A shadow enhancement method for SAR video based on multi-component decomposition

Abstract

The present invention discloses a video SAR shadow enhancement method based on multi-component decomposition. It realizes the decomposition of shadow, background and noise components in input video SAR data by iterative solution. In each iteration, the shadow component matrix is ​​first updated; then, the background component matrix is ​​updated; secondly, the noise component matrix is ​​updated by solving the denoising equation based on the Fibonacci norm regularization of the noise component; finally, it is determined whether to stop the iteration according to the relative change between the shadow component updated in this iteration and the shadow component updated in the last iteration, and the latest updated shadow component is output as the video SAR shadow enhancement result. Compared with the shadow enhancement method based on histogram equalization, the method of the present invention has the characteristics of high shadow-background contrast of the shadow enhancement result, complete shadow contour features, and good shadow enhancement effect.

Description

Technical Field

[0001] The invention belongs to the technical field of synthetic aperture radar (SAR), and particularly relates to the technical field of video SAR imaging. Background Art

[0002] Synthetic aperture radar is a radar with all-day and all-weather imaging capabilities, which overcomes the shortcomings of optical and infrared imaging systems that cannot be imaged at night when there is a lack of light or in bad weather. However, traditional SAR can only provide short-term imaging results of the observation scene, and cannot achieve long-term continuous observation of the scene, which is not conducive to monitoring moving targets such as vehicles, that is, to achieve continuous detection and tracking of moving targets. In order to overcome this defect, video SAR came into being. Different from the traditional SAR system that only obtains a single-frame image of the scene, video SAR continuously observes the observation scene, can obtain images of multiple time frames of the scene, and obtain video imaging results of the observation area, so as to further monitor the moving targets in the scene for a long time, which is conducive to the continuous changes in the motion state of the observation target. It has significant application value in fields such as traffic flow monitoring in the civilian field and detection of important hostile targets in the military field.

[0003] In the video SAR imaging results, there are two response manifestations of moving targets in the video. The first is the response manifestation generated by the target itself, specifically, there is an offset in the distance position and defocus blur in the azimuth direction in each frame of the video; the second is the response manifestation of the shadow generated by the target blocking the ground. Unlike the former, the generated shadow does not have offset and defocus, so it can reflect the true position of the moving target. At present, for the detection and tracking of moving targets in video SAR imaging results, in order to obtain higher detection and tracking accuracy, the detection and tracking of related moving targets is mainly achieved through the detection and tracking of shadow areas.

[0004] However, unlike the target which usually has strong scattering energy, the shadow energy generated by the occlusion mechanism is relatively weak, which is easily confused with the background with lower scattering energy around it, and may also be submerged by the energy of noise, resulting in loss of accuracy in shadow detection and tracking. Therefore, in order to improve the accuracy of shadow detection and tracking, it can be achieved by enhancing the shadow, that is, it is necessary to propose an effective video SAR shadow enhancement method.

[0005] The existing video SAR shadow enhancement method mainly adopts the shadow enhancement method based on histogram equalization, which is mainly applicable to optical images. However, due to the large difference between the video SAR system and the optical photography system, the imaging result data of the two are very different. Therefore, the current method can only play a limited role in video SAR shadow enhancement, and has limited improvement on the accuracy of shadow detection and tracking. In order to achieve better video SAR shadow enhancement effect, the present invention proposes a video SAR shadow enhancement method based on multi-component decomposition. Summary of the invention

[0006] The present invention proposes a video SAR shadow enhancement method based on multi-component decomposition. The method realizes the decomposition of shadow, background and noise components in input video SAR data by iterative solution. In each iteration, firstly, an L1 norm regularized denoising equation based on shadow component is established, and the shadow component matrix is ​​updated by solving the equation; then, a nuclear norm regularized denoising equation based on background component is established, and the background component matrix is ​​updated by solving the equation; secondly, a Fibonacci norm regularized denoising equation based on noise component is established, and the noise component matrix is ​​updated by solving the equation; finally, whether to stop iteration is determined according to the relative change between the shadow component updated in this iteration and the shadow component updated in the last iteration. When the relative change is greater than a threshold, the iteration is continued, and when it is less than the threshold, the iteration is stopped, and the latest updated shadow component is output as the video SAR shadow enhancement result. Compared with the shadow enhancement method based on histogram equalization, the shadow enhancement result of the method of the present invention has a higher shadow-background contrast, a more complete shadow contour feature, and a better shadow enhancement effect.

