A SAR image despeckling method and system based on maximum a posteriori probability estimation

Abstract

The present invention discloses a SAR image despeckling method and system based on maximum a posteriori probability estimation, the method comprising: calculating the SAR image by the maximum a posteriori probability estimation algorithm to construct the SAR image objective function; decomposing the SAR image objective function by the alternating direction multiplier method to obtain a sub-function; solving the sub-function based on the update condition rule and iteratively optimizing the SAR image objective function to obtain a despeckled and noise-free SAR image. The system comprises: a construction module, a decomposition module and an optimization module. By using the present invention, it is possible to improve the optimization accuracy of the SAR image when the SAR image objective function is not constrained. As a SAR image despeckling method and system based on maximum a posteriori probability estimation, the present invention can be widely used in the field of SAR image processing.

Description

Technical Field

[0001] The present invention relates to the field of SAR image processing, and in particular to a SAR image despeckling method and system based on maximum a posteriori probability estimation. Background Art

[0002] Synthetic aperture radar (SAR) remote sensing has the advantages of all-day, all-weather, and high resolution, and has been widely used in many fields such as agriculture, forestry, environmental protection, disaster prevention and mitigation, marine monitoring, and military. However, due to the unique imaging mechanism of SAR, there is serious speckle noise interference in SAR images. The existence of speckle noise will greatly affect the subsequent interpretation of SAR images. In order to improve the interpretability of SAR images, the common practice is to use a despeckle algorithm to pre-process the original SAR images for denoising before image processing and application. For example, the existing denoising methods include a SAR image despeckle algorithm based on the spatial domain and an image despeckle method based on learning. The SAR image is pre-processed for denoising through a local spatial filter of a linear model, but the local spatial filter does not consider the correlation between structural textures, and only uses a simple local weighted average to suppress noise, resulting in incomplete despeckle or blurred edges, excessive calculation, and limitations on the scenes that the despeckle model can handle. Summary of the invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a SAR image despeckling method and system based on maximum a posteriori probability estimation, which can optimize SAR images in different occasions and improve the optimization accuracy of SAR images.

[0004] The first technical solution adopted by the present invention is: a SAR image despeckling method based on maximum a posteriori probability estimation, comprising the following steps:

[0005] The SAR image is calculated by the maximum a posteriori probability estimation algorithm to construct the SAR image objective function;

[0006] The SAR image objective function is decomposed by the alternating direction multiplier method to obtain sub-functions;

[0007] Based on the updating condition rules, the sub-functions are solved and the SAR image objective function is iteratively optimized to obtain the despeckled and noise-free SAR image.

[0008] Furthermore, the step of calculating the SAR image by using the maximum a posteriori probability estimation algorithm to construct the SAR image objective function specifically includes:

[0009] Acquire an observation image and perform logarithm processing on the observation image to obtain an observation image with additive noise;

[0010] Based on the maximum a posteriori probability estimation algorithm, the observed image with additive noise is processed by taking the negative logarithm to obtain the prior information of the noise-free image;

[0011] The prior information of the noise-free image is substituted into the observed image with additive noise to construct the SAR image objective function.

[0012] Further, the SAR image representation is as follows:

[0013] I=R×N

[0014] In the above formula, I represents the observed image, R represents the ideal noise-free image, and N represents the speckle noise.

[0015] Further, the SAR image objective function is as follows:

[0016]

[0017] In the above formula, X represents the independent variable, L represents the equivalent number of views, represents the prior information of the noise-free image, represents the denoising result, e X represents the exponential function, and Y represents the original SAR image.

[0018] Furthermore, the step of decomposing the SAR image objective function by the alternating direction multiplier method to obtain sub-functions specifically includes:

[0019] Auxiliary variables are introduced into the SAR image objective function to construct the augmented Lagrangian function;

[0020] Based on the alternating direction multiplier method, the augmented Lagrangian multiplier and the penalty coefficient are substituted into the augmented Lagrangian function to obtain the Lagrangian function;

[0021] Decompose the Lagrangian function to obtain sub-functions;

[0022] The sub-functions include a first sub-function, a second sub-function and a third sub-function.

