An underwater polarization imaging method and system based on mueller matrix polarization analysis

Abstract

The application discloses an underwater polarization imaging method and system based on Mueller matrix polarization analysis, and comprises the following steps: taking multiple polarization images of an underwater scene; calculating a Mueller matrix of the underwater scene according to a corresponding Fourier series simultaneous equation of each polarization image; estimating the backscattering light intensity at infinity; performing a Cloude decomposition on the Mueller matrix of the underwater scene to obtain eigenvalues, and calculating a polarization entropy and an overall purity index according to the eigenvalues; using a robust principal component analysis based on an alternating direction multiplier method to obtain a low-rank part of the polarization entropy and the overall purity index; calculating a transmittance map according to the polarization entropy, the overall purity index and the low-rank parts of the polarization entropy and the overall purity index; taking the first element of the Mueller matrix as the total light intensity of the underwater scene, and substituting the total light intensity of the underwater scene, the backscattering light intensity at infinity and the transmittance map into an underwater polarization imaging model to calculate and perform histogram equalization to obtain an underwater recovered image.

Description

Technical Field

[0001] This invention belongs to the field of underwater polarization imaging technology, specifically an underwater polarization imaging method and system based on Mueller matrix polarization analysis. Background Technology

[0002] Underwater imaging technology has wide applications in underwater scientific research, underwater rescue, and other fields. Among underwater imaging technologies, underwater polarization imaging technology starts from the dimension of polarization. It utilizes the characteristic that backscattered light has partial polarization to establish a physical model between total light intensity, target light, and backscattered light to suppress backscattered light. Furthermore, it uses imaging algorithms to further process the image and overcome the impact of backscattered light on image quality, thus achieving clear underwater imaging.

[0003] Currently, underwater polarization imaging technology employs various image acquisition methods, including acquiring images with orthogonal polarization directions, Stokes vectors, and Mueller matrices. Among these, the Mueller matrix has garnered significant attention due to its ability to acquire and utilize more comprehensive polarization information. However, most existing research still relies on polarization parameters from traditional methods such as polarization degree and polarization angle, leaving room for improvement in the utilization of polarization information. Furthermore, achieving imaging typically requires calculating the polarization degree of the target and backscattered light, a process that presents the challenge of calculating differential polarization degrees. Summary of the Invention

[0004] Purpose of the invention: To address the problems of single polarization parameters and difficulty in calculating differential polarization degrees in existing underwater polarization imaging technologies based on the Mueller matrix, this invention proposes an underwater polarization imaging method and system based on Mueller matrix polarization analysis. This invention utilizes more promising polarization parameters for polarization analysis, avoiding the need to calculate differential polarization degrees.

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

[0006] Step 1: Take multiple polarization images of the underwater scene using the Mueller matrix underwater polarization imaging system;

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

[0008] Step 3: Estimate the intensity of backscattered light 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: Apply nonlocal mean filtering to 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 parts of the polarization entropy and the overall purity index.

[0011] Step 6: Calculate the transmittance map based on the polarization entropy, the overall purity index, the low-rank component of the polarization entropy, and the low-rank component of the overall purity index.

[0012] Step 7: 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.

[0013] Furthermore, 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% of the brightest pixels, calculating the average value of the 0.1% of the remaining pixels with the highest brightness, and estimating the backscattered light intensity at infinity.

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

[0015] The covariance matrix H(M) of the Mueller matrix for the underwater scene is calculated using the Pauli matrix σ:

[0016]

[0017] In the formula, m ij σ is an element in the Mueller matrix. i Let σ represent the i-th Pauli matrix. j Let j be the j-th Pauli matrix;

[0018] Find the eigenvalues ​​λ of the covariance matrix H(M). 1～4 The eigenvalues ​​are then arranged in descending order to achieve the Claude decomposition of the Mueller matrix.