[0007] In order to facilitate the description of the present invention, the following terms are first defined:

[0008] Definition 1. Synthetic Aperture Radar

[0009] Synthetic Aperture Radar (SAR) is a high-resolution microwave imaging radar that obtains high-resolution and high-precision microwave images through signal processing. It has the advantages of working all day and all weather, and has been widely used in various fields, such as terrain mapping, guidance, environmental remote sensing and resource exploration. For details, see "Pi Yiming, Yang Jianyu, Fu Yusheng, Yang Xiaobo. Principles of Synthetic Aperture Radar Imaging [M]. University of Electronic Science and Technology Press. 2007".

[0010] Definition 2. Video SAR Data

[0011] Video SAR data refers to the data obtained by the video SAR system after the imaging processing algorithm and image registration algorithm are processed. Its characteristics are that it contains the two-dimensional imaging results of multiple time frames, and the static targets in the scene have the same spatial position in the two-dimensional imaging results of different time frames. Video SAR data has three dimensions: I x×y× z represents, where x represents the number of rows of a single-frame two-dimensional imaging result, y represents the number of columns of a single-frame image, and z represents the number of time frames. For details, see "Bao J, Zhang X, Zhang T, et al. ShadowDeNet: A Moving Target Shadow Detection Network for VideoSAR[J]. Remote Sensing, 2022, 14(2): 320".

[0012] Definition 3. Shadow, background and noise components in video SAR data

[0013] Video SAR data contains three main components: shadow, background and noise. The shadow component is the imaging result produced by the occlusion of moving targets during radar imaging. Its characteristics include the same position as the moving target, low energy and close to the energy of noise, showing a dim shadow appearance in a single-frame two-dimensional imaging result, and the position changes continuously in multi-frame two-dimensional imaging results, and the multi-frame positions are consistent with the target motion trajectory in chronological order; the background component is the imaging result produced by static background objects such as roads, grass and trees during radar imaging. Its characteristics include that the energy is usually higher than the shadow and noise energy, and the position remains basically stable in multi-frame two-dimensional imaging results; the noise component is the imaging result produced by the system's own internal noise, coherent accumulation of adjacent scattering units and other factors during radar imaging. Its characteristics include multiplicative noise characteristics in the complex domain and additive Gaussian characteristics in the amplitude logarithmic domain. For details, see "Bao J, Zhang X, ZhangT, et al. ShadowDeNet: A Moving Target Shadow Detection Network for Video SAR[J]. Remote Sensing, 2022, 14(2): 320".

[0014] Definition 4. Traditional Matrix Vectorization Operator Method

[0015] The matrix vectorization operator vec(A) method refers to an operation method that arranges each column of the input matrix A in columns to form a column vector. Specifically, the matrix vectorization operator arranges each column of an m×n matrix A from left to right to form a column vector vec(A):

[0016] vec(A)=[a1，1 …a m，1 a 1，2 …a m，2 a 1，n …a m，n ] T

[0017] where a i，j A(i, j) represents the element in the i-th row and j-th column of matrix A; the superscript T represents the matrix transpose operation. For details on the traditional matrix vectorization operator method, please refer to "Zhang Xianda. Matrix Analysis and Applications [M]. Tsinghua University Press Co., Ltd., 2004".

[0018] Definition 5. Traditional vector matrix diagonal operator method

[0019] The traditional vector matrix diagonal operator diag(a) method refers to an operation method that generates a matrix A with an input vector a, and the diagonal elements of A are composed of vector a. Specifically, the vector matrix diagonal operator constructs the diagonal elements of the matrix A from top to bottom by the elements of a column vector a with a dimension of n×1 in order from top to bottom, and the other elements of the matrix are 0. diag(a) is expressed as:

[0020]

[0021] where a i , i = 1, 2, 3, ... N represents the i-th element of a. For details of the traditional vector matrix diagonal operator method, please refer to "Zhang Xianda. Matrix Analysis and Applications [M]. Tsinghua University Press Co., Ltd., 2004".