[0023] Further, the augmented Lagrangian function is expressed as follows:

[0024]

[0025] In the above formula, A represents the augmented Lagrange multiplier, ρ represents the penalty coefficient, represents the prior information of Z, Z represents the elastic constraint variable introduced, A T represents the transpose of the introduced augmented Lagrange multiplier matrix.

[0026] Furthermore, the step of solving the sub-function based on the update condition rule and iteratively optimizing the SAR image objective function to obtain the despeckled and noise-free SAR image specifically includes:

[0027] Solve the first subfunction by Newton's method to obtain a first optimization value;

[0028] Solving the second sub-function by a deep learning method to obtain a second optimized value;

[0029] The augmented Lagrange multiplier is updated by the third sub-function to obtain a third optimization value;

[0030] Based on the update condition rule, the first optimization value, the second optimization value and the third optimization value are integrated to iteratively optimize the SAR image objective function;

[0031] The solution step and the update step are repeated until the iterative optimization condition reaches the preset termination condition, the optimization is stopped, and the despeckled and noise-free SAR image is output.

[0032] Furthermore, the step of solving the second sub-function by a deep learning method to obtain a second optimized value specifically includes:

[0033] Perform equivalent transformation on the second sub-function and construct the loss function of the convolutional neural network model in the SAR image denoising problem;

[0034] Add multiplicative speckle noise to the SAR image to obtain a simulated SAR image;

[0035] Based on the loss function, the simulated SAR image is input into the convolutional neural network model for feature fusion processing to obtain a high-resolution feature map;

[0036] Based on the convolutional neural network model, the feature information of the high-resolution feature map is repeatedly subjected to feature fusion processing and downsampling processing until a SAR image with feature mapping information is obtained, and the fusion step and downsampling step are stopped;

[0037] The SAR image with the feature mapping information is used as the second optimization value.

[0038] Furthermore, the update condition rules are specifically as follows:

[0039] ρ k+1 =μ×ρ k

[0040] In the above formula, μ represents a given constant, ρ k Represents the penalty coefficient for the kth iteration optimization.

[0041] The second technical solution adopted by the present invention is: a SAR image despeckling system based on maximum a posteriori probability estimation, comprising:

[0042] A construction module is used to calculate the SAR image through the maximum a posteriori probability estimation algorithm and construct the SAR image objective function;

[0043] A decomposition module is used to decompose the SAR image objective function by an alternating direction multiplier method to obtain sub-functions;

[0044] The optimization module solves the sub-functions and iteratively optimizes the SAR image objective function based on the update condition rules to obtain the despeckled and noise-free SAR image.

[0045] The beneficial effects of the method and system of the present invention are as follows: the present invention derives an objective function that conforms to the speckle noise characteristics of SAR images through a maximum a posteriori probability estimation method, and uses an alternating direction multiplier method to decompose and optimize the SAR image objective function, thereby making the optimization method more flexible, being able to improve the SAR image optimization accuracy, and being applicable to SAR image optimization in more different occasions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the steps of a SAR image despeckling method based on maximum a posteriori probability estimation of the present invention;

[0047] Figure 2 It is a structural block diagram of a SAR image despeckling system based on maximum a posteriori probability estimation of the present invention; DETAILED DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0049] Reference Figure 1 The present invention provides a SAR image despeckling method based on maximum a posteriori probability estimation, the method comprising the following steps:

[0050] S1. Calculate the SAR image through the maximum a posteriori probability estimation algorithm and construct the SAR image objective function;

[0051] S11, acquiring an observation image and performing logarithm processing on the observation image to obtain an observation image with additive noise;

[0052] Specifically, the SAR image is represented as follows:

[0053] I=R×N

[0054] In the above formula, I represents the observed image, R represents the ideal noise-free image, and N represents the speckle noise;

[0055] The speckle noise N follows a gamma distribution:

[0056]

[0057] In the above formula, L represents the equivalent number of views, p N The probability density function of speckle noise is represented by L L represents the Lth power of the equivalent view number L, Γ(L) represents the gamma function, N L-1 represents N to the power of L-1, e -LN Represents an exponential function.

