Sparse SAR imaging method and system based on non-convex-non-local total variation regularization

Abstract

The present disclosure provides a sparse SAR imaging method based on non-convex-nonlocal total variation regularization, including: introducing non-convex penalty terms and non-local total variation norm penalty terms in the sparse SAR imaging model to construct a sparse SAR imaging model based on non-convex-nonlocal total variation regularization; using improved variable separation and alternating direction multiplier method to solve the sparse SAR imaging model based on non-convex-nonlocal total variation regularization to complete SAR imaging. The present disclosure also provides a sparse SAR imaging system, electronic device, storage medium and computer program product based on non-convex-nonlocal total variation regularization.

Description

Technical Field

[0001] The present disclosure relates to the field of radar imaging technology, and in particular to a sparse SAR imaging method and system based on non-convex-non-local total variation regularization. Background Art

[0002] Synthetic aperture radar (SAR) is an active microwave imaging system with the characteristics of all-day, all-weather and high-resolution imaging. It is widely used in environmental monitoring and land resource management. With the development of SAR technology, the resolution and mapping bandwidth of radar systems are required to be continuously improved, and the bottleneck of large data volume is becoming more and more obvious. Sparse SAR imaging is a new system that uses sparse signal processing methods to achieve SAR imaging. In the past decade, with the development of compressed sensing technology, this new imaging system has been widely studied.

[0003] The SAR imaging method based on L1 regularization can effectively suppress noise and clutter and improve image quality under full sampling conditions; under the condition of downsampling rate, it can effectively reconstruct SAR images and maintain target details. L1 regularization can enhance the point target features in SAR images; total variation (TV) regularization can enhance the surface target features in SAR images and maintain the continuity and uniformity of the surface target backscattering coefficient. A simple linear combination of the L1 norm penalty term and the TV norm penalty term generates a composite penalty function, and the L1-TV regularization model can be obtained. This model can enhance both point target features and surface target features. However, L1-TV regularization has the following two problems: 1) The L1 regularization method is a convex optimization method, which underestimates the amplitude of the SAR reconstructed target, causing errors at the signal processing end, and thus affecting the accuracy of SAR calibration; 2) TV regularization will over-smooth isolated point targets in the scene, resulting in a contradiction between enhancing surface target features and maintaining point target reconstruction accuracy. Summary of the invention

[0004] To solve the problems existing in the prior art, the embodiments of the present invention provide a sparse SAR imaging method, system, electronic device, storage medium and program product based on non-convex-nonlocal total variation regularization. Compared with the prior art, this method can effectively suppress additive noise and clutter, enhance point target features, suppress speckle noise and maintain the continuity and uniformity of the backscattering coefficient of the surface target.

[0005] A first aspect of the present disclosure provides a sparse SAR imaging method based on non-convex-nonlocal total variation regularization, comprising: introducing a non-convex penalty term and a non-local total variation norm penalty term into a sparse SAR imaging model to construct a sparse SAR imaging model based on non-convex-nonlocal total variation regularization; solving the sparse SAR imaging model based on non-convex-nonlocal total variation regularization by using an improved variable separation and alternating direction multiplier method to complete SAR imaging.

[0006] Furthermore, the sparse SAR imaging model based on non-convex-non-local total variation regularization is as follows:

[0007]

[0008] Among them, λ1 and λ2 are Lagrange multipliers, y is the vectorization result of the two-dimensional echo, x is the vectorization result of the two-dimensional scene, Φ is the observation matrix corresponding to the vectorization of the two-dimensional echo and the two-dimensional scene, and p nonconvex (x) is a non-convex penalty term, p NLTV (|x|) is the non-local total variation norm penalty term.

[0009] Furthermore, the non-local total variation norm penalty term p NLTV (|x|) is defined as:

[0010]

[0011] Where X is the SAR two-dimensional scene image; i = (i1, i2), indicating the position of pixel i in image X; |X| i represents the element at position i in image X; means |X| i The non-local gradient vector, M NLTV Represents the matrix composed of the module of the non-local gradient vector of each pixel; where,

[0012]

[0013]

[0014] Where w(i, j) represents the non-local weight between pixel i and pixel j; j = (j1, j2), represents the position of pixel j in image X; |X| j represents the element at position j in image X; M NLTV，i Represents the matrix composed of the module of the non-local gradient vector of pixel i; N i (D) represents a window centered on i and of size D×D, where D is a real number.

[0015] Furthermore, the non-local weight w(i, j) between pixels i and j is defined as:

[0016]

[0017] in, represents the weighted Euclidean distance; a represents the standard deviation of the Gaussian kernel, and a>0; N i (d) represents a window centered on i and of size d×d, where d is a real number; N j (d) represents a window centered on j with a size of d×d; σ r represents the control parameter, and σ r >0.

[0018] Furthermore, the non-convex penalty term is defined as:

[0019]

[0020] Among them, p MC (x) represents a typical non-convex penalty term p nonconvex (x); x i represents the i-th element in x; p MC (x i ) represents the element x i The non-convex penalty term; θ represents the non-convex penalty term p MC (x i ) adjustment parameters; i and N are both positive integers, 1≤i≤N.