[0022] Definition 6. Traditional element-wise signed operator method

[0023] sign(·) represents the element-wise sign operator, which finds the sign of each element of a matrix or vector. The calculation formula is as follows:

[0024] For matrices: For vectors: where x ij is the element in the i-th row and j-th column of the matrix, |x| ij Indicates the amplitude value of the element; x i is the i-th element of the vector, |x| iRepresents the amplitude value of the element. For details on the traditional element-by-element sign operator method, see "Wang Y, He Z, Yang F, et al. 3D SparseSAR Image Reconstruction Based on Cauchy Penalty and Convex Optimization [J]. Remote Sensing, 2022, 14 (10): 2308".

[0025] Definition 7. Traditional element-wise hard threshold operator method

[0026] thr(·) represents the matrix or vector element-by-element hard threshold operator, which calculates the hard threshold for each element of the matrix or vector, that is, if the amplitude value of the element is less than 0, the element is changed to 0, otherwise it remains unchanged. For details of the traditional element-by-element hard threshold operator method, please refer to "Wang Y, He Z, Yang F, et al. 3D Sparse SAR Image Reconstruction Based on Cauchy Penalty and Convex Optimization [J]. Remote Sensing, 2022, 14 (10): 2308".

[0027] Definition 8. Traditional singular value decomposition method

[0028] The traditional singular value decomposition method is an important matrix decomposition method in linear algebra. Performing singular value decomposition on a matrix A can obtain the equation A = Udiag(σ(A))V H , where U and V H For the left singular matrix and the right singular matrix of the matrix, σ(A) is the singular value vector formed by the singular values ​​of the matrix, and diag(σ(A)) is the singular value matrix formed by the singular value vector σ(A) through the vector matrix diagonal operator in Definition 5. For details of the traditional singular value decomposition method, please refer to "Zhang Xianda. Matrix Analysis and Applications [M]. Tsinghua University Press Co., Ltd., 2004".

[0029] Definition 9. Traditional video SAR shadow enhancement method based on histogram equalization

[0030] The video SAR shadow enhancement method based on histogram equalization adjusts the histogram of each frame of the two-dimensional imaging result of the video SAR data to make it tend to be balanced, so as to achieve contrast enhancement and thus enhance the shadow. For details of the traditional video SAR shadow enhancement method based on histogram equalization, please refer to "Jinyu Bao, Xiaoling Zhang, Tianwen Zhang, Xiaowo Xu. ShadowDeNet: A Moving Target Shadow Detection Network for Video SAR[J]. RemoteSensing, 2022, 14(2)".

[0031] The present invention provides a SAR shadow enhancement method based on multi-component decomposition video, which is characterized by comprising the following steps:

[0032] Step 1. Initialize relevant parameters

[0033] The number of pixels in the azimuth direction of a single frame of two-dimensional imaging result of video SAR data is recorded as N a ; The number of pixels in the range direction of a single frame of two-dimensional imaging result of video SAR data, denoted as N r , the number of video SAR data frames, denoted as N t ; The video SAR data to be enhanced by shadow is recorded as The shadow component initialization matrix is ​​denoted as S(0); the background component initialization matrix is ​​denoted as B(0); the noise component initialization matrix is ​​denoted as N(0); the Lagrange multiplier initialization matrix is ​​denoted as Y(0); the background decomposition weight coefficient is denoted as ξ; the noise decomposition weight coefficient is denoted as γ; the iterative convergence threshold is denoted as ε.

[0034] Step 2. Timeframe rearrangement

[0035] The video SAR data obtained by step 1 initialization Each frame in is rearranged into a column vector using the traditional matrix vectorization operator method described in Definition 4, denoted as d(i), and the dimension of the vector is (N a ×N r )×1, i=1, 2, ..., N t , N t is the number of video SAR data frames, and then the column vectors corresponding to each frame are arranged from left to right in frame order to form a video SAR matrix

[0036] Step 3. Establish the three-component decomposition equation of shadow, background and noise

[0037] Based on the video SAR data to be shadow enhanced obtained by initialization in step 2 The background decomposition weight coefficient ξ and the noise decomposition weight coefficient γ are used to establish the three-component decomposition equation of shadow, background and noise.

[0038]

[0039] where argmin B，S，N，Y Indicates Take the minimum value of B, S, N and Y, where B, S, N and Y are the background component, target component, noise component and Lagrange multiplier matrix respectively; ||·||1 represents the L1 norm of the matrix, ||·|| * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm, Tr(·) represents the matrix trace, (·) H Represents matrix transpose conjugate.