[0058] The following expression must be satisfied for the equivalent number of views:

[0059]

[0060] In the above formula, E(I) represents the average intensity of the image, and var(I) represents the image variance.

[0061] Taking the logarithm of I, we get ln(I)=ln(R)+ln(N), which can be written as Y=X+S. Then S=ln(N) obeys the following probability density distribution function:

[0062]

[0063] In the above formula, p S represents the probability density function that S obeys, e -LS , Both represent exponential functions.

[0064] S12, based on the maximum a posteriori probability estimation algorithm, performing negative logarithm processing on the observed image with additive noise to obtain prior information of the noise-free image;

[0065] Specifically, in order to find the observed image X=ln(R) with additive noise, the maximum a posteriori probability estimation method is equivalent to finding max P(X|Y).

[0066] P(X|Y)∝P(Y|X)×P(X)

[0067] In the above formula, P(X|Y) represents the probability of event X, and P(Y|X) represents the probability of event Y occurring given that event X has occurred.

[0068] Then there is

[0069]

[0070] In the above formula, It means to find the X with the largest probability P(Y|X), Denotes X that maximizes the probability P(Y|X).

[0071] Taking the negative logarithm of the above formula, we can transform the maximization problem into a minimization problem.

[0072]

[0073] The above formula can also be expressed in the following form:

[0074]

[0075] In the above formula, D(X,Y)=-ln(P(Y|X)) represents the fidelity term used to measure the similarity between X and Y. Represents the prior information of X;

[0076] S13, substituting the prior information of the noise-free image into the observed image with additive noise to construct the SAR image objective function;

[0077] Specifically, for the above formula It is generally used to constrain X to achieve the purpose of denoising. For D(X,Y)=-ln(P(Y|X)), it satisfies

[0078] D(X,Y)=-ln(P Y|X (Y|X))=-ln(P S (YX))∝L(e Y-X +XY)

[0079] Substitute D(X,Y) into The SAR image objective function can be obtained, which is specifically expressed as follows:

[0080]

[0081] In the above formula, X represents the independent variable, L represents the equivalent number of views, represents the prior information of the noise-free image, represents the denoising result, e X represents the exponential function, and Y represents the original SAR image.

[0082] S2, decomposing the SAR image objective function by the alternating direction multiplier method to obtain sub-functions;

[0083] S21, introducing auxiliary variables into the SAR image objective function and constructing the augmented Lagrangian function;

[0084] Specifically, the auxiliary variable Z is introduced into the SAR image objective function, and we have

[0085]

[0086] Further introducing the augmented Lagrangian multiplier A and the penalty coefficient ρ, the augmented Lagrangian function is expressed as follows:

[0087]

[0088] In the above formula, A represents the augmented Lagrange multiplier, ρ represents the penalty coefficient, represents the prior information of Z, Z represents the elastic constraint variable introduced, A T represents the transpose of the introduced augmented Lagrange multiplier matrix.

[0089] S22, based on the alternating direction multiplier method, substituting the augmented Lagrangian multiplier and the penalty coefficient into the augmented Lagrangian function to obtain the Lagrangian function;

[0090] S23, decomposing the Lagrangian function to obtain sub-functions;

[0091] S24. The sub-functions include a first sub-function, a second sub-function and a third sub-function.

[0092] Specifically, using the alternating direction multiplier method, the optimization problem represented by the augmented Lagrangian function can be decomposed into three sub-optimization problems. Assuming that in the (k+1)th round of iteration, the three optimization sub-functions can be expressed as follows:

[0093] The first subfunction:

[0094]

[0095] The second sub-function:

[0096]

[0097] The third sub-function:

[0098] A k+1 =A k +ρ k (X k+1 -Z k+1

[0099] S3. Based on the updating condition rules, the sub-function is solved and the SAR image objective function is iteratively optimized to obtain a despeckled and noise-free SAR image.