[0021] Furthermore, the improved variable separation and alternating direction multiplier method are used to solve the sparse SAR imaging method model based on non-convex-non-local total variation regularization to complete SAR imaging, including: initializing iterative parameters: radar echo is y, observation matrix is ​​Φ, radar scene is initialized as x 0 =0, intermediate variable z1 0 =0, z2 0 =0 and p i，j 0 = 0, Lagrangian multipliers λ1, λ2, augmented Lagrangian penalty parameter γ, non-local total variation regularization iteration step τ; set the maximum number of iterations to T max , set the initial value of the iteration step t = 0, the iteration termination condition ε; perform iteration, update the iteration parameters; calculate the iteration parameters.

[0022] Furthermore, the two-dimensional scene vectorization result x after iteration t+1 is updated (t+1) satisfy:

[0023]

[0024] Among them, x (t)represents the two-dimensional scene vectorization result after updating iterations t times; y is the two-dimensional echo vectorization result; Represents the gradient descent iteration step size; and Both represent intermediate parameters, H H Represents the conjugate transposed matrix of the intermediate variable H; G = [I T , I T ] T Represents x and auxiliary variable z = [z1 T , z2 T ]; I T represents the transposed matrix of the identity matrix I; z1 T With z2 T are the two components of the auxiliary variable z respectively; Represents the auxiliary variable z i Update the iteration result after t iterations; d represents the iteration variable of the alternating multiplier method, d (t) represents the iteration variable of the alternating multiplier method after updating the iteration t times, Indicates d (t) , where i is 1 and 2; Φ is the measurement matrix corresponding to the vectorized two-dimensional echo and two-dimensional scene; Φ H represents the conjugate transposed matrix of Φ.

[0025] Further, update z1 after iteration t+1 (t+1) satisfy:

[0026]

[0027] Among them, λ MC represents the non-convex penalty term p MC (x i ) regularized threshold, ψ MC (x i ,λ) represents the threshold function; p MC (z1) represents the non-convex penalty function of the auxiliary variable component z1; d1 represents the component 1 of the alternating multiplier iteration variable d, d1 (t) represents the iteration result after component d1 is updated t times; where,

[0028]

[0029] Among them, λ represents the threshold; x i represents the i-th element in x; θ represents the non-convex penalty term p MC (x i ) adjustment parameters.

[0030] Further, update z2 after iteration t+1 (t+1) satisfy:

[0031]

[0032] Where d2 represents the second component of the alternating multiplier iteration variable d; represents the iteration result after updating component 2 d2 for t times; p NLTV (|z2|) represents the non-local total variation norm penalty function of the auxiliary variable component z2; λ NLTV Indicates the threshold of NLTV regularization, div NLTV (·) represents the nonlocal divergence operator; p (t+1) To solve the auxiliary variables in the NLTV regularization process, ° represents the matrix Hadamard product.

[0033] Furthermore, the iteration parameters are calculated as:

[0034] res=||x (t+1) -x (t) ||2 / ||x (t) ||2

[0035] t=t+1

[0036] Among them, it is judged whether res>ε and t<T are satisfied at the same time max , if the conditions are not met at the same time, continue to iterate.

[0037] The second aspect of the present disclosure provides a sparse SAR imaging system based on non-convex-nonlocal total variation regularization, including: a SAR imaging model construction module, used to introduce non-convex penalty terms and non-local total variation norm penalty terms into the sparse SAR imaging model to construct a sparse SAR imaging model based on non-convex-nonlocal total variation regularization; a SAR imaging module, used to solve the sparse SAR imaging model based on non-convex-nonlocal total variation regularization by using improved variable separation and alternating direction multiplier method to complete SAR imaging.

[0038] The third aspect of the present disclosure provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the sparse SAR imaging method based on non-convex-non-local total variation regularization provided by the first aspect of the present disclosure is implemented.

[0039] The fourth aspect of the present disclosure provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the sparse SAR imaging method based on non-convex-non-local total variation regularization provided by the first aspect of the present disclosure is implemented.

[0040] A fifth aspect of the present disclosure provides a computer program product, comprising a computer program, which, when executed by a processor, implements the sparse SAR imaging method based on non-convex-non-local total variation regularization provided by the first aspect of the present disclosure.

[0041] The present invention discloses a sparse SAR imaging method, system, electronic device, storage medium and program product based on non-convex-non-local total variation regularization. The method first constructs an imaging model based on non-convex-non-local total variation regularization, and then solves the model using an improved variable separation-alternating direction multiplier method. Compared with the traditional matched filtering algorithm (Chirp Scaling), the method can effectively suppress additive noise and clutter, enhance point target features, and suppress speckle noise, and maintain the continuity and uniformity of the backscattering coefficient of the surface target. Compared with the L1-TV regularization method, the non-convex-non-local total variation regularization can effectively suppress the deviation effect caused by L1 regularization and improve the target reconstruction accuracy; and can avoid excessive smoothing of point targets by TV regularization, and can maintain the reconstruction accuracy of point targets while enhancing the features of surface targets, so as to achieve joint feature enhancement of point and surface targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] For a more complete understanding of the present disclosure and its advantages, reference will now be made to the following description taken in conjunction with the accompanying drawings, in which:

[0043] Figure 1 A flowchart of a sparse SAR imaging method based on non-convex-non-local total variation regularization according to an embodiment of the present disclosure is schematically shown;