[0040] Step 4. Iterative decomposition of shadow, background and noise components

[0041] According to the noise decomposition weight coefficient γ, background decomposition weight coefficient ξ and iterative convergence threshold ε initialized in step 1, the three-component decomposition equation of shadow, background and noise established in step 3 is solved iteratively to achieve iterative decomposition of the three components of shadow, background and noise. In the kth iteration, the following steps are performed:

[0042] Step 4.1. Establish the denoising equation based on the L1 norm regularization of the shadow component:

[0043]

[0044] O=DB(k-1)-N(k-1)+Y(k-1)

[0045] where argmin s Indicates Take the minimum value of S, where S is the shadow component and O is the noisy shadow component; ||·||1 represents the matrix L1 norm, represents the square of the matrix Fibonacci norm; D, B(k-1), N(k-1) and Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the background component matrix, the noise component matrix and the Lagrange multiplier matrix obtained in the k-1th iteration, respectively.

[0046] Step 4.2 Shadow component decomposition:

[0047] According to the shadow component L1 norm regularization denoising equation established in step 4.1, the shadow component decomposition is achieved using the following formula.

[0048]

[0049] O=DB(k-1)-N(k-1)+Y(k-1)

[0050] where sign(·) is the element-wise sign operator defined in Definition 6, thr(·) is the element-wise hard threshold operator defined in Definition 7, and ⊙ represents the matrix Hadamard product; The dimension is (N a ×N r )×N t The matrix whose elements are all 1. O is the noisy shadow component, D, B(k-1), N(k-1) and Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the background component matrix obtained in the k-1th iteration, the noise component matrix and the Lagrange multiplier matrix. S(k) is the shadow component matrix updated in the kth iteration.

[0051] Step 4.3. Establish a regularized denoising equation based on the background component nuclear norm:

[0052]

[0053] P=DN(k-1)-S(k)+Y(k-1)

[0054] where argmin B Indicates Take the minimum value of B, where B is the background component and P is the noisy background component; ||·|| * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm; D, N(k-1), and Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the noise component matrix and the Lagrange multiplier matrix obtained in the k-1th iteration, respectively; S(k) is the updated shadow component matrix obtained in step 4.2; ξ is the background decomposition weight coefficient.

[0055] Step 4.4 Background component decomposition:

[0056] According to the background component nuclear norm regularization denoising equation established in step 4.3, the background component decomposition is achieved using the following formula.

[0057] B(k)=U·M·V H

[0058]

[0059] Y=diag(σ(P))

[0060] P=DN(k-1)-S(k)+Y(k-1)

[0061] Where P is the noisy background component, U and V are the left singular matrix and right singular matrix obtained by decomposing P according to the matrix singular value defined in Definition 8; V H represents the conjugate transpose of V; Y is the singular value matrix of P, σ(P) is the singular value vector of P, ξ is the background decomposition weight coefficient, The dimension is (N a ×N r )×N t The matrix whose elements are all 1, sign(·) is the element-wise sign operator defined in Definition 6, thr(·) is the element-wise hard threshold operator defined in Definition 7, diag(·) is the vector matrix diagonal operator defined in Definition 5, ⊙ represents the matrix Hadamard product, M is the singular value matrix after denoising, and ξ is the background decomposition weight coefficient. D, N(k-1), Y(k-1) are the video SAR data to be enhanced by shadows initialized in step 2, the noise component matrix obtained in the k-1th iteration, and the Lagrange multiplier matrix, respectively. S(k) is the updated shadow component matrix obtained in step 4.2. B(k) is the background component matrix updated in the kth iteration.

[0062] Step 4.5. Establish a denoising equation based on the Fibonacci norm regularization of the noise component:

[0063]

[0064] Q=DB(k)-S(k)+Y(k-1)

[0065] where argmin N Indicates Take the minimum value of N, where N is the noise component and Q is the noise component containing error; represents the square of the matrix Fibonacci norm; D is the video SAR data to be shadow enhanced initialized in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, B(k) and S(k) are the background component matrix and shadow component matrix updated in the kth iteration obtained in steps 4.2 and 4.4, respectively, and γ is the noise decomposition weight coefficient.

[0066] Step 4.6 Noise component decomposition:

[0067] According to the Fibonacci norm regularization denoising equation established in step 4.5, the noise component decomposition is achieved using the following formula.