[0019] Based on the eigenvalues ​​λ of the covariance matrix H(M) 1～4 The polarization entropy S(H) is calculated as follows:

[0020]

[0021] In the formula, λ i Let H(M) be the eigenvalues ​​of the covariance matrix H(M).

[0022] Based on the eigenvalues ​​λ of the covariance matrix H(M) 1～4 The overall purity index PI is calculated and expressed as:

[0023]

[0024] In the formula, P1, P2, and P3 are polarization purity indices, expressed as:

[0025]

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

[0027] Furthermore, in step 5, the low-rank component of the polarization entropy and overall purity index obtained using robust principal component analysis based on the alternating direction multiplier method 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 These represent the low-rank and sparse components of the polarization entropy S(H), respectively; PI Low PI S These represent the low-rank and sparse components 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, and N... max This represents the maximum number of iterations.

[0031] Furthermore, in step 6, the transmittance map is obtained based on the polarization entropy, the overall purity index, the low-rank portion of the polarization entropy, and the low-rank portion of the overall purity index, and is expressed as follows:

[0032]

[0033] In the formula, t(x) is the transmittance map, and γ is the nonlinear adjustment factor.

[0034] Furthermore, 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 m of the underwater scene 11 The intensity of backscattered light at infinity, A ∞ Substituting the transmittance map t(x) into the following equation, we obtain the underwater target reconstruction image L(x):

[0036]

[0037] Histogram equalization is performed on the underwater target reconstruction image L(x) to generate the final image.

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

[0039] The polarization image acquisition module is used to capture multiple polarization images of underwater scenes in the Mueller matrix underwater polarization imaging system.

[0040] The Mueller matrix calculation module is used to calculate the Mueller matrix of the underwater scene by solving the simultaneous equations of the Fourier series corresponding to each polarization image.

[0041] The backscattered light intensity estimation module at infinity is used to estimate the backscattered light intensity at infinity based on the first element of the Mueller matrix of the underwater scene.

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

[0043] The low-rank component extraction module is used to apply nonlocal mean filtering to polarization entropy and overall purity index, and to extract the low-rank components of polarization entropy and overall purity index using robust principal component analysis based on the alternating direction multiplier method.

[0044] The transmittance map acquisition module is used to acquire the transmittance map 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.

[0045] The underwater reconstruction 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 reconstruction image.

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

[0047] The covariance matrix H(M) of the Mueller matrix for the underwater scene is calculated using the Pauli matrix σ:

[0048]

[0049] In the formula, m ij σ is an element in the Mueller matrix. i Let σ represent the i-th Pauli matrix. j Let j be the j-th Pauli matrix;

[0050] Find the eigenvalues ​​λ of the covariance matrix H(M). 1～4 The eigenvalues ​​are then arranged in descending order to achieve the Claude decomposition of the Mueller matrix.

[0051] Based on the eigenvalues ​​λ of the covariance matrix H(M) 1～4 The polarization entropy S(H) is calculated as follows:

[0052]

[0053] In the formula, λ i Let H(M) be the eigenvalues ​​of the covariance matrix H(M).

[0054] Based on the eigenvalues ​​λ of the covariance matrix H(M) 1～4 The overall purity index PI is calculated and expressed as:

[0055]

[0056] In the formula, P1, P2, and P3 are polarization purity indices, expressed as:

[0057]

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

[0059] The method of robust principal component analysis based on alternating direction multipliers to obtain the low-rank components of polarization entropy and overall purity index is expressed as follows:

[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 These represent the low-rank and sparse components of the polarization entropy S(H), respectively; PI Low PI SThese represent the low-rank and sparse components 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, and N... max This represents the maximum number of iterations.

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

[0064]

[0065] In the formula, t(x) is the transmittance map, and γ is the nonlinear adjustment factor.

[0066] Furthermore, 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 m of the underwater scene 11 The intensity of backscattered light at infinity, A ∞ Substituting the transmittance map t(x) into the following equation, we obtain the underwater target reconstruction image L(x):

[0068]

[0069] Histogram equalization is performed on the underwater target reconstruction image L(x) 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 this invention introduces polarization entropy and overall purity index. These two polarization parameters are different from polarization degree and polarization angle in traditional methods and perform better than polarization degree in some image evaluation indicators.