[0044] Figure 2 A flowchart of sparse SAR imaging model iteration based on non-convex-non-local total variation regularization according to an embodiment of the present disclosure is schematically shown;

[0045] Figure 3 A comparison diagram of reconstruction results of simulation data using matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization is schematically shown;

[0046] Figures 4A to 4D A schematic diagram shows the comparison of the reconstructed slice analysis results of the simulation data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization, and non-convex-non-local total variation regularization;

[0047] Figure 5 The comparison diagram of the reconstruction results of Gaofen-3 data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization is schematically shown;

[0048] Figures 6A-6BThe figure schematically shows the comparison of the local imaging results of Gaofen-3 data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization;

[0049] Figures 7A to 7D The comparison diagram of the reconstructed slice analysis results of Gaofen-3 data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization, and non-convex-non-local total variation regularization is schematically shown;

[0050] Figure 8 A block diagram of a sparse SAR imaging system based on non-convex-non-local total variation regularization according to an embodiment of the present disclosure is schematically shown;

[0051] Fig. 9 A block diagram of a sparse SAR imaging system based on non-convex-non-local total variation regularization according to another embodiment of the present disclosure is schematically shown;

[0052] Fig.10 A block diagram of an electronic device suitable for implementing the method described above according to an embodiment of the present disclosure is schematically shown. DETAILED DESCRIPTION

[0053] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present disclosure. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present disclosure. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present disclosure.

[0054] The terms used herein are only for describing specific embodiments and are not intended to limit the present disclosure. The terms "comprise", "include", etc. used herein indicate the existence of the features, steps, operations and / or components, but do not exclude the existence or addition of one or more other features, steps, operations or components.

[0055] All terms (including technical and scientific terms) used herein have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification, and should not be interpreted in an idealized or overly rigid manner.

[0056] In the case of using expressions such as "at least one of A, B, and C, etc.", it should generally be interpreted in accordance with the meaning of the expression generally understood by those skilled in the art (for example, "a system having at least one of A, B, and C" should include but is not limited to a system having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, C, etc.). In the case of using expressions such as "at least one of A, B, or C, etc.", it should generally be interpreted in accordance with the meaning of the expression generally understood by those skilled in the art (for example, "a system having at least one of A, B, or C" should include but is not limited to a system having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, C, etc.).

[0057] Some block diagrams and / or flow charts are shown in the accompanying drawings. It should be understood that some boxes or combinations thereof in the block diagrams and / or flow charts can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that these instructions can create a device for implementing the functions / operations described in these block diagrams and / or flow charts when executed by the processor. The technology of the present disclosure can be implemented in the form of hardware and / or software (including firmware, microcode, etc.). In addition, the technology of the present disclosure can take the form of a computer program product on a computer-readable storage medium storing instructions, which can be used by an instruction execution system or used in conjunction with an instruction execution system.

[0058] The embodiment of the present disclosure provides a sparse SAR imaging method based on non-convex-nonlocal total variation regularization, comprising: introducing a non-convex penalty term and a non-local total variation norm penalty term into a sparse SAR imaging model to construct a sparse SAR imaging model based on non-convex-nonlocal total variation regularization; solving the sparse SAR imaging model based on non-convex-nonlocal total variation regularization by using an improved variable separation and alternating direction multiplier method to complete SAR imaging.

[0059] According to the embodiments of the present disclosure, an imaging model based on non-convex-non-local total variation regularization is first constructed, and then the model is solved using the improved variable separation-alternating direction multiplier method. Compared with the traditional matched filtering algorithm, this method can not only effectively suppress additive noise and clutter, enhance point target features, but also suppress speckle noise and maintain the continuity and uniformity of the backscattering coefficient of the surface target. Compared with the L1-TV regularization method, the non-convex-non-local total variation regularization can effectively suppress the deviation effect caused by L1 regularization and improve the target reconstruction accuracy; and can avoid the excessive smoothing of point targets by TV regularization, and can maintain the reconstruction accuracy of point targets while enhancing the features of surface targets, thereby achieving joint feature enhancement of point and surface targets.

[0060] Figure 1 The flowchart of the sparse SAR imaging method based on non-convex-non-local total variation regularization according to an embodiment of the present disclosure is schematically shown. Figure 1 As shown, the method includes: steps S101 to S102.

[0061] In operation S101, a non-convex penalty term and a non-local total variation norm penalty term are introduced into a sparse SAR imaging model to construct a sparse SAR imaging model based on non-convex-non-local total variation regularization.

[0062] In operation S102, the sparse SAR imaging model based on non-convex-non-local total variation regularization is solved by using an improved separation of variables and alternating direction multiplier method to complete SAR imaging.

[0063] The following will describe in detail the various steps of the sparse SAR imaging method based on non-convex-non-local total variation regularization of this embodiment. It should be understood that Figure 2 The principle diagrams and result schematic diagrams shown in 7 are merely exemplary to help those skilled in the art understand the technical solutions of the present disclosure, and are not intended to limit the protection scope of the present disclosure.

[0064] According to an embodiment of the present disclosure, before operation step S101, the method further includes: constructing a sparse SAR observation model, wherein the sparse SAR imaging model is constructed based on the sparse SAR observation model.