[0068] N(k)=(1+2γ) -1 Q

[0069] Q=DB(k)-S(k)+Y(k-1)

[0070] Where γ is the noise decomposition weight coefficient. Q is the noise component containing errors, D is the video SAR data to be shadow enhanced initialized in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, B(k) and S(k) are the background component matrix and shadow component matrix updated in the kth iteration obtained in step 4.2 and step 4.4, respectively. N(k) is the noise component matrix updated in the kth iteration.

[0071] Step 4.7. Use the following formula to update the Lagrange multiplier matrix:

[0072] Y(k)=Y(k-1)+DB(k)-S(k)-N(k)

[0073] Y(k) is the Lagrange multiplier matrix updated in the k-th iteration. Y(k-1) is the Lagrange multiplier matrix updated in the k-1-th iteration. D is the video SAR data to be shadow enhanced initialized in step 2. B(k), S(k) and N(k) are the background component matrix, shadow component matrix and noise component matrix updated in the k-th iteration obtained in steps 4.2, 4.4 and 4.6 respectively.

[0074] Step 4.8. Iteration stop judgment:

[0075] Using the formula d(k) = ||(S(k)-S(k-1)) / S(k-1)|| F , the relative change rate of the shadow component d(k) is calculated, where S(k) and S(k-1) are the shadow component matrices updated in the kth and k-1th iterations, respectively, ||·|| F Represents the matrix Fibonacci norm.

[0076] If d(k)≥ε, repeat the steps and proceed to the next iteration; otherwise, stop the iteration. At this time, S(k) is the final video SAR shadow enhancement result, where ε is the iteration convergence threshold.

[0077] The innovation and advantage of the present invention lies in that: a video SAR shadow enhancement method different from the one based on histogram equalization is adopted, shadow enhancement is realized from the innovative perspective of image component decomposition, video SAR data is regarded as a combination of shadow component, background component and noise component, and video SAR shadow enhancement is realized by an iterative decomposition method; the advantage of the present method lies in that the characteristics of video SAR data are fully considered, and the characteristics of shadow component, background component and noise component in video SAR data are respectively characterized by using L1 norm, nuclear norm and Fibonacci norm, so that the decomposition is more accurate, and a more significant shadow enhancement effect can be achieved than that based on the histogram equalization method, which is helpful for the subsequent application of video SAR data, such as target shadow detection and tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 This is the flow chart of the present invention

[0079] Figure 2 The simulation experiment verification result of the present invention is DETAILED DESCRIPTION

[0080] The present invention is mainly verified by simulation experiment method, and all steps and conclusions are verified correct on the mathematical calculation software Matlab2019b. The specific implementation steps are as follows:

[0081] Step 1. Initialize relevant parameters

[0082] The number of pixels N in the azimuth direction of a single frame of two-dimensional imaging results of video SAR data a =512; Number of pixels in the range direction of a single frame of two-dimensional imaging result of video SAR data N r =512, number of video SAR data frames N r =128; Video SAR data to be enhanced by shadow D 512×512×128 ; Shadow component initialization matrix Indicates that the dimension is 512 2 ×100 matrix with all elements set to 0; background component initialization matrix Noise component initialization matrix Lagrange multiplier initialization matrix Background decomposition weight coefficient ξ=1; noise decomposition weight coefficient γ=0.5; iterative convergence threshold ε=0.001.

[0083] Step 2. Timeframe rearrangement

[0084] The video SAR data D obtained by step 1 initialization 512×512×128 Each frame in is rearranged into a column vector d(i) by the matrix vectorization operator described in Definition 4, and the dimension of the vector is 512 2×1, i = 1, 2, ..., 100. Then the column vectors corresponding to each frame are arranged from left to right in frame order to form a video SAR matrix

[0085] Step 3. Establish the three-component decomposition equation of shadow, background and noise

[0086] The video SAR data to be enhanced by shadows obtained by initialization in step 2 The background decomposition weight coefficient ξ=1 and the noise decomposition weight coefficient γ=0.5, and the decomposition equation of the three components of shadow, background and noise is established.

[0087]

[0088]

[0089] where argmin B，s，N，Y Indicates Take the minimum value of B, S, N and Y, where B, S, N and Y are the background component, target component, noise component and Lagrange multiplier matrix respectively; ||·||1 represents the L1 norm of the matrix, ||·|| * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm, Tr(·) represents the matrix trace, (·) H Represents matrix transpose conjugate.

