d) is a diagram showing the effect of the method of the present invention at high concentration. DETAILED DESCRIPTION

[0080] The technical solution of the present invention is now further described in conjunction with the accompanying drawings and embodiments.

[0081] like Figure 1 As shown, this embodiment discloses an underwater polarization imaging method based on Mueller matrix polarization analysis, which mainly includes the following steps:

[0082] Step 1: In the Mueller matrix underwater polarization imaging system, take multiple polarization images of the underwater scene, calculate the Mueller matrix of the underwater scene according to the Fourier series simultaneous equations, and estimate the backscattered light intensity at infinity according to the first element of the Mueller matrix; the specific operations include:

[0083] Figure 2The figure shows a Mueller matrix underwater polarization imaging system, in which the initial light beam emitted by the LED light source 1 first passes through the first polarizer 2, then passes through the first 1 / 4 wave plate 3 in the electric rotating table, and then penetrates the transparent water tank 4 and irradiates the underwater target 5. The target reflected light reflected by the underwater target 5 and the backscattered light generated by the medium in the water pass through the second 1 / 4 wave plate 6 and the second polarizer 7 in the electric rotating table in turn, and are finally received by the CMOS camera 8, wherein the polarization directions of the first polarizer 2 and the second polarizer 7 are both horizontal.

[0084] In this embodiment, the first 1 / 4 wave plate 3 and the second 1 / 4 wave plate 6 are set to a rotation speed ratio of 5:1 through the control of the electric rotating stage, and 36 polarization images are continuously rotated and taken. In this embodiment, the polarization image is collected by the Daheng Optoelectronics MER2-2000-19U3M / CL camera. Based on the 36 polarization images of the underwater scene, the Mueller matrix is ​​calculated by combining 16 equations according to the Fourier series corresponding to each image; Figure 3 An example diagram of the Mueller matrix image of the present invention is shown, the example being a complex polarization target of a 38.0 NTU turbid water body.

[0085] For the first element of the Mueller matrix, after removing the 30% pixels with the highest brightness, the average value of the 0.1% pixels with the highest brightness among the remaining pixels is calculated to estimate the backscattered light intensity A at infinity. ∞ .

[0086] Step 2: Perform Claude decomposition on the Mueller matrix to obtain its eigenvalues, and calculate the polarization entropy and the overall purity index based on the eigenvalues; use non-local mean filtering on the polarization entropy and the overall purity index, and use robust principal component analysis based on the alternating direction multiplier method to obtain the low-rank part of the polarization entropy and the overall purity index; the specific operations include:

[0087] Use the Pauli matrix σ to calculate the covariance matrix H(M) of the Mueller matrix and find the eigenvalue λ of the covariance matrix H(M) 1:4 And arrange the eigenvalues ​​in descending order to achieve the Claude decomposition of the Mueller matrix:

[0088]

[0089] In the formula, m ij is the Mueller matrix element, σ i represents the ith Pauli matrix, σ j represents the j-th Pauli matrix.

[0090] According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the polarization entropy S(H), expressed as:

[0091]

[0092] In the formula, λ i is the eigenvalue of the covariance matrix H(M).

[0093] According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the overall purity index PI, expressed as:

[0094]

[0095] In the formula, P1, P2, and P3 are polarization purity indicators, and the expression is:

[0096]

[0097] In the formula, m 11 Represents the first element of the Mueller matrix.

[0098] A non-local mean filtering algorithm is used for polarization entropy and overall purity indicators to reduce the noise impact caused by multiple polarization parameters.

[0099] The low-rank part of polarization entropy and overall purity index is obtained by robust principal component analysis based on alternating direction multiplier method, which is expressed as:

[0100] [S(H) Low ,S(H) S ]=RobustPCA(S(H),λ,μ,tol,N max )

[0101] [PI Low ,PI S ]=RobustPCA(PI,λ,μ,tol,N max )

[0102] In the formula, S(H) Low 、S(H) S are the low-rank and sparse parts of the polarization entropy S(H), respectively; PI Low ,PI S are the low-rank and sparse parts of the overall purity index PI respectively; RobustPCA represents robust principal component analysis, λ is the regularization parameter, μ is the augmented Lagrangian parameter, tol is the reconstruction error tolerance, N max is the maximum number of iterations.

[0103] In this embodiment, λ is set to the reciprocal of the square root of the maximum value of the image dimension, μ is 10 times λ, and tol is 10 -6 , N max is 100.

[0104] Step 3: Obtain the transmittance map based on the polarization entropy, overall purity, and the low-rank part of these parameters; the specific operations include:

[0105]

[0106] Wherein, t(x) is the transmittance diagram; γ is a nonlinear adjustment factor, which can be set according to actual conditions. In this embodiment, γ is 0.5. Figure 4 The transmittance of the present invention is shown Figure 3 Dimensional example diagram, the example is a complex polarization target of 38.0NTU turbid water.