[0065] Specifically, according to the SAR geometric relationship, a sparse SAR two-dimensional observation model is constructed to satisfy:

[0066] Y=ΞX+N

[0067] Where Y is the SAR two-dimensional echo, X is the SAR two-dimensional scene image, Ξ is the observation matrix constructed according to the SAR observation geometry, and N is the two-dimensional additive noise.

[0068] The sparse SAR two-dimensional observation model is vectorized to obtain a one-dimensional observation model as follows:

[0069] y=Φx+n

[0070] Among them, y is the vectorization result of the two-dimensional echo, x is the vectorization result of the two-dimensional scene, Φ is the observation matrix corresponding to the vectorization of the two-dimensional echo and the two-dimensional scene, and n represents the vectorized additive noise.

[0071] In operation S101, a non-convex penalty term and a non-local total variation norm penalty term are introduced into the sparse SAR imaging model, and the constructed sparse SAR imaging model based on non-convex-non-local total variation regularization satisfies:

[0072]

[0073] Among them, λ1 and λ2 are Lagrange multipliers, p nonconvex (x) is a non-convex penalty term, p NLTV (|x|) is the non-local total variation norm penalty term.

[0074] In the embodiment of the present disclosure, a typical non-convex penalty term MC is defined as:

[0075]

[0076] Among them, p MC (x) represents a typical non-convex penalty term p nonconvex (x); x i represents the i-th element in x; p MC (x i ) represents the element x i The non-convex penalty term; θ represents the non-convex penalty term p MC (x i ) adjustment parameters; i and N are both positive integers, 1≤i≤N.

[0077] Non-local total variation norm penalty term p NLTV (|x|) is defined as:

[0078]

[0079] Where i = (i1, i2), represents the position of pixel i in image X; |X| i represents the element at position i in image X; means |X| i The non-local gradient vector, M NLTV Represents the matrix composed of the module of the non-local gradient vector of each pixel; where,

[0080]

[0081]

[0082] Where w(i, j) represents the non-local weight between pixel i and pixel j; |X| j represents the element at position j in image X; j = (j1, j2), represents the position of pixel j in image X; M NLTV，i Represents the matrix composed of the module of the non-local gradient vector of pixel i; N i (D) represents a window centered on i and of size D×D, where D is a real number.

[0083] The non-local weight w(i, j) between pixel i and pixel j is defined as:

[0084]

[0085] in, represents the weighted Euclidean distance; a represents the standard deviation of the Gaussian kernel, and a>0; N i (d) represents a window centered on i and of size d×d, where d is a real number; N j (d) represents a window centered on j with a size of d×d; σ r represents the control parameter, and σ r >0.

[0086] In operation S102, the sparse SAR imaging model based on non-convex-non-local total variation regularization is solved by using an improved variable separation and alternating direction multiplier method to complete SAR imaging, such as Figure 2 As shown, specifically including:

[0087] In operation S201, the iteration parameters are initialized: the radar echo is y, the observation matrix is ​​Φ, and the radar scene is initialized as x. 0 =0, intermediate variable z1 0 =0, z2 0 =0 and p i，j 0 = 0, Lagrangian multipliers λ1, λ2, augmented Lagrangian penalty parameter γ, non-local total variation regularization iteration step τ; set the maximum number of iterations to T max , let the initial value of the iteration step t = 0, and the iteration termination condition ε.

[0088] In operation S202, iteration is performed and iteration parameters are updated.

[0089] In the embodiment of the present disclosure, the specific updated parameters include: the two-dimensional scene vectorization result x (t+1) 、Intermediate variable z1 (t+1) 、z2 (t+1) and (t+1) .

[0090] Among them, the two-dimensional scene vectorization result x after updating iteration t+1 times (t+1) satisfy:

[0091]

[0092] Wherein, the superscript (t+1) indicates the current iteration step number, and t is a positive integer; G = [I T , I T ] T Represents x and auxiliary variable z = [z1 T , z2 T ]; I Trepresents the transposed matrix of the identity matrix I; z1 T With z2 T are the two components of the auxiliary variable z respectively; and Both represent intermediate parameters, H H represents the conjugate transposed matrix of the intermediate variable H; z (t) represents the intermediate variable z after updating iterations t times; d represents the iterative variable of the alternating multiplier method, d (t) represents the alternating multiplier method iteration variable after t iterations of d update.

[0093] In addition to the above least squares solution, the quadratic optimization problem can also be solved by the following gradient descent method:

[0094]

[0095] Among them, x (t) Represents the vectorization result of the two-dimensional scene after updating iteratively t times; Represents the gradient descent iteration step size; Represents the auxiliary variable z i Update the iteration result after t iterations; Indicates d (t) , where i is 1 and 2; Φ H Represents the conjugate transposed matrix of the observation matrix Φ.

[0096] Further, update the intermediate variable z1 after iteration t+1 times (t+1) satisfy:

[0097]

[0098] Among them, λ MC represents the non-convex penalty term p MC (x i ) regularized threshold, ψ MC (x i ,λ) represents the threshold function; p MC (z1) represents the non-convex penalty function of the auxiliary variable component z1; d1 represents the component 1 of the alternating multiplier iteration variable d, and d1(t) represents the iteration result after the component d1 is updated and iterated t times; where,

[0099]

[0100] Among them, λ represents the threshold; x i represents the i-th element in x; θ represents the non-convex penalty term p MC (x i ) adjustment parameters.