[0090] Step 4. Iterative decomposition of shadow, background and noise components

[0091] With the noise decomposition weight coefficient γ=0.5, the background decomposition weight coefficient ξ=1 and the iterative convergence threshold ε=0.001 initialized in step 1, the three-component decomposition equation of shadow, background and noise established in step 3 is solved by iteration to achieve the three-component decomposition of shadow, background and noise. The following steps are performed in k iterations:

[0092] Step 4.1. Establish the denoising equation based on the L1 norm regularization of the shadow component:

[0093]

[0094] O=DB(k-1)-N(k-1)+Y(k-1)

[0095] where argmin S Indicates Take the minimum value of S, where S is the shadow component and O is the noisy shadow component; ||·||1 represents the matrix L1 norm, represents the square of the matrix Fibonacci norm; B(k-1), N(k-1) and Y(k-1) are the background component matrix, noise component matrix and Lagrange multiplier matrix obtained in the k-1th iteration respectively.

[0096] Step 4.2 Shadow component decomposition:

[0097] According to the shadow component L1 norm regularization denoising equation established in step 4.1, the formula

[0098]

[0099] O=DB(k-1)-N(k-1)+Y(k-1)

[0100] where sign(·) is the element-wise sign operator defined in Definition 6, thr(·) is the element-wise hard threshold operator defined in Definition 7, and ⊙ represents the matrix Hadamard product; Indicates that the dimension is 512 2 ×100 matrix with all elements being 1. O is the noisy shadow component, D, B(k-1), N(k-1) and Y(k-1) are the video SAR data to be enhanced by shadows initialized in step 2, the background component matrix obtained in the k-1th iteration, the noise component matrix and the Lagrange multiplier matrix. S(k) is the shadow component matrix updated in the kth iteration.

[0101] Step 4.3. Establish a regularized denoising equation based on the background component nuclear norm:

[0102]

[0103] P=DN(k-1)-S(k)+Y(k-1)

[0104] where argmin B Indicates Take the minimum value of B, where B is the background component and P is the noisy background component; ||·|| * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm; D, N(k-1), Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the noise component matrix and the Lagrange multiplier matrix obtained in the k-1th iteration, respectively; S(k) is the updated shadow component matrix obtained in step 4.2.

[0105] Step 4.4 Background component decomposition:

[0106] According to the background component nuclear norm regularization denoising equation established in step 4.3, the formula

[0107] B(k)=U·M·V H

[0108]

[0109] Y=diag(σ(P))

[0110] P=DN(k-1)-S(k)+Y(k-1)

[0111] Among them, P is the noisy background component, U and V H are the left singular matrix and the right singular matrix obtained by decomposing the matrix P according to Definition 8; V H represents the conjugate transpose of V; Y is the singular value matrix of P, σ(P) is the singular value vector of P, The dimension is The matrix whose elements are all 1, sign(·) is the element-wise sign operator defined in Definition 6, thr(·) is the element-wise hard threshold operator defined in Definition 7, diag(·) is the vector matrix diagonal operator defined in Definition 5, ⊙ represents the matrix Hadamard product, and M is the denoised singular value matrix. D, N(k-1), and Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the noise component matrix obtained in the k-1th iteration, and the Lagrange multiplier matrix, respectively. S(k) is the updated shadow component matrix obtained in step 4.2. B(k) is the background component matrix required for updating in the kth iteration.

[0112] Step 4.5. Establish a denoising equation based on the Fibonacci norm regularization of the noise component:

[0113]

[0114] Q=DB(k)-S(k)+Y(k-1)

[0115] where argmin N Indicates Take the minimum value of N, where N is the noise component and Q is the noise component containing error; represents the square of the matrix Fibonacci norm; D is the video SAR data to be shadow enhanced initialized in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, B(k) and S(k) are the background component matrix and shadow component matrix updated in the kth iteration obtained in step 4.2 and step 4.4, respectively.

[0116] Step 4.6 Noise component decomposition:

[0117] According to the Fibonacci norm regularization denoising equation based on the noise component established in step 4.5, the formula

[0118]

[0119] Q=DB(k)-S(k)+Y(k-1)

[0120] Where Q is the noise component containing errors, D is the video SAR data to be shadow enhanced initialized in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, B(k) and S(k) are the background component matrix and shadow component matrix updated in the kth iteration obtained in steps 4.2 and 4.4, respectively. N(k) is the noise component matrix updated in the kth iteration.