[0100] S31, solving the first sub-function by Newton's method to obtain a first optimization value;

[0101] Specifically, Newton's method is used to solve the problem. The specific iterative formula for solving the first subfunction using Newton's method is:

[0102]

[0103] In the above formula, X ij k , Y ij , Z ij k and A ij k They represent the i-th row and j-th column elements in matrices X, Y, Z, and A in the k-th update iteration, respectively. Represents a numeric value.

[0104] S32, solving the second sub-function by a deep learning method to obtain a second optimized value;

[0105] S321, performing equivalent transformation processing on the second sub-function to construct a loss function of a convolutional neural network model in the SAR image denoising problem;

[0106] Specifically, for the second sub-problem represented by the second sub-function, it can be regarded as the loss function of the convolutional neural network in the image denoising problem. For easier understanding, the second function is transformed as follows:

[0107]

[0108] In the above formula, represents Gaussian noise, Z k+1 , X k+1 , A k and ρ k They respectively represent the values ​​of Z, X, A and ρ obtained in the k+1th loop iteration.

[0109] The Gaussian noise denoiser represented by the equivalent transformation of the second subfunction is used to remove the variance In order to adapt the fitting optimization scheme to various scenarios, No constraints are imposed, but a convolutional neural network in the deep learning method is used to fit and solve the optimization problem represented by the second sub-function;

[0110] S322, adding multiplicative speckle noise to the SAR image to obtain a simulated SAR image;

[0111] Specifically, multiplicative speckle noise is added to an ordinary grayscale image, i.e., a SAR image, as a simulated SAR image, and the original grayscale image is used as a label. A convolutional neural network is trained using the above data set as a training set, and the convolutional neural network is used to optimize and solve the second sub-problem represented by the second sub-function.

[0112] S323, based on the loss function, inputting the simulated SAR image into the convolutional neural network model for feature fusion processing to obtain a high-resolution feature map;

[0113] Specifically, the framework of the neural network is set as follows: first, the depth of the neural network is limited to eight layers, so that the neural network has good performance while having a small amount of computation; second, the neural network should always maintain the high resolution of the image being processed. To achieve this goal, the neural network should treat the denoising task as a pixel-level task; the network is set to connect multi-resolution networks in parallel, and multi-resolution features are repeatedly fused. The network designed in this way can maintain high-resolution detailed information throughout the feature extraction process, thereby improving the SAR image denoising accuracy.

[0114] S324, based on the convolutional neural network model, repeatedly performing feature fusion processing and downsampling processing on the feature information of the high-resolution feature map until a SAR image with feature mapping information is obtained, and stopping the fusion step and the downsampling step;

[0115] S325. The SAR image with feature mapping information is used as a second optimization value.

[0116] Specifically, the first stage of neural network training includes a feature extraction branch; a high-resolution feature map (resolution and feature channels are numbered H, W, and C) is input into a repeated bottleneck module; and the downsampling operation includes two new feature maps, A (resolution and feature channels are numbered H, W, and C) and B (resolution and feature channels are numbered H / 2, W / 2, and 2C).

[0117] The second stage includes two feature extraction branches; the input of the first branch is feature map A, and the input of the second branch is feature map B. After inputting four repeated bottleneck modules, a downsampling operation step is performed to obtain feature maps A'(H, W, C), B'(H / 2, W / 2, 2C), D(H / 2, W / 2, 2C) and E(H / 4, W / 4, 4C). At the same time, the information fusion layer first adjusts the resolution and number of channels of the second branch feature map B' to be the same as A' to obtain feature map B', and then adds and fuses A' and B' to obtain feature map F. Images D and B' are added and merged to obtain feature image G. After the information fusion layer, three feature maps, namely E, F and G, are finally output in the second stage.