[0101] Further, update the intermediate variable z2 after iteration t+1 (t+1) satisfy:

[0102]

[0103] Where d2 represents the second component of the alternating multiplier iteration variable d, represents the iteration result after updating component 2 d2 for t times; p NLTV (|z2|) represents the non-local total variation norm penalty function of the auxiliary variable component z2; λ NLTV Indicates the threshold of NLTV regularization, div NLTV (·) represents the nonlocal divergence operator; p (t+1) is the auxiliary variable in solving the NLTV regularization process; ο represents the matrix Hadamard product. Among them, the non-local divergence operator div NLTV (·)satisfy:

[0104]

[0105] in, To solve the auxiliary variables in the NLTV regularization process, P (t+1) For p (t+1) The form before vectorization, represents the auxiliary variable of the pixel at i = (i1, i2), which satisfies:

[0106]

[0107] in, express The element corresponding to j in satisfy:

[0108]

[0109] in, Represents d2 (t) The matrix before vectorization, for The element at position i in x (t+1) Represents x (t +1) The matrix before vectorization, is located at x (t+1) The element at position i.

[0110] Further, update d after iteration t+1 (t+1) satisfy:

[0111] d (t+1) =[d1 T , d2 T ]T =d (t) -Gx (t+1) +z (t+1)

[0112] Among them, d1 T With d2 T They represent the transposed matrices of the alternating multiplier method iteration variables d1 and d2 respectively.

[0113] In operation S203, an iteration parameter is calculated.

[0114] In the embodiment of the present disclosure, the calculation iteration parameter is specifically:

[0115] res=||x (t+1) -x (t) ||2 / ||x (t) ||2

[0116] t=t+1

[0117] Among them, it is judged whether res>ε and t<T are satisfied at the same time max If the conditions are not met at the same time, the iteration continues and the process goes to step S202.

[0118] In the embodiments of the present disclosure, the sparse SAR imaging method based on non-convex-non-local total variation regularization provided in the present disclosure is verified through simulation experiments and Gaofen-3 measured data experiments.

[0119] Figure 3 The figure schematically shows the reconstruction results comparison of the simulation data by the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization (MC-TV) and non-convex-non-local total variation regularization (MC-NLTV), where: Figure 3 a is a comparison chart of the reconstruction results when the echo SNR is 30dB. Figure 3 b shows the reconstruction result comparison chart under echo SNR = -5dB. Figure 3 As shown in the figure, it can be seen that the non-convex-non-local total variation regularization MC-NLTV can effectively suppress the coherent speckle noise and significantly enhance the surface target features.

[0120] Table 1 below summarizes the reconstruction results of Gaofen-3 data by four methods, including the reconstruction amplitude (AMP) and relative bias (RB) of point targets, and the mean reconstruction amplitude (μ A ), comparison results of equivalent number of looks (ENL) and radiometric resolution (γ).

[0121] Table 1

[0122]

[0123] Figures 4A to 4D The figure schematically shows the comparison of the reconstructed slice analysis results of the simulation data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization. Figure 5 The figure schematically shows the comparison of the reconstruction results of Gaofen-3 data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization. Figures 6A-6B The figure schematically shows the comparison of the local imaging results of Gaofen-3 data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization. Fig. 6A Specifically, the comparison of local imaging results under Tar=P1 and Tar=P2 is shown below. Figure 6B Specifically, it is a comparison diagram of local imaging results under Tar=D1 and Tar=D2. Figures 7A to 7D The comparison diagrams of the reconstructed slice analysis results of Gaofen-3 data using the matched filtering algorithm, L1-TV regularization, non-convex-TV regularization and non-convex-non-local total variation regularization are schematically shown respectively.

[0124] from Figures 4A to 4D , Figure 5 , Figures 6A-6B , Figures 7A to 7D As can be seen from Table 1, compared with the traditional matched filtering algorithm, the method provided by the present disclosure can not only effectively suppress additive noise and clutter, enhance the characteristics of point targets, but also suppress speckle noise and maintain the continuity and uniformity of the backscattering coefficient of surface targets. Compared with the L1-TV regularization method, the non-convex-non-local total variation regularization can effectively suppress the bias effect caused by L1 regularization and improve the target reconstruction accuracy; and can avoid the excessive smoothing of point targets by TV regularization, and can maintain the reconstruction accuracy of point targets while enhancing the characteristics of surface targets, and realize the joint feature enhancement of point and surface targets.

[0125] It should be noted that the above simulation results are only exemplary descriptions and do not constitute limitations on the embodiments of the present disclosure. In other practical application scenarios, they may be substitutes for other results, and the embodiments of the present disclosure do not limit this.

[0126] Figure 8 A block diagram of a sparse SAR imaging system based on non-convex-non-local total variation regularization according to an embodiment of the present disclosure is schematically shown.

[0127] like Figure 8As shown, the sparse SAR imaging system 800 based on non-convex-non-local total variation regularization includes: a SAR imaging model building module 810 and a SAR imaging module 820. The system 800 can be used to implement reference Figure 1 The described sparse SAR imaging method based on non-convex-non-local total variation regularization.

