A L 2,1 / 2 norm-based unambiguous sparse SAR imaging method

Abstract

The application discloses a kind of based on L 2,1 / 2 Norm's blur-free sparse SAR imaging method, the method faces the data of acquisition downsampling, constructs blur-free sparse SAR imaging model, proposes the regularized optimization reconstruction problem based on L 2,1 / 2 Norm, and high-precision sparse reconstruction of scene is realized by threshold iteration recovery algorithm.This application is based on sparse signal processing research, to solve the azimuth ambiguity problem caused by data downsampling, and proposes the blur-free sparse SAR imaging method based on L 2,1 / 2 Norm.Compared with prior art, the method of the application can be based on the accurate reconstruction of sparse scene of downsampling data, effectively suppresses azimuth ambiguity, and obtains high-quality blur-free sparse SAR image.

Description

TECHNICAL FIELD

[0001] The present application relates to a non-ambiguous sparse synthetic aperture radar (SAR) imaging method based on L 2,1 / 2 norm, and belongs to the field of sparse signal processing and microwave imaging. BACKGROUND

[0002] SAR is a main research direction of modern high-resolution microwave imaging technology. Compared with traditional optical imaging, SAR has all-weather and all-day observation capability, and is widely used in military and civilian fields. Range-Doppler algorithm and Chirp-Scaling algorithm (CSA) are commonly used matched filtering (MF) SAR imaging algorithms based on full sampling data. However, when the collected data is down-sampling, the image recovered by the MF algorithm has serious azimuth ambiguity, and even leads to reconstruction failure.

[0003] Sparse SAR imaging technology is a combination of sparse signal processing technology and SAR imaging, which can realize high-resolution sparse reconstruction of the observed area by solving the L q (q < 0 ≤ 1) norm regularization problem. Since the down-sampling signal does not satisfy the Nyquist sampling theorem, the traditional MF algorithm cannot be used for scene recovery, and the sparse SAR imaging technology can improve the image performance and realize sparse scene recovery based on down-sampling data. Therefore, in order to solve the azimuth ambiguity problem caused by data down-sampling, a non-ambiguous sparse SAR imaging method based on L 2,1 / 2 norm is proposed. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a non-ambiguous sparse SAR imaging method based on L 2,1 / 2 norm, which carries out processing work on down-sampling data based on sparse signal processing technology, and ensures the SAR imaging quality based on down-sampling data.

[0005] The present application adopts the following technical solutions to solve the above technical problems:

[0006] A non-ambiguous sparse SAR imaging method based on L 2,1 / 2 norm, comprising the following steps:

[0007] Step 1: constructing a non-ambiguous sparse SAR imaging model according to the collected down-sampling data;

[0008] Step 2: proposing a regularization optimization reconstruction problem based on L 2,1 / 2 norm based on the non-ambiguous sparse SAR imaging model;

[0009] Step 3: Solve the problem based on L proposed in Step 2 using the threshold iterative recovery algorithm. 2,1 / 2 The problem of reconstructing observation scenes by optimizing the regularization of norms is solved, thereby achieving sparse reconstruction of the observation scene.

[0010] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0011] This invention performs accurate reconstruction of sparse scenes based on downsampled data, which can effectively suppress azimuth ambiguity and obtain high-quality, unambiguous sparse SAR images. Attached Figure Description

[0012] Figure 1 This invention is based on L 2,1 / 2 Flowchart of the implementation of the norm-based unambiguous sparse SAR imaging method.

[0013] Figure 2 This is a flowchart of the iterative recovery implementation in the method of this invention.