[0107] Step 4: Substitute the total light intensity of the underwater image, the backscattered light intensity at infinity, and the transmittance map into the underwater polarization imaging model for calculation and perform histogram equalization to obtain the underwater restored image. The specific operations include:

[0108] The first element m of the Mueller matrix 11 As the total light intensity of the underwater scene, the total light intensity of the underwater image m 11 , the backscattered light intensity A at infinity ∞ Substitute the transmittance map t(x) into the underwater polarization imaging model to calculate the underwater target restoration image L(x) as follows:

[0109]

[0110] The underwater target restoration image L(x) is processed by histogram equalization to generate the final image.

[0111] In order to verify the effectiveness of this embodiment, experiments were carried out in water environments with different turbidity. Figure 5 (a) and (c) in the figure show the total light intensity in water at 38.0 NTU and 71.5 NTU turbidity, respectively. It can be observed that the unprocessed image is subjectively more blurred and details are obviously lost. After being processed by the method of this embodiment, the clarity and visibility of the image are significantly improved, as shown in FIG. Figure 5 As shown in (b) and (d) in FIG. 5 , it is possible to automatically restore underwater targets with complex polarization characteristics and adapt to underwater environments with different turbidities.

[0112] In addition, objective quality evaluation indicators such as image enhancement evaluation standard (EME), average gradient (AG) and information entropy (Entorpy) are used to evaluate the restored image. The higher the value of these indicators, the better the image quality. The specific results are shown in Table 1 and Table 2:

[0113] Table 1 Quality evaluation of restored images of complex polarization targets in 38.0 NTU turbid water

[0114] EME Entorpy AG Total light intensity diagram 1.0837 6.0808 0.0018 After adopting the method of this embodiment 9.5304 7.6972 0.0228

[0115] Table 2 Quality evaluation of restored images of complex polarization targets in 71.5 NTU turbid water

[0116]

[0117]

[0118] It can be seen from the data in the table that the restored image processed by the method of this embodiment has significant improvements in various objective evaluation indicators compared to the original total light intensity image, which shows that the method of this embodiment has good effectiveness in underwater image restoration.

Claims

1. An underwater polarization imaging method based on Mueller matrix polarization analysis, characterized in that: The following steps are involved: Step 1: In the Mueller matrix underwater polarization imaging system, take multiple polarization images of underwater scenes; Step 2: Calculate the Mueller matrix of the underwater scene based on the Fourier series simultaneous equations corresponding to each polarization image; Step 3: Estimate the backscattered light intensity at infinity based on the first element of the Mueller matrix of the underwater scene; Step 4: Perform Claude decomposition on the Mueller matrix of the underwater scene to obtain its eigenvalues, and calculate the polarization entropy and overall purity index based on the eigenvalues; Step 5: Use non-local mean filtering on the polarization entropy and the overall purity index, and use robust principal component analysis based on the alternating direction multiplier method to obtain the low-rank part of the polarization entropy and the overall purity index; Step 6: Obtain a transmittance map according to the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index; Step 7: Use the first element of the Mueller matrix as the total light intensity of the underwater scene, substitute the total light intensity of the underwater scene, the backscattered light intensity at infinity, and the transmittance map into the underwater polarization imaging model for calculation, and perform histogram equalization to obtain the underwater restored image.

2. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 1, characterized in that: In step 3, the estimation of the backscattered light intensity at infinity based on the first element of the Mueller matrix of the underwater scene specifically includes: For the first element of the Mueller matrix, after removing the 30% pixels with the highest brightness, the average value of the 0.1% pixels with the highest brightness among the remaining pixels is calculated to estimate the backscattered light intensity at infinity.

3. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 1, characterized in that: In step 4, the Mueller matrix of the underwater scene is subjected to Claude decomposition to obtain its eigenvalues, and polarization entropy and overall purity index are calculated based on the eigenvalues. The specific operations include: The Pauli matrix σ is used to calculate the covariance matrix H(M) of the Mueller matrix of the underwater scene: In the formula, m ij is the element in the Mueller matrix, σ i represents the ith Pauli matrix, σ j represents the jth Pauli matrix; Find the eigenvalue λ of the covariance matrix H(M) 1～4 And arrange the eigenvalues ​​in descending order to achieve the Claude decomposition of the Mueller matrix; According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the polarization entropy S(H), expressed as: In the formula, λ i is the eigenvalue of the covariance matrix H(M); According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the overall purity index PI, expressed as: In the formula, P1, P2, and P3 are polarization purity indicators, and the expression is: In the formula, m 11 Represents the first element of the Mueller matrix.

4. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 3, characterized in that: In step 5, the low-rank part of the polarization entropy and the overall purity index is obtained by using the robust principal component analysis based on the alternating direction multiplier method, which is expressed as: [S(H) Low ,S(H) S ]=RobustPCA(S(H),λ,μ,tol,N max ) [PI Low ,PI S ]=RobustPCA(PI,λ,μ,tol,N max ) In the formula, S(H) Low 、S(H) S are the low-rank and sparse parts of the polarization entropy S(H), respectively; PI Low ,PI S are the low-rank and sparse parts of the overall purity index PI, respectively; RobustPCA(·) represents robust principal component analysis, λ is the regularization parameter, μ is the augmented Lagrangian parameter, tol is the reconstruction error tolerance, N max is the maximum number of iterations.

5. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 4, characterized in that: In step 6, the transmittance graph is obtained according to the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index, which is expressed as: Where t(x) is the transmittance diagram and γ is the nonlinear adjustment factor.

6. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 5, characterized in that: In step 7, the first element of the Mueller matrix is ​​used as the total light intensity of the underwater scene, the total light intensity of the underwater scene, the backscattered light intensity at infinity and the transmittance map are substituted into the underwater polarization imaging model for calculation, and histogram equalization is performed to obtain the underwater restored image. The specific operations include: The first element m of the Mueller matrix 11 As the total light intensity of the underwater scene, the total light intensity of the underwater scene m 11 , the backscattered light intensity A at infinity ∞ Substitute the transmittance map t(x) into the following formula to obtain the underwater target restoration image L(x): The underwater target restoration image L(x) is processed by histogram equalization to generate the final image.

7. An underwater polarization imaging system based on Mueller matrix polarization analysis, characterized in that: include: A polarization image acquisition module, used to capture multiple polarization images of underwater scenes in a Mueller matrix underwater polarization imaging system; A Mueller matrix calculation module is used to calculate the Mueller matrix of the underwater scene according to the Fourier series simultaneous equations corresponding to each polarization image; A backscattered light intensity estimation module at infinity, used to estimate the backscattered light intensity at infinity according to the first element of the Mueller matrix of the underwater scene; A polarization entropy and overall purity index calculation module is used to perform Claude decomposition on the Mueller matrix of the underwater scene, obtain its eigenvalue, and calculate the polarization entropy and overall purity index based on the eigenvalue; A low-rank part obtaining module is used to apply non-local mean filtering to the polarization entropy and the overall purity index, and to obtain the low-rank part of the polarization entropy and the overall purity index using robust principal component analysis based on the alternating direction multiplier method; A transmittance map obtaining module, used for obtaining a transmittance map according to the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index; The underwater restored image output module is used to take the first element of the Mueller matrix as the total light intensity of the underwater scene, substitute the total light intensity of the underwater scene, the backscattered light intensity at infinity and the transmittance map into the underwater polarization imaging model for calculation, and perform histogram equalization to obtain the underwater restored image.

8. The underwater polarization imaging system based on Mueller matrix polarization analysis according to claim 7, characterized in that: The aforementioned Claude decomposition is performed on the Mueller matrix of the underwater scene to obtain its eigenvalue, and the polarization entropy and the overall purity index are calculated according to the eigenvalue. The specific operations include: The Pauli matrix σ is used to calculate the covariance matrix H(M) of the Mueller matrix of the underwater scene: In the formula, m ij is the element in the Mueller matrix, σ i represents the ith Pauli matrix, σ j represents the jth Pauli matrix; Find the eigenvalue λ of the covariance matrix H(M) 1～4 And arrange the eigenvalues ​​in descending order to achieve the Claude decomposition of the Mueller matrix; According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the polarization entropy S(H), expressed as: In the formula, λ i is the eigenvalue of the covariance matrix H(M); According to the eigenvalue λ of the covariance matrix H(M) 1～4 Calculate the overall purity index PI, expressed as: In the formula, P1, P2, and P3 are polarization purity indicators, and the expression is: In the formula, m 11 represents the first element of the Mueller matrix; The robust principal component analysis based on the alternating direction multiplier method is used to obtain the low-rank part of the polarization entropy and the overall purity index, which is expressed as: [S(H) Low ,S(H) S ]=RobustPCA(S(H),λ,μ,tol,N max ) [PI Low ,PI S ]=RobustPCA(PI,λ,μ,tol,N max ) In the formula, S(H) Low 、S(H) S are the low-rank and sparse parts of the polarization entropy S(H), respectively; PI Low ,PI S are the low-rank and sparse parts of the overall purity index PI, respectively; RobustPCA(·) represents robust principal component analysis, λ is the regularization parameter, μ is the augmented Lagrangian parameter, tol is the reconstruction error tolerance, N max is the maximum number of iterations.

9. The underwater polarization imaging system based on Mueller matrix polarization analysis according to claim 8, characterized in that: The transmittance graph is obtained based on the polarization entropy, the overall purity index, the low-rank part of the polarization entropy and the low-rank part of the overall purity index, and is expressed as: Where t(x) is the transmittance diagram and γ is the nonlinear adjustment factor.

10. The underwater polarization imaging system based on Mueller matrix polarization analysis according to claim 9, characterized in that: In step 7, the first element of the Mueller matrix is ​​used as the total light intensity of the underwater scene, the total light intensity of the underwater scene, the backscattered light intensity at infinity and the transmittance map are substituted into the underwater polarization imaging model for calculation, and histogram equalization is performed to obtain the underwater restored image. The specific operations include: The first element m of the Mueller matrix 11 As the total light intensity of the underwater scene, the total light intensity of the underwater scene m 11 , the backscattered light intensity A at infinity ∞ Substitute the transmittance map t(x) into the following formula to obtain the underwater target restoration image L(x): The underwater target restoration image L(x) is processed by histogram equalization to generate the final image.

Images