[0073] (3) The method of the present invention introduces the use of robust principal component analysis. The low-rank part of polarization entropy and overall purity index is obtained by using robust principal component analysis, which can better analyze and utilize the polarization characteristics of backscattered light.

[0074] (4) The method of this 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 polarization information and the optical characteristics of the image itself, it can better cope with complex imaging environments, thereby improving the visual effect and analysis accuracy of the image. Attached Figure Description

[0075] Figure 1 This is a flowchart of an underwater polarization imaging method based on Mueller matrix polarization analysis proposed in this invention;

[0076] Figure 2 This is a schematic diagram of the Mueller matrix underwater polarization imaging system proposed in this invention;

[0077] Figure 3 This is an example image of the Mueller matrix proposed in this invention, specifically a complex polarized target in turbid water at 38.0 NTU.

[0078] Figure 4 The transmittance proposed in this invention Figure 3 Example image, the example is a complex polarized target in turbid water with a volume of 38.0 NTU;

[0079] Figure 5 The image shows the effect of high and low concentration experiments using the method of this invention. Figure 5 Image (a) shows the total light intensity underwater at low concentrations. Figure 5 (b) in the figure shows the effect of using the method of the present invention at low concentrations. Figure 5 Image (c) shows the total light intensity underwater under high concentration conditions. Figure 5 (d) in the figure shows the effect of using the method of the present invention at high concentrations. Detailed Implementation

[0080] The technical solution of the present invention will now be 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, capture multiple polarization images of the underwater scene. Calculate the Mueller matrix of the underwater scene using simultaneous Fourier series equations. Estimate the backscattered light intensity at infinity based on the first element of the Mueller matrix. Specific operations include:

[0083] Figure 2A Mueller matrix underwater polarization imaging system is illustrated. In this system, the initial beam emitted by the LED light source 1 first passes through the first polarizer 2, then through the first quarter-wave plate 3 in the motorized rotating stage, and finally through the transparent water tank 4 to illuminate the underwater target 5. The target reflected light and the backscattered light generated by the medium in the water pass sequentially through the second quarter-wave plate 6 and the second polarizer 7 in the motorized rotating stage, and are finally received by the CMOS camera 8. The polarization directions of the first polarizer 2 and the second polarizer 7 are both horizontal.

[0084] In this embodiment, the first quarter-wave plate 3 and the second quarter-wave plate 6 are controlled by an electric rotary table, with a rotation speed ratio of 5:1, and are continuously rotated to capture 36 polarization images. In this embodiment, the polarization images are acquired 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 solving 16 equations simultaneously based on the Fourier series corresponding to each image. Figure 3 An example image of the Mueller matrix described in this invention is shown, with the example being a complex polarized target in turbid water at a depth of 38.0 NTU.

[0085] For the first element of the Mueller matrix, after removing the 30% of brightest pixels, the average value of the 0.1% of brightest 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 overall purity index based on the eigenvalues; apply nonlocal mean filtering to the polarization entropy and overall purity index, and use robust principal component analysis based on the alternating direction multiplier method to obtain the low-rank components of the polarization entropy and overall purity index; specific operations include:

[0087] Calculate the covariance matrix H(M) of the Mueller matrix using the Pauli matrix σ, and then find the eigenvalues ​​λ of the covariance matrix H(M). 1:4 The Claude decomposition of the Mueller matrix is ​​then achieved by arranging the eigenvalues ​​in descending order:

[0088]

[0089] In the formula, m ij For the elements of the Mueller matrix, σ i Let σ represent the i-th Pauli matrix. j Let represent the j-th Pauli matrix.