[0014] Figures 3(a)-3(e) This invention's algorithm, L 2,1 Imaging results of simulated point targets using the L1 norm method, L2 norm method, and CSA for full-sampled and downsampled conditions are presented. Figure 3(a) shows the CSA simulation results for full-sampled conditions; Figure 3(b) shows the CSA simulation results for downsampled conditions; Figure 3(c) shows the simulation results using the L1 norm method for downsampled conditions; and Figure 3(d) shows the simulation results using the L1 norm method for downsampled conditions. 2,1 Simulation results of the norm method; Figure 3(e) shows the L-symmetric model of the present invention under downsampling. 2,1 / 2 Norm simulation results. Detailed Implementation

[0015] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0016] For downsampled data, traditional MF methods cannot suppress orientation ambiguity, leading to reconstruction failure. Therefore, this invention studies sparse signal processing to solve the orientation ambiguity problem caused by data downsampling, and proposes a method based on L... 2,1 / 2 The L-norm-based unambiguous sparse SAR imaging method constructs an unambiguous sparse SAR imaging model based on the acquired downsampled data, and proposes a method based on L-norm. 2,1 / 2 The problem of reconstructing a scene by regularizing the norm is solved, and a threshold iterative recovery algorithm is used to achieve high-precision sparse reconstruction of the scene.

[0017] like Figure 1 As shown, this is an embodiment of the present invention based on L 2,1 / 2 The flowchart for the implementation of the norm-based unambiguous sparse SAR imaging method is shown below, with the specific implementation steps as follows:

[0018] Step S1: Constructing the unambiguous sparse SAR imaging model

[0019] Let the azimuth frequency of the main Doppler spectrum be f η The Doppler frequency of the azimuth ambiguous region caused by the periodic sampling in the azimuth direction can be expressed as:

[0020] f a = f η + i·PRF, i∈Z and i≠0 (1)

[0021] where PRF is the pulse repetition frequency, and i represents the i-th block of the azimuth ambiguous region.

[0022] For the main Doppler region, three main operations in the CSA are constructed, i.e., the range migration correction and compression operator the azimuth focusing and phase correction operator and the range migration correction and compression operator and The operators and represent the MF process of the main Doppler region and the azimuth ambiguous region, respectively, and The operators and represent the inverse MF process of the main Doppler region and the azimuth ambiguous region, respectively. F r and represent the Fourier transform operator and the inverse Fourier transform operator in the azimuth and range directions, respectively. Based on the constructed operators, the main Doppler region MF process and the inverse MF process can be expressed as:

[0023]

[0024]

[0025] Similarly, by replacing the Doppler center frequency f η with the azimuth ambiguous region frequency f a , the CSA operators of the azimuth ambiguous region and and the corresponding MF process and the inverse MF process

[0026] The unambiguous sparse SAR imaging model based on the approximate observation can be expressed by using the constructed operators:

[0027]

[0028] where Y is the two-dimensional down-sampling data, Y a is the full-sampling data, and Ξa and Ξ r Let X and N0 represent the downsampling matrices in the azimuth and range directions, respectively, where N0 is the noise matrix and X and N0 are the downsampling matrices in the range direction. These represent the target scene and the area with ambiguous orientation, respectively.

[0029] Step S2: Based on L 2,1 / 2 Norm optimization and reconstruction

[0030] For the sparse SAR imaging model constructed in (4), it can be solved by addressing the following L 2,1 / 2 Norm regularization is used to reconstruct the scene:

[0031]

[0032] in, X is a reconstructed 2D sparse SAR image. β1 is a regularization parameter controlling the overall scene sparsity, including the target scene and the azimuth-ambiguous region, while β2 is a regularization parameter controlling the target scene sparsity. all The total image, which includes the target scene and the orientation-blurred region, is represented as:

[0033]

[0034] X all The norm can be expressed as:

[0035]

[0036] Among them, X np and Representing X and The np-th row, where np = 1, 2, ..., N P N P It is the total number of points in the azimuth direction of the observed scene.