[0121] Step 4.7. Lagrange multiplier matrix update:

[0122] Y(k)=Y(k-1)+DB(k)-S(k)-N(k)

[0123] Y(k) is the Lagrange multiplier matrix updated in the k-th iteration. Y(k-1) is the Lagrange multiplier matrix updated in the k-1-th iteration. D is the video SAR data to be shadow enhanced initialized in step 2. B(k), S(k) and N(k) are the background component matrix, shadow component matrix and noise component matrix updated in the k-th iteration obtained in steps 4.2, 4.4 and 4.6 respectively.

[0124] Step 4.8. Iteration stop judgment:

[0125] According to the formula d(k) = ||(S(k)-S(k-1)) / S(k-1)|| F Calculate the relative change rate of the shadow component d(k), where S(k) and S(k-1) are the shadow component matrices updated in the kth and k-1th iterations, ||·|| F represents the matrix Fibonacci norm. If d(k)≥0.001, repeat step 3 and continue to the next iteration; otherwise, stop the iteration, and S(k) is the final video SAR shadow enhancement result. The computer simulation results are Figure 2 shown.

[0126] Computer simulation results show that the present invention enhances the shadow of video SAR data by decomposing shadow, background and noise. Compared with the histogram equalization enhancement method, the shadow enhancement result of the present invention has a higher shadow-background contrast, more complete shadow contour features and better shadow enhancement effect.

Claims

1. A method for SAR shadow enhancement based on multi-component decomposition video, characterized in that it The following steps are involved: Step 1. Initialize relevant parameters The number of pixels in the azimuth direction of a single frame of two-dimensional imaging result of video SAR data is recorded as N a ; The number of pixels in the range direction of a single frame of two-dimensional imaging result of video SAR data, denoted as N r , the number of video SAR data frames, denoted as N t ; The video SAR data to be shadow enhanced is denoted as The shadow component initialization matrix is ​​denoted as S(0); the background component initialization matrix is ​​denoted as B(0); the noise component initialization matrix is ​​denoted as N(0); the Lagrange multiplier initialization matrix is ​​denoted as Y(0); the background decomposition weight coefficient is denoted as ξ; the noise decomposition weight coefficient is denoted as γ; the iterative convergence threshold is denoted as ε; Step 2. Timeframe rearrangement The video SAR data initialized in step 1 Each frame in the image is rearranged into a column vector using the traditional matrix vectorization operator method, denoted as d(i), and the dimension of the vector is (N a ×N r )×1, i=1, 2, …, N t , N t is the number of video SAR data frames, and then the column vectors corresponding to each frame are arranged from left to right in frame order to form a video SAR matrix Step 3. Establish the three-component decomposition equation of shadow, background and noise Based on the video SAR data to be enhanced by shadows obtained by initialization in step 2 The background decomposition weight coefficient ξ and the noise decomposition weight coefficient γ are used to establish the three-component decomposition equation of shadow, background and noise; where argmin B,S,N,Y Indicates Take the minimum value of B, S, N and Y, where B, S, N and Y are the background component, target component, noise component and Lagrange multiplier matrix respectively; ‖·‖1 represents the L1 norm of the matrix, ‖·‖ * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm, Tr(·) represents the matrix trace, (·) H represents the matrix transpose conjugate; Step 4. Iterative decomposition of shadow, background and noise components According to the noise decomposition weight coefficient γ, background decomposition weight coefficient ξ and iterative convergence threshold ε initialized in step 1, the three-component decomposition equation of shadow, background and noise established in step 3 is solved iteratively to achieve iterative decomposition of the three components of shadow, background and noise. In the kth iteration, the following steps are performed: Step 4.

1. Establish the denoising equation based on the L1 norm regularization of the shadow component: O=DB(k-1)-N(k-1)+Y(k-1) where argmin S Indicates Take the minimum value of S, where S is the shadow component and O is the noisy shadow component; ‖·‖1 represents the matrix L1 norm, represents the square of the matrix Fibonacci norm; D, B(k-1), N(k-1) and Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the background component matrix, the noise component matrix and the Lagrange multiplier matrix obtained in the k-1th iteration, respectively; Step 4.2 Shadow component decomposition: According to the shadow component L1 norm regularization denoising equation established in step 4.1, the shadow component decomposition is achieved using the following formula; O=DB(k-1)-N(k-1)+Y(k-1) where sign(·) is the element-wise sign operator, thr(·) is the element-wise hard threshold operator, and ⊙ represents the matrix Hadamard product; The dimension is (N a ×N r )×N t The matrix whose elements are all 1; O is the noisy shadow component, D, B(k-1), N(k-1) and Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the background component matrix, the noise component matrix and the Lagrange multiplier matrix obtained in the k-1th iteration respectively; S(k) is the shadow component matrix updated in the kth iteration; Step 4.