[0118] The third stage contains three feature extraction branches; the inputs of the three branches correspond to E, F, and G respectively, and the specific operation process of this stage is similar to that of the second stage; however, the third branch no longer performs downsampling operations, and the final information fusion layer repeatedly merges the features of the three branches to obtain feature maps H, I, and J. H is used as the feature output extracted by the network for final prediction and classification.

[0119] The network designed in this way connects multi-resolution subnetworks in parallel, repeatedly fuses information, and preserves a large number of detailed features in shallow low-resolution features, which helps to improve the SAR image denoising accuracy;

[0120] The above steps S321 to S325 are that the second sub-function is highly consistent with the loss function of the common Gaussian denoising neural network, and the neural network can be regarded as optimizing and solving its loss function under certain rules. Therefore, the neural network method can be used to solve the second sub-function, and in the network design, the H image is designed as the final output image, and other images are only used as variables required in some calculations, such as feature images, down-sampled images, etc. Therefore, the output result only selects the H image, and the neural network method is designed to solve the second sub-problem. Therefore, the final output H image of the neural network can be regarded as the solution to the second sub-problem;

[0121] S33, updating the augmented Lagrange multiplier by a third sub-function to obtain a third optimized value;

[0122] S34, based on the update condition rule, integrating the first optimization value, the second optimization value and the third optimization value to iteratively optimize the SAR image objective function;

[0123] Specifically, the third subfunction is used to update the augmented Lagrangian multiplier A k , update the penalty coefficient ρ through the update rule k , the update condition rules are as follows:

[0124] ρ k+1 =μ×ρ k

[0125] In the above formula, μ represents a given constant, ρ k Represents the penalty coefficient for the kth iteration optimization.

[0126] S35, repeating steps S31 to S34 until the iterative optimization condition reaches a preset iterative termination condition, stopping the optimization, and outputting a despeckled and noise-free SAR image.

[0127] Specifically, the process of decomposing, solving and fitting the SAR image objective function is repeated until the iterative optimization condition reaches the preset iterative termination condition, the optimization is stopped, and the despeckled and noise-free SAR image X is output. k+1 , through reasonable mathematical calculations and experience, the termination conditions for the update are as follows:

[0128] ||X k+1 -X k || F ≤10 -6

[0129] ||X k+1 -Z k+1 || F ≤10 -6

[0130] ||Z k+1 -Z k || F ≤10 -6

[0131] In the above formula, X k+1 represents the despeckled and noise-free image, X k Represents the matrix X, Z obtained in the kth loop k+1 represents the value of the matrix Z obtained in the k+1th cycle, Z k represents the matrix Z obtained in the kth loop, ||·|| F Represents the F-norm of the matrix.

[0132] Reference Figure 2 , a SAR image despeckling system based on maximum a posteriori probability estimation, comprising:

[0133] A construction module is used to calculate the SAR image through the maximum a posteriori probability estimation algorithm and construct the SAR image objective function;

[0134] A decomposition module is used to decompose the SAR image objective function by an alternating direction multiplier method to obtain sub-functions;

[0135] The optimization module solves the sub-functions and iteratively optimizes the SAR image objective function based on the update condition rules to obtain the despeckled and noise-free SAR image.