[0128] The SAR imaging model construction module 810 is used to introduce non-convex penalty terms and non-local total variation norm penalty terms into the sparse SAR imaging model to construct a sparse SAR imaging model based on non-convex-non-local total variation regularization. According to an embodiment of the present disclosure, the SAR imaging model construction module 810 can be used to perform the above reference Figure 1 The described step S101 will not be repeated here.

[0129] The SAR imaging module 820 is used to solve the sparse SAR imaging model based on non-convex-non-local total variation regularization by using the improved variable separation and alternating direction multiplier method to complete SAR imaging. According to an embodiment of the present disclosure, the SAR imaging module 820 can be used to perform the above reference Figure 1 The described step S102 will not be repeated here.

[0130] According to the embodiments of the present disclosure, Fig. 9 As shown, the system further includes: a SAR observation model construction module 830, which is used to construct a sparse SAR observation model. The sparse SAR imaging model is constructed based on the sparse SAR observation model.

[0131] According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits, or at least part of the functions of any one of them can be implemented in one module. According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits can be split into multiple modules for implementation. According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits can be at least partially implemented as hardware circuits, such as field programmable gate arrays (FPGAs), programmable logic arrays (PLAs), systems on chips, systems on substrates, systems on packages, application specific integrated circuits (ASICs), or can be implemented by hardware or firmware in any other reasonable way of integrating or packaging the circuit, or implemented in any one of the three implementation methods of software, hardware, and firmware, or in any appropriate combination of any of them. Alternatively, according to the embodiments of the present invention, one or more of the modules, submodules, units, and subunits can be at least partially implemented as computer program modules, and when the computer program modules are run, the corresponding functions can be performed.

[0132] For example, any multiple of the SAR imaging model construction module 810, the SAR imaging module 820, and the SAR observation model construction module 830 can be combined in one module for implementation, or any one of the modules can be split into multiple modules. Alternatively, at least part of the functions of one or more of these modules can be combined with at least part of the functions of other modules and implemented in one module. According to an embodiment of the present disclosure, at least one of the SAR imaging model construction module 810, the SAR imaging module 820, and the SAR observation model construction module 830 can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on a chip, a system on a substrate, a system on a package, an application specific integrated circuit (ASIC), or can be implemented by hardware or firmware such as any other reasonable way of integrating or packaging the circuit, or implemented in any one of the three implementation methods of software, hardware, and firmware, or in any appropriate combination of any of them. Alternatively, at least one of the SAR imaging model construction module 810, the SAR imaging module 820, and the SAR observation model construction module 830 can be at least partially implemented as a computer program module, and when the computer program module is run, the corresponding function can be executed.

[0133] Fig.10 A block diagram of an electronic device suitable for implementing the method described above according to an embodiment of the present disclosure is schematically shown. Fig.10 The electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present disclosure.

[0134] like Fig.10 As shown, the electronic device 1000 described in this embodiment includes: a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage part 1008 to a random access memory (RAM) 1003. The processor 1001 may include, for example, a general-purpose microprocessor (such as a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (for example, an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include an onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0135] In RAM 1003, various programs and data required for the operation of system 1000 are stored. Processor 1001, ROM 1002 and RAM 1003 are connected to each other through bus 1004. Processor 1001 performs various operations of the method flow according to the embodiment of the present disclosure by executing the program in ROM 1002 and / or RAM 1003. It should be noted that the program can also be stored in one or more memories other than ROM 1002 and RAM 1003. Processor 1001 can also perform various operations of the method flow according to the embodiment of the present disclosure by executing the program stored in the one or more memories.

[0136] According to an embodiment of the present disclosure, the electronic device 1000 may further include an input / output (I / O) interface 1005, which is also connected to the bus 1004. The system 1000 may further include one or more of the following components connected to the I / O interface 1005: an input section 1006 including a keyboard, a mouse, etc.; an output section 1007 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, a modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as needed. A removable medium 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 1010 as needed, so that a computer program read therefrom is installed into the storage section 1008 as needed.

[0137] According to an embodiment of the present disclosure, the method flow according to an embodiment of the present disclosure can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program contains a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1009, and / or installed from the removable medium 1011. When the computer program is executed by the processor 1001, the above-mentioned functions defined in the system of the embodiment of the present disclosure are executed. According to an embodiment of the present disclosure, the system, equipment, device, module, unit, etc. described above can be implemented by a computer program module.

[0138] The embodiment of the present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiment; or may exist independently without being assembled into the device / apparatus / system. The above computer-readable storage medium carries one or more programs, and when the above one or more programs are executed, the sparse SAR imaging method based on non-convex-non-local total variation regularization according to the embodiment of the present disclosure is implemented.

[0139] According to an embodiment of the present disclosure, the computer-readable storage medium may be a non-volatile computer-readable storage medium, for example, may include but is not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In an embodiment of the present disclosure, the computer-readable storage medium may be any tangible medium containing or storing a program, which may be used by or in combination with an instruction execution system, an apparatus or a device. For example, according to an embodiment of the present disclosure, the computer-readable storage medium may include the ROM 1002 and / or RAM 1003 described above and / or one or more memories other than ROM 1002 and RAM 1003.