3. Establish a regularized denoising equation based on the background component nuclear norm: P=DN(k-1)-S(k)+Y(k-1) where argmin B Indicates Take the minimum value of B, where B is the background component and P is the noisy background component; ‖·‖ * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm; D, N(k-1), Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the noise component matrix and the Lagrange multiplier matrix obtained in the k-1th iteration, respectively; S(k) is the updated shadow component matrix obtained in step 4.2; ξ is the background decomposition weight coefficient; Step 4.4 Background component decomposition: According to the background component nuclear norm regularization denoising equation established in step 4.3, the background component decomposition is achieved using the following formula; B(k)=U·M·V H Y=diag(σ(P)) P=DN(k-1)-S(k)+Y(k-1) Where P is the noisy background component, U and V are the left singular matrix and right singular matrix obtained by the traditional matrix singular value decomposition method for P; V H represents the conjugate transpose of V; Y is the singular value matrix of P, σ(P) is the singular value vector of P, ξ is the background decomposition weight coefficient, The dimension is (N a ×N r )×N t The matrix whose elements are all 1, sign(·) is the element-by-element sign operator, thr(·) is the element-by-element hard threshold operator, diag(·) is the vector matrix diagonal operator, ⊙ represents the matrix Hadamard product, M is the singular value matrix after denoising, ξ is the background decomposition weight coefficient; D, N(k-1), Y(k-1) are the video SAR data to be shadow enhanced initialized in step 2, the noise component matrix obtained in the k-1th iteration and the Lagrange multiplier matrix, respectively, S(k) is the updated shadow component matrix obtained in step 4.2; B(k) is the background component matrix updated in the kth iteration; Step 4.

5. Establish a denoising equation based on the Fibonacci norm regularization of the noise component: Q=DB(k)-S(k)+Y(k-1) where argmin N Indicates Take the minimum value of N, where N is the noise component and Q is the noise component containing error; represents the square of the matrix Fibonacci norm; D is the video SAR data to be shadow enhanced initialized in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, B(k) and S(k) are the background component matrix and shadow component matrix updated in the kth iteration obtained in steps 4.2 and 4.4, respectively, and γ is the noise decomposition weight coefficient; Step 4.6 Noise component decomposition: According to the Fibonacci norm regularization denoising equation established in step 4.5, the noise component decomposition is achieved using the following formula; N(k)=(1+2γ) -1 Q Q=DB(k)-S(k)+Y(k-1) Where γ is the noise decomposition weight coefficient; Q is the noise component containing errors, D is the video SAR data to be shadow enhanced initialized in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, B(k) and S(k) are the background component matrix and shadow component matrix updated in the kth iteration obtained in steps 4.2 and 4.4 respectively; N(k) is the noise component matrix updated in the kth iteration; Step 4.

7. Use the following formula to update the Lagrange multiplier matrix: Y(k)=Y(l-1)+DB(k)-S(k)-N(k) Y(k) is the Lagrange multiplier matrix updated in the k-th iteration; Y(k-1) is the Lagrange multiplier matrix updated in the k-1-th iteration; D is the video SAR data to be shadow enhanced initialized in step 2, B(k), S(k) and N(k) are the background component matrix, shadow component matrix and noise component matrix updated in the k-th iteration obtained in steps 4.2, 4.4 and 4.6 respectively; Step 4.

8. Iteration stop judgment: Using the formula d(k) = ‖(S(k)-S(k-1)) / S(k-1)‖ F , the relative change rate of the shadow component d(k) is calculated, where S(k) and S(k-1) are the shadow component matrices updated in the kth and k-1th iterations, ‖·‖ F represents the matrix Fibonacci norm; If d(k)≥ε, repeat the steps and proceed to the next iteration; Otherwise, the iteration is stopped. At this time, S(k) is the final video SAR shadow enhancement result, where ε is the iteration convergence threshold.

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