[0136] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0137] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A SAR image despeckling method based on maximum a posteriori probability estimation, characterized in that: The following steps are involved: The SAR image is calculated by the maximum a posteriori probability estimation algorithm to construct the SAR image objective function; The SAR image objective function is decomposed by the alternating direction multiplier method to obtain sub-functions; Based on the updating condition rules, the sub-functions are solved and the SAR image objective function is iteratively optimized to obtain the despeckled and noise-free SAR image. The SAR image objective function is as follows: In the above formula, X represents the independent variable, L represents the equivalent number of views, represents the prior information of the noise-free image, represents the denoising result, e represents the exponential function, and Y represents the original SAR image; The step of decomposing the SAR image objective function by the alternating direction multiplier method to obtain sub-functions specifically includes: Auxiliary variables are introduced into the SAR image objective function to construct the augmented Lagrangian function; Based on the alternating direction multiplier method, the augmented Lagrangian multiplier and the penalty coefficient are substituted into the augmented Lagrangian function to obtain the Lagrangian function; Decompose the Lagrangian function to obtain sub-functions; The sub-functions include a first sub-function, a second sub-function and a third sub-function; The step of solving the sub-function based on the update condition rule and iteratively optimizing the SAR image objective function to obtain the despeckled and noise-free SAR image specifically includes: Solve the first subfunction by Newton's method to obtain a first optimization value; Solving the second sub-function by a deep learning method to obtain a second optimized value; The augmented Lagrange multiplier is updated by the third sub-function to obtain a third optimization value; Based on the update condition rule, the first optimization value, the second optimization value and the third optimization value are integrated to iteratively optimize the SAR image objective function; The solution step and the update step are repeated until the iterative optimization condition reaches the preset termination condition, the optimization is stopped, and the despeckled and noise-free SAR image is output.

2. The SAR image despeckling method based on maximum a posteriori probability estimation according to claim 1, characterized in that: The step of calculating the SAR image by the maximum a posteriori probability estimation algorithm and constructing the SAR image objective function specifically includes: Acquire an observation image and perform logarithm processing on the observation image to obtain an observation image with additive noise; Based on the maximum a posteriori probability estimation algorithm, the observed image with additive noise is processed by taking the negative logarithm to obtain the prior information of the noise-free image; The prior information of the noise-free image is substituted into the observed image with additive noise to construct the SAR image objective function.

3. The SAR image despeckling method based on maximum a posteriori probability estimation according to claim 2, characterized in that: The SAR image representation is as follows: I=R×N In the above formula, I represents the observed image, R represents the ideal noise-free image, and N represents the speckle noise.

4. The SAR image despeckling method based on maximum a posteriori probability estimation according to claim 3, characterized in that: The augmented Lagrangian function is expressed as follows: In the above formula, A represents the augmented Lagrange multiplier, ρ represents the penalty coefficient, represents the prior information of Z, Z represents the elastic constraint variable introduced, A T represents the transpose of the introduced augmented Lagrange multiplier matrix.

5. The SAR image despeckling method based on maximum a posteriori probability estimation according to claim 4, characterized in that: The step of solving the second sub-function by a deep learning method to obtain a second optimized value specifically includes: Perform equivalent transformation on the second sub-function and construct the loss function of the convolutional neural network model in the SAR image denoising problem; Add multiplicative speckle noise to the SAR image to obtain a simulated SAR image; Based on the loss function, the simulated SAR image is input into the convolutional neural network model for feature fusion processing to obtain a high-resolution feature map; Based on the convolutional neural network model, the feature information of the high-resolution feature map is repeatedly subjected to feature fusion processing and downsampling processing until a SAR image with feature mapping information is obtained, and the fusion step and downsampling step are stopped; The SAR image with the feature mapping information is used as the second optimization value.

6. The SAR image despeckling method based on maximum a posteriori probability estimation according to claim 5, characterized in that: The update condition rules are as follows: r k+1 =μ×ρ k In the above formula, μ represents a given constant, ρ k Represents the penalty coefficient for the kth iteration optimization.

7. A SAR image despeckling system based on maximum a posteriori probability estimation, characterized in that: The method for removing speckles from a SAR image based on maximum a posteriori probability estimation as claimed in claim 1 comprises the following modules: A construction module is used to calculate the SAR image through the maximum a posteriori probability estimation algorithm and construct the SAR image objective function; The decomposition module is used to decompose the SAR image objective function through the alternating direction multiplier method to obtain sub-functions; the optimization module solves the sub-functions based on the update condition rules and iteratively optimizes the SAR image objective function to obtain a despeckled and noise-free SAR image.

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