[0140] The embodiment of the present disclosure also includes a computer program product, which includes a computer program, and the computer program contains program code for executing the method shown in the flowchart. When the computer program product is run in a computer system, the program code is used to enable the computer system to implement the sparse SAR imaging method based on non-convex-non-local total variation regularization provided by the embodiment of the present disclosure.

[0141] The above functions defined in the system / device of the embodiment of the present disclosure are performed when the computer program is executed by the processor 1001. According to the embodiment of the present disclosure, the system, device, module, unit, etc. described above can be implemented by a computer program module.

[0142] In one embodiment, the computer program may rely on tangible storage media such as optical storage devices, magnetic storage devices, etc. In another embodiment, the computer program may also be transmitted and distributed in the form of signals on a network medium, and downloaded and installed through the communication part 1009, and / or installed from the removable medium 1011. The program code contained in the computer program may be transmitted using any appropriate network medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0143] In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1009, and / or installed from the removable medium 1011. When the computer program is executed by the processor 1001, the above functions defined in the system of the embodiment of the present disclosure are performed. According to the embodiment of the present disclosure, the system, device, means, module, unit, etc. described above can be implemented by a computer program module.

[0144] According to an embodiment of the present disclosure, the program code for executing the computer program provided by the embodiment of the present disclosure can be written in any combination of one or more programming languages. Specifically, these computing programs can be implemented using high-level process and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, Java, C++, python, "C" language or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, partially on the remote computing device, or entirely on the remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (for example, using an Internet service provider to connect through the Internet).

[0145] It should be noted that the functional modules in the various embodiments of the present disclosure may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module. The above-mentioned integrated modules may be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they may be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention may essentially or in other words, the part that contributes to the prior art or all or part of the technical solution may be embodied in the form of a software product.

[0146] The flow charts and block diagrams in the accompanying drawings illustrate the possible architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a module, a program segment, or a part of a code, and the above-mentioned module, program segment, or a part of a code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flow chart, and the combination of the boxes in the block diagram or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0147] It will be appreciated by those skilled in the art that the features described in the various embodiments and / or claims of the present disclosure may be combined and / or combined in a variety of ways, even if such combinations and / or combinations are not explicitly described in the present disclosure. In particular, the features described in the various embodiments and / or claims of the present disclosure may be combined and / or combined in a variety of ways without departing from the spirit and teachings of the present disclosure. All of these combinations and / or combinations fall within the scope of the present disclosure.

[0148] Although the present disclosure has been shown and described with reference to specific exemplary embodiments of the present disclosure, it should be understood by those skilled in the art that various changes in form and details may be made to the present disclosure without departing from the spirit and scope of the present disclosure as defined by the appended claims and their equivalents. Therefore, the scope of the present disclosure should not be limited to the above-mentioned embodiments, but should be determined not only by the appended claims, but also by the equivalents of the appended claims.

Claims

1. A sparse SAR imaging method based on non-convex-non-local total variation regularization, characterized in that: include: Non-convex penalty term and non-local total variation norm penalty term are introduced into the sparse SAR imaging model, and a sparse SAR imaging model based on non-convex-non-local total variation regularization is constructed. The sparse SAR imaging model based on non-convex-non-local total variation regularization is solved by using an improved variable separation and alternating direction multiplier method to complete SAR imaging; The sparse SAR imaging model based on non-convex-non-local total variation regularization is as follows: in, , is the Lagrange multiplier, y is the quantization result of the two-dimensional echo vector, is the vectorization result of the two-dimensional scene, is the observation matrix corresponding to the vectorized two-dimensional echo and two-dimensional scene, is a non-convex penalty term, is the non-local total variation norm penalty term; The non-local total variation norm penalty term is defined as: in, Represents a SAR two-dimensional scene image; , which means pixel i in the image Position in Representing images Centrally located Elements of express The non-local gradient vector of Represents the matrix composed of the module of the non-local gradient vector of each pixel; where, in, Represents the non-local weight between pixel i and pixel j; , represents the position of pixel j in image X; Representing images Centrally located Elements of Represents the matrix composed of the module of the non-local gradient vector of pixel i; It means that i is the center and the size is window, D is a real number; the non-local weight between pixels i and j Defined as: in, represents weighted Euclidean distance; represents the standard deviation of the Gaussian kernel, and ; It means that i is the center and the size is Window, is a real number; It means that the center is j and the size is Window; represents the control parameter, and ; The method of using improved variable separation and alternating direction multiplier method to solve the sparse SAR imaging method model based on non-convex-non-local total variation regularization to complete SAR imaging includes: Initialize iterative parameters: radar echo is , the observation matrix is , the radar scene is initialized as , intermediate variable , and , the Lagrange multiplier , , the augmented Lagrangian penalty parameter , non-local total variation regularization iteration step size ; Set the maximum number of iterations to , let the initial value of the iteration step t = 0, and the iteration termination condition ; Perform iteration and update iteration parameters; Calculate iteration parameters; Update the vectorization result of the two-dimensional scene after iteration t+1 satisfy: in, represents the two-dimensional scene vectorization result after updating iterations t times; y is the two-dimensional echo vectorization result; Represents the gradient descent iteration step size; and Both represent intermediate parameters. Represents an intermediate variable The conjugate transposed matrix of ; express and auxiliary variables The mapping relationship between them; Represents the identity matrix The transposed matrix of Auxiliary variables The two components of Represents auxiliary variables Update the iteration result after t iterations; represents the alternating multiplier method iteration variable, represents the iteration variable of the alternating multiplier method after updating the iteration t times, express , where i is 1 and 2; is the observation matrix corresponding to the vectorized two-dimensional echo and two-dimensional scene; Represents the observation matrix The conjugate transposed matrix of .

