Harmonic wavelet inverse synthetic aperture radar imaging method and device based on ADMM

Abstract

The invention relates to a harmonic wavelet inverse synthetic aperture radar imaging method and device based on ADMM. The method comprises the following steps: acquiring a distance unit signal, and constructing a discrete Fourier transform matrix based on the distance unit signal; determining a window function, processing each time point of the distance unit signal according to a sliding window, and determining a signal in a local time window; constructing a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; constructing an optimization model according to the local harmonic wavelet basis matrix and the signals in the local time window; introducing an auxiliary variable and a dual variable to iteratively update the optimization model to obtain a final harmonic wavelet coefficient; and calculating local energy distribution based on the harmonic wavelet coefficient, constructing a time-frequency matrix through the local energy distribution, and reconstructing the target image according to the time-frequency matrix to obtain a final ISAR image. According to the invention, resolution can be improved, cross term interference is reduced, and imaging precision is high.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular, to a harmonic wavelet inverse synthetic aperture radar imaging method and device based on ADMM. Background Art

[0002] Inverse synthetic aperture radar (ISAR) technology is an important means for obtaining two-dimensional imaging of targets in modern radar systems. ISAR utilizes the relative motion between the radar and the target to generate an equivalent synthetic aperture, and reconstructs the two-dimensional reflection distribution image of the target by performing time-frequency analysis on the radar echo data. Traditional ISAR imaging mainly uses the range-Doppler (RD) algorithm, which is based on the Fourier transform principle and requires the target to maintain uniform motion during the observation time. However, in practical applications, the target often has complex motions, such as rotation, pitching, rolling and other non-uniform motions, resulting in the Doppler frequency of the echo signal changing with time, generating non-stationary characteristics, and further causing problems such as defocusing, blurring and cross-term interference in the image obtained by the traditional RD algorithm.

[0003] To solve the problem of non-stationary signal processing, researchers have proposed a variety of improvement methods, which are mainly divided into three categories: motion compensation technology, parametric time-frequency analysis methods, and non-parametric time-frequency analysis methods. Among them, non-parametric time-frequency analysis methods such as short-time Fourier transform (STFT), pseudo Wigner-Ville distribution (PWVD), and smoothed pseudo Wigner-Ville distribution (SPWVD) have been widely used in ISAR imaging due to their flexibility and adaptability. However, STFT has an inherent contradiction in time-frequency resolution and it is difficult to obtain good time and frequency resolutions simultaneously; although PWVD has high time-frequency focusing performance, it will generate significant cross-term interference; SPWVD reduces the cross-term interference by smoothing PWVD, but also reduces the time-frequency resolution. Summary of the Invention

[0004] Based on this, it is necessary to provide a harmonic wavelet inverse synthetic aperture radar imaging method and device based on ADMM that can improve the resolution, reduce cross-term interference, and have high imaging accuracy for the above technical problems.

[0005] A harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM, the method comprising: Obtaining range cell signals, and constructing a discrete Fourier transform matrix based on the range cell signals; Determining a window function, processing each time point of the range cell signals according to a sliding window, and determining the signals within a local time window; Construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then construct an optimization model according to the local harmonic wavelet basis matrix and the signal within the local time window; Introduce auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients; Calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, and reconstruct the target image according to the time-frequency matrix to obtain the final ISAR image.

[0006] A harmonic wavelet inverse synthetic aperture radar imaging device based on ADMM, the device includes: A Fourier transform module, configured to obtain range cell signals and construct a discrete Fourier transform matrix based on the range cell signals; A local time window signal determination module, configured to determine a window function, process each time point of the range cell signals according to a sliding window, and determine the signal within the local time window; An optimization model construction module, configured to construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then construct an optimization model according to the local harmonic wavelet basis matrix and the signal within the local time window; A harmonic wavelet coefficient calculation module, configured to introduce auxiliary variables and dual variables to iteratively solve the optimization model to obtain harmonic wavelet coefficients; An imaging module, configured to calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, and reconstruct the target image according to the time-frequency matrix to obtain the final ISAR image.

[0007] The above harmonic wavelet inverse synthetic aperture radar imaging method and device based on ADMM obtain range cell signals, construct a discrete Fourier transform matrix based on the range cell signals; determine a window function, process each time point of the range cell signals according to a sliding window to determine the signal within the local time window; construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then construct an optimization model according to the local harmonic wavelet basis matrix and the signal within the local time window; introduce auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients; calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, and reconstruct the target image according to the time-frequency matrix to obtain the final ISAR image.