[0090] Based on the eigenvalues ​​λ of the covariance matrix H(M) 1～4 The polarization entropy S(H) is calculated as follows:

[0091]

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

[0093] Based on the eigenvalues ​​λ of the covariance matrix H(M) 1～4 The overall purity index PI is calculated and expressed as:

[0094]

[0095] In the formula, P1, P2, and P3 are polarization purity indices, expressed as:

[0096]

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

[0098] Nonlocal mean filtering algorithm is used for polarization entropy and overall purity index to reduce the noise impact of multiple polarization parameters.

[0099] Robust principal component analysis based on the alternating direction multiplier method is used to obtain the low-rank components of the polarization entropy and the overall purity index, expressed as follows:

[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 These represent the low-rank and sparse components of the polarization entropy S(H), respectively; PI Low PI S These represent the low-rank and sparse components 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, and N... max This represents 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 It is 100.

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

[0105]

[0106] In the formula, t(x) is the transmittance map; γ is a nonlinear adjustment factor, which can be set according to the actual situation. In this embodiment, γ is 0.5. Figure 4 The transmittance described in this invention is shown. Figure 3 Example image, the example is a complex polarized target in turbid water with a volume of 38.0 NTU.

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

[0108] The first element m of the Mueller matrix 11 The total light intensity of the underwater scene is represented by the total light intensity m of the underwater image. 11 The intensity of backscattered light at infinity, A ∞ Substituting the transmittance map t(x) into the underwater polarization imaging model, the underwater target reconstruction image L(x) is obtained as follows:

[0109]

[0110] Histogram equalization is performed on the underwater target reconstruction image L(x) to generate the final image.

[0111] To verify the effectiveness of this embodiment, experiments were conducted in water environments with different turbidity levels. Figure 5 Images (a) and (c) in the figure show the total light intensity in water at turbidity levels of 38.0 NTU and 71.5 NTU, respectively. It can be observed that the unprocessed image exhibits significant subjective blurring and noticeable loss of detail. After processing using the method described in this embodiment, the image clarity and visibility are significantly improved, as shown in the figure. Figure 5 As shown in (b) and (d) in the figure, it can realize the automatic restoration of underwater targets with complex polarization characteristics and adapt to underwater environments with different turbidity.

[0112] In addition, objective quality evaluation metrics such as Image Enhancement Evaluation (EME), Average Gradient (AG), and Entropy were used to evaluate the restored images. Higher values ​​for these metrics indicate better image quality. Specific results are shown in Tables 1 and 2:

[0113] Table 1. Quality evaluation of the restored images of complex polarized targets in turbid water bodies of 38.0 NTU.

[0114] 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 assessment of the restored images of complex polarized targets in 71.5 NTU turbid water.

[0116]

[0117]

[0118] As can be seen from the data in the table, the restored image processed by the method of this embodiment shows a significant improvement in all objective evaluation indicators compared with the original total light intensity image, which indicates 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: Includes the following steps: Step 1: Take multiple polarization images of the underwater scene using the Mueller matrix underwater polarization imaging system; Step 2: Solve the simultaneous equations of the Fourier series corresponding to each polarization image to calculate the Mueller matrix of the underwater scene; Step 3: Estimate the intensity of backscattered light 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; specific operations include: Pauli matrix Calculate the covariance matrix of the Mueller matrix for an underwater scene. : ； In the formula, For the elements in the Mueller matrix, Let i represent the i-th Pauli matrix. Let j be the j-th Pauli matrix; Find the covariance matrix eigenvalues The eigenvalues ​​are then arranged in descending order to achieve the Claude decomposition of the Mueller matrix. Based on the covariance matrix eigenvalues Calculate polarization entropy , is represented as: ； In the formula, Covariance matrix eigenvalues; Based on the covariance matrix eigenvalues Calculate the overall purity index , is represented as: ； In the formula, , , The polarization purity index is expressed as: ； In the formula, This represents the first element of the Mueller matrix; Step 5: Apply nonlocal mean filtering to the polarization entropy and overall purity index, and use robust principal component analysis based on the alternating direction multiplier method to obtain the low-rank components of the polarization entropy and overall purity index, expressed as: ； ； In the formula, , These are polarization entropy. The low-rank and sparse parts; , These are the overall purity indicators. The low-rank and sparse parts; This indicates robust principal component analysis. For regularization parameters, To augment the Lagrange parameters, To reconstruct the error tolerance, This represents the maximum number of iterations. Step 6: Based on the polarization entropy, overall purity index, low-rank component of the polarization entropy, and low-rank component of the overall purity index, obtain the transmittance map, expressed as: ； In the formula, This is a transmittance diagram. It is a non-linear adjustment factor; Step 7: 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.

2. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 1, characterized in that: Step 3, which involves estimating 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% of the brightest pixels, the average value of the 0.1% of the remaining pixels with the highest brightness is calculated to estimate the intensity of the backscattered light at infinity.

3. The underwater polarization imaging method based on Mueller matrix polarization analysis according to claim 1, 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 of the Mueller matrix As the total light intensity of the underwater scene, the total light intensity of the underwater scene Backscattered light intensity at infinity and transmittance diagram Substituting into the following formula, we obtain the underwater target reconstruction image. : ； Reconstructed images of underwater targets Perform histogram equalization to generate the final image.

4. An underwater polarization imaging system based on Mueller matrix polarization analysis, characterized in that: include: The polarization image acquisition module is used to capture multiple polarization images of underwater scenes in the Mueller matrix underwater polarization imaging system. The Mueller matrix calculation module is used to calculate the Mueller matrix of the underwater scene by solving the simultaneous equations of the Fourier series corresponding to each polarization image. The backscattered light intensity estimation module at infinity is used to estimate the backscattered light intensity at infinity based on the first element of the Mueller matrix of the underwater scene. The polarization entropy and overall purity index calculation module is used to perform Claude decomposition on the Mueller matrix of the underwater scene, obtain its eigenvalues, and calculate the polarization entropy and overall purity index based on the eigenvalues; specific operations include: Pauli matrix Calculate the covariance matrix of the Mueller matrix for an underwater scene. : ； In the formula, For the elements in the Mueller matrix, Let i represent the i-th Pauli matrix. Let j be the j-th Pauli matrix; Find the covariance matrix eigenvalues The eigenvalues ​​are then arranged in descending order to achieve the Claude decomposition of the Mueller matrix. Based on the covariance matrix eigenvalues Calculate polarization entropy , is represented as: ； In the formula, Covariance matrix eigenvalues; Based on the covariance matrix eigenvalues Calculate the overall purity index , is represented as: ； In the formula, , , The polarization purity index is expressed as: ； In the formula, This represents the first element of the Mueller matrix; The low-rank component extraction module is used to apply nonlocal mean filtering to the polarization entropy and overall purity index, and to extract the low-rank components of the polarization entropy and overall purity index using robust principal component analysis based on the alternating direction multiplier method, denoted as: ； ； In the formula, , These are polarization entropy. The low-rank and sparse parts; , These are the overall purity indicators. The low-rank and sparse parts; This indicates robust principal component analysis. For regularization parameters, To augment the Lagrange parameters, To reconstruct the error tolerance, This represents the maximum number of iterations. The transmittance map generation module is used to generate a transmittance map based on polarization entropy, overall purity index, the low-rank component of polarization entropy, and the low-rank component of overall purity index, as shown below: ； In the formula, This is a transmittance diagram. It is a non-linear adjustment factor; The underwater reconstruction 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 reconstruction image.

5. An underwater polarization imaging system based on Mueller matrix polarization analysis according to claim 4, 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 of the Mueller matrix As the total light intensity of the underwater scene, the total light intensity of the underwater scene Backscattered light intensity at infinity and transmittance diagram Substituting into the following formula, we obtain the underwater target reconstruction image. : ； Reconstructed images of underwater targets Perform histogram equalization to generate the final image.

Images