[0037] Step S3: Iterative Recovery

[0038] For the optimization problem in (5), sparse reconstruction of the observation scene can be achieved through iterative recovery. The threshold iteration algorithm takes as input the acquired downsampled echo data Y and the operator... Let X be the target scene for sparse reconstruction. (0) and areas with ambiguous orientation The initial values ​​of all elements are 0, and their corresponding gradient values ​​U (0) ,and All are also 0. The iteration parameter is μ, the error parameter is ε, and the maximum number of iterations is T. max When the condition t≤T is satisfied. max And when the residual Resi > ε, such as Figure 2 As shown, perform the following steps.

[0039] Step S31: Estimate residual data values

[0040]

[0041] Step S32: Update gradient values

[0042]

[0043]

[0044] Where μ is a parameter that controls the convergence speed of the algorithm, and is usually set as a constant.

[0045] Step S33: Update the parameter β2 that controls the sparsity of the target scene.

[0046]

[0047] Among them, |U (t-1) | K+1 Represents the magnitude value of the target scene |U (t-1) The (K+1)th largest component, sorted in descending order.

[0048] Step S34: Threshold shrinkage of the main imaging region

[0049] Threshold operator for

[0050]

[0051]

[0052] The threshold function can be expressed as:

[0053]

[0054] Step S35: Update the parameter β1 that controls the overall scene sparsity.

[0055]

[0056] in, It can be represented as

[0057]

[0058] Represents the total scene amplitude value The (K+1)th largest component arranged in descending order.

[0059] Step S36: Threshold shrinkage of the total imaging region

[0060]

[0061] where the threshold operator may be expressed as

[0062]

[0063] where the threshold function can be expressed as

[0064]

[0065] where,

[0066]

[0067] Step S37: calculating the residual of the recovered image

[0068] Resi = ||X (t) -X (t-1) || F (21)

[0069] If the condition t≤T max is satisfied, the iteration is continued, i.e., t = t + 1, and the above steps are repeated. If the condition is not satisfied, the iteration is ended, and the recovered sparse image is output

[0070] The following experiment is used to verify the L 2,1 / 2 norm-based non-blurred sparse SAR imaging method provided in the present application. Figures 3(a)-3(e) All have five simulation points, respectively, T1, T2, T3, T4 and T5. Among them, the azimuth interval and the range interval between T1 and T2, T2 and T3, and T3 and T4 are all 100m, and the range interval between T4 and T5 is 100m, and the azimuth interval is 10m. In this simulation, full sampling and down-sampling data with a rate of 75% are used. Fig. 3(a) is the CSA imaging result when full sampling; Fig. 3(b) is the CSA imaging result when down-sampling; Fig. 3(c) is the L1 norm method imaging result when down-sampling; Fig. 3(d) is the L 2,1 norm method imaging result when down-sampling; Fig. 3(e) is the L 2,1 / 2 norm method imaging result when down-sampling. It can be seen that for full sampling data, the traditional MF method can be accurately recovered, but cannot distinguish two point targets with small azimuth interval, and the resolution is low. For down-sampling data, the traditional MF method cannot suppress the azimuth blur and ghost, and cannot distinguish two point targets with small azimuth interval, resulting in reconstruction failure. The L1 norm method can effectively suppress the ghost, but it is difficult to suppress due to the large energy of the ghost near the main lobe region and the azimuth blur. The L 2,1 norm method can effectively suppress the azimuth blur. And the L 2,1 / 2The norm algorithm can not only restrain the azimuth ambiguity, but also has higher resolution, and effectively improves the imaging performance.

[0071] The above examples only illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the present application.