2. The sparse SAR imaging method according to claim 1, characterized in that: The non-convex penalty term is defined as: ， in, represents a typical non-convex penalty term ; express The i-th element in ; Representation elements The non-convex penalty term of represents the non-convex penalty term The adjustment parameters of , i and N are both positive integers, 1≤i≤N.

3. The sparse SAR imaging method according to claim 1, characterized in that: Update after iteration t+1 satisfy: in, represents the non-convex penalty term The regularization threshold, represents the threshold function; Represents auxiliary variable component one Non-convex penalty function of ; Represents the alternating multiplier iteration variable The weight of one, Indicates the amount of Update the iteration result after t iterations; where, in, Indicates the threshold value; express The i-th element in ; represents the non-convex penalty term adjustment parameters.

4. The sparse SAR imaging method according to claim 3, characterized in that: Update after iteration t+1 satisfy: in, Represents the alternating multiplier iteration variable The weight of two; Indicates the amount of two Update the iteration result after t iterations; Represents auxiliary variable component 2 Non-local total variation norm penalty function; represents the threshold of NLTV regularization, represents the nonlocal divergence operator; To solve the auxiliary variables in the NLTV regularization process, represents the matrix Hadamard product.

5. The sparse SAR imaging method according to claim 4, characterized in that: The calculation iteration parameters are: t=t+1 Among them, determine whether and , if the conditions are not met at the same time, continue to iterate.

6. A sparse SAR imaging system based on non-convex-non-local total variation regularization, characterized in that: include: SAR imaging model construction module, used to introduce non-convex penalty terms and non-local total variation norm penalty terms into the sparse SAR imaging model, and construct a sparse SAR imaging model based on non-convex-non-local total variation regularization; A SAR imaging module, used for solving the sparse SAR imaging model based on non-convex-non-local total variation regularization by using an improved variable separation and alternating direction multiplier method to complete SAR imaging; The sparse SAR imaging model based on non-convex-non-local total variation regularization is as follows: in, , is the Lagrange multiplier, y is the quantization result of the two-dimensional echo vector, is the vectorization result of the two-dimensional scene, is the observation matrix corresponding to the vectorized two-dimensional echo and two-dimensional scene, is a non-convex penalty term, is the non-local total variation norm penalty term; The non-local total variation norm penalty term is defined as: in, Represents a SAR two-dimensional scene image; , which means pixel i in the image Position in Representing images Centrally located Elements of express The non-local gradient vector of Represents the matrix composed of the module of the non-local gradient vector of each pixel; where, in, Represents the non-local weight between pixel i and pixel j; , represents the position of pixel j in image X; Representing images Centrally located Elements of Represents the matrix composed of the module of the non-local gradient vector of pixel i; It means that i is the center and the size is window, D is a real number; the non-local weight between pixels i and j Defined as: in, represents weighted Euclidean distance; represents the standard deviation of the Gaussian kernel, and ; It means that i is the center and the size is Window, is a real number; It means that the center is j and the size is Window; represents the control parameter, and ; The method of using improved variable separation and alternating direction multiplier method to solve the sparse SAR imaging method model based on non-convex-non-local total variation regularization to complete SAR imaging includes: Initialize iterative parameters: radar echo is , the observation matrix is , the radar scene is initialized as , intermediate variable , and , the Lagrange multiplier , , the augmented Lagrangian penalty parameter , non-local total variation regularization iteration step size ; Set the maximum number of iterations to , let the initial value of the iteration step t = 0, and the iteration termination condition ; Perform iteration and update iteration parameters; Calculate iteration parameters; Update the vectorization result of the two-dimensional scene after iteration t+1 satisfy: in, represents the two-dimensional scene vectorization result after updating iterations t times; y is the two-dimensional echo vectorization result; Represents the gradient descent iteration step size; and Both represent intermediate parameters. Represents an intermediate variable The conjugate transposed matrix of ; express and auxiliary variables The mapping relationship between them; Represents the identity matrix The transposed matrix of Auxiliary variables The two components of Represents auxiliary variables Update the iteration result after t iterations; represents the alternating multiplier method iteration variable, represents the iteration variable of the alternating multiplier method after updating the iteration t times, express , where i is 1 and 2; is the observation matrix corresponding to the vectorized two-dimensional echo and two-dimensional scene; Represents the observation matrix The conjugate transposed matrix of .

7. An electronic device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the sparse SAR imaging method based on non-convex-non-local total variation regularization as described in any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the sparse SAR imaging method based on non-convex-non-local total variation regularization according to any one of claims 1 to 5 is implemented.

9. A computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the sparse SAR imaging method based on non-convex-non-local total variation regularization according to any one of claims 1 to 5 is implemented.

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