[0008] The beneficial effects of the method proposed in the present invention are as follows: a discrete Fourier transform matrix is constructed once in the initial stage, so that repeated calculation of Fourier transform in subsequent iterations is avoided, and the complexity of calculation is greatly reduced; at the same time, such processing can also ensure the conservatism of energy, so that subsequent transformations based on the matrix have higher numerical stability. By using the pre-constructed discrete Fourier transform matrix and adding a window function, a harmonic wavelet basis matrix suitable for local signal description can be constructed in a very short time; and such a method makes full use of the efficient algorithm of large-scale matrix multiplication, accelerates the generation process of the basis matrix, and can also adaptively adjust the local analysis window according to the actual signal distribution, avoiding the cross-interference between different frequency components in traditional time-frequency analysis. By introducing auxiliary variables and dual variables, decomposition and efficient iteration are realized, and artifacts and cross terms in time-frequency distribution can also be avoided, so that energy is only concentrated on real signal components. The present invention effectively breaks through the contradiction between calculation time and accuracy in traditional time-frequency analysis, can improve resolution, reduce cross-term interference, and has high imaging accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0010] Figure 1 A schematic flow chart of the ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method provided in Example 1; Figure 2 Schematic diagram of the imaging result of the RD method provided in Example 1; Figure 3 Schematic diagram of the imaging result of the STFT method provided in Example 1; Figure 4 Schematic diagram of the imaging results of the SPWVD method provided in Example 1; Figure 5 A schematic diagram of the imaging result of the method of the present invention provided in Example 1; Figure 6 This is a structural block diagram of the ADMM-based harmonic wavelet inverse synthetic aperture radar imaging device provided in Example 2.

[0011] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments. DETAILED DESCRIPTION

[0012] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0013] It can be understood that the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0014] The implementation modes of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0015] Example 1 This embodiment discloses a harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM. In the initial stage, a discrete Fourier transform matrix is first constructed once, avoiding repeated calculation of Fourier transform in subsequent iterative processes, greatly reducing the complexity of calculation; at the same time, such processing can also ensure the conservatism of energy, so that subsequent transformations based on the matrix have higher numerical stability.

[0016] By using the pre-constructed discrete Fourier transform matrix and the window function, a harmonic wavelet basis matrix suitable for local signal description can be constructed in a very short time. Moreover, this method makes full use of the efficient algorithm of large-scale matrix multiplication, accelerates the generation process of the basis matrix, and can adaptively adjust the local analysis window according to the actual signal distribution, avoiding cross-interference between different frequency components in traditional time-frequency analysis.

[0017] By introducing auxiliary variables and dual variables, decomposition and efficient iteration are achieved, and artifacts and cross terms in the time-frequency distribution can be avoided, so that the energy is only concentrated on the real signal components. The present invention effectively breaks through the contradiction between the calculation time and accuracy of traditional time-frequency analysis, and can improve the resolution, reduce the interference of cross terms, and have high imaging accuracy.

[0018] like Figure 1 As shown, the harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM provided in this embodiment includes the following steps: Step 201: Acquire a range unit signal, and construct a discrete Fourier transform matrix based on the range unit signal.

[0019] Step 202, determine the window function, process each time point of the range unit signal according to the sliding window, and determine the signal in the local time window.

[0020] Step 203: Construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then construct an optimization model based on the local harmonic wavelet basis matrix and the signal within the local time window.

[0021] Step 204: Introduce auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients.

[0022] Step 205: Calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, and reconstruct the target image according to the time-frequency matrix to obtain the final ISAR image.

[0023] In the specific implementation process of step 201, the echo signal received by each range cell is denoted as the range cell signal , and the number of samples per range cell is . Based on the range cell signal, construct a discrete Fourier transform matrix , and each element in the matrix is defined as: ; In the formula, represents the element in the discrete Fourier transform matrix; represents the imaginary unit; represents the row index of the matrix; represents the column index of the matrix.

[0024] It can be understood that the matrix constructed in this way has the properties of a unitary matrix, that is, energy conservation, making the subsequent transformation based on this matrix have higher numerical stability, and at the same time facilitating matrix multiplication and transformation calculations. The matrix after one-time pre-calculation can be reused in multiple subsequent time steps, thus avoiding the redundant overhead caused by repeated calculations and reducing the computational complexity.

[0025] In the specific implementation process of step 202, first determine the window function, and the expression is: ; In the formula, represents the window function; represents the index variable of the window function; represents the window function length; Then, based on the window function length , which is set to 4 in this embodiment. For each time point of the range cell signal according to the sliding window, select a local time window for processing, and the local time window is determined by the start index and the end index. Among them, the expression of the start index is: ; The expression for the end index is: ; Determine the signal within the local time window according to the local time window. The expression for the signal within the local time window is: ; In the formula, represents the signal within the local time window; represents the signal of the range cell; represents the start index; represents the end index; represents the number of sampling points of the azimuth cell.