Claims

1. A method for unambiguous sparse SAR imaging based on L 2,1 / 2 norm, characterized in that The method comprises the following steps: Step 1, constructing a non-ambiguous sparse SAR imaging model according to the collected down-sampling data; the specific process is as follows: Let the azimuth Doppler spectrum azimuth frequency be f η The Doppler frequency f of the azimuth ambiguity area caused by azimuth periodic sampling is a is expressed as: f a = f η + i · PRF, i ∈ Z and d ≠ 0 Wherein, PRF is the pulse repetition frequency, i represents the i-th block azimuth ambiguity area, and Z represents an integer; CSA operators to construct the main Doppler region, including a variable index operator range migration correction and compression operators and azimuth focusing and phase correction operators MF process for the main Doppler region based on the constructed operators and inverse MF process is represented as: where F a and denote the Fourier transform operator and inverse Fourier transform operator in azimuth direction, respectively, F r and denote the Fourier transform operator and inverse Fourier transform operator in range direction, respectively, and the superscript * denotes the conjugate. Similarly, the CSA operator constructing the azimuth blurring zone, including the variable index operator The range migration correction and compression operator And the azimuth focusing and phase correction operator Based on the constructed operator, the MF process of the azimuth blurring zone is obtained And the inverse MF process Then, the non-ambiguous sparse SAR imaging model based on the approximate observation is represented as: where Y is the two-dimensional down-sampled echo data, Y a is the full-sampled data, a and Ξ r are the down-sampling matrices in azimuth and range, respectively, N0 is the noise matrix, X and represent the target scene and the azimuth blurring region, respectively; Step 2, based on the non-blurring sparse SAR imaging model, proposes a L 2,1 / 2 norm-based regularization optimization reconstruction problem; Step 3, solve the regularization optimization reconstruction problem based on L 2,1 / 2 norm proposed in Step 2 by threshold iteration recovery algorithm, realize sparse reconstruction of the observed scene.

2. The L 2,1 / 2 A method for blur-free sparse SAR imaging based on L The specific process of the step 2 is as follows: For the unambiguous sparse SAR imaging model constructed in Step 1, the reconstruction of the target scene is achieved by solving the L 2,1 / 2 norm regularization problem as follows: wherein, is the reconstructed two-dimensional sparse SAR image, β1is a regularization parameter controlling the sparsity of the total scene including the target scene and the azimuth blurring region, β2is a regularization parameter controlling the sparsity of the target scene, X all denotes the total image including the target scene and the azimuth blurring region, is denoted as; X all The norm of is denoted as: where X np and represent X and respectively, and P , N P is the total number of points in the azimuth direction of the observed scene, represents the azimuth ambiguity region when i = -1, and the superscript T represents the transpose.

3. The L 2,1 / 2 The method for blur-free sparse SAR imaging based on norm, characterized in that, The specific process of the step 3 is as follows: The threshold iterative recovery algorithm is used for solving the regularization optimization reconstruction problem based on L 2,1 / 2 norm, and sparse reconstruction of the observed scene is realized; the threshold iterative recovery algorithm inputs the collected down-sampling echo data Y and The target scene X of sparse reconstruction is set (0) The initialization of the azimuth ambiguity region is 0, and the corresponding gradient value U (0) and are also 0, the error parameter is ε, and the maximum iteration step number is T max When the tth iteration satisfies the condition t≤T max and the residual error Resi>ε, the following steps are executed: Step 31, estimate residual data value Δ (t-1) : Step 32, update gradient value U (t-1) and : Wherein, μ is a parameter for controlling the convergence speed of the algorithm; Step 33, updating the regularization parameter β2 for controlling the sparsity of the target scene: wherein |U (t-1) | K+1 represents the target scene amplitude value |U (t-1) the (K+1)th largest component in descending order Step 34, threshold shrinkage of the main imaging area: Threshold operator is: wherein the threshold function is represented as: Step 35, updating the regularization parameter β1 for controlling the sparsity of the total scene: wherein, denotes the total scene amplitude value the (K+1)th largest component in descending order; Step 36, threshold shrinkage of the total imaging area: wherein the threshold operator is represented as: where I max is the number of azimuth ambiguities, the threshold function is expressed as: Wherein, Step 37, calculating the residual error of the recovered image: Let t = t + 1, if the condition t ≤ T is satisfied... max If Resi > ε, continue iterating and repeat steps 31-37; if the condition is not met, end the iteration and output the recovered sparse image. X (t) X (t-1) Let represent the sparse images output in the t-th and t-1-th iterations, respectively.

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