[0026] It can be understood that in the process of signal extraction and window selection in this embodiment, boundary protection is carried out using the start index and the end index. For the start and end of the signal, a strategy of dynamically adjusting the window length is adopted to avoid the adverse effects of edge effects on signal reconstruction.

[0027] Through the signal within the local time window, local features can be fully captured, avoiding the fuzziness of time-varying features by global transformation, breaking the non-stationarity of the signal, and providing high-purity and high-resolution feature inputs for subsequent high-precision imaging.

[0028] In the specific implementation process of step 203, construct the local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function. The expression for the local harmonic wavelet basis matrix is: ; In the formula, represents the local harmonic wavelet basis matrix; represents the window function; represents the discrete Fourier transform matrix.

[0029] It can be understood that based on the pre-constructed discrete Fourier transform matrix , by weighting the Fourier basis matrix through the window function , the local harmonic wavelet basis matrix suitable for local signal description can be constructed in a very short time. The local harmonic wavelet basis matrix can better adapt to the change of the frequency domain distribution of the signal within the local time. Since the Fourier basis matrix has been pre-computed, the operation of extracting a certain row can be completed in constant time, significantly improving the construction efficiency of the basis matrix.

[0030] After constructing the local harmonic wavelet basis matrix , for local problems, considering that the actual signal usually has the characteristics of sparse representation, an optimization model with sparse constraints is constructed, and the expression is: ; In the formula, Denote the local harmonic wavelet basis matrix; Denote the harmonic wavelet coefficients to be solved; Denote the signal within the local time window; Denote the regularization parameter.

[0031] It can be understood that in the optimization model, the first term is the data fidelity term, which is used to ensure a high consistency between the reconstructed signal and the original observed signal; the second term is the regularization term, which forces the absolute values of most harmonic wavelet coefficients to approach zero by imposing norm constraint, so as to achieve sparse representation while retaining the key features of the signal; the regularization parameter is used to balance the relationship between data error and sparsity.

[0032] In the specific implementation process of step 204, in order to split the complex optimization problem into sub-problems that are easier to solve, so as to ensure convergence to a better solution within fewer iterations. The ADMM method is adopted, and auxiliary variables and dual variables are introduced; based on the auxiliary variable , the optimization model is transformed into a constraint model; the expression of the constraint model is: ; subject to: ; Based on the constraint model, the harmonic wavelet coefficients to be solved, the auxiliary variable and the dual variable are iteratively updated. When the iteration termination condition is satisfied, the final harmonic wavelet coefficients are obtained.

[0033] Specifically, first, the harmonic wavelet coefficients to be solved are iteratively updated, including: Construct an update model for the harmonic wavelet coefficients, and the expression is: ; Write out the first-order optimality condition of the update model to obtain a regularized linear function, and the expression is: ; Since the matrix usually has a good condition number, it is efficiently solved by Cholesky decomposition. Let be a lower triangular matrix, such that ; then the harmonic wavelet coefficients at the th step can be quickly obtained through two triangular matrix solutions.

[0034] In the formula, Denote the step auxiliary variable; Denote the step dual variable; Denote the penalty parameter; Denote vector transpose, where denotes a replaceable variable.

[0035] Iteratively update the auxiliary variable , including: Through the step harmonic wavelet coefficient and the step dual variable Iteratively update the said auxiliary variable , and the expression is: ; where the definition of the soft threshold operator is: ; In the formula, denotes the step auxiliary variable; denotes the penalty parameter; , denote replacement variables, where , .

[0036] It can be understood that during the iterative update of the auxiliary variable , for the sub-problem containing regular term, a vectorized soft threshold operation is adopted to solve it, and this operation can process each component separately to ensure the sparsity of the solution.

[0037] Iteratively update the dual variable , including: Through the harmonic wavelet coefficient and the auxiliary variable Iteratively update the said dual variable , and the expression is: ; In the formula, denotes the step dual variable; denotes the step dual variable.

[0038] It can be understood that during the entire iterative update process, the Cholesky decomposition is used to solve the positive definite quadratic optimization sub-problem, and combined with the vectorized soft threshold operation, making the entire iterative process efficient and stable. When setting the iterative termination condition, in addition to setting the number of iterations, a convergence threshold can also be preset , after every certain number of iterations, the updated variable is checked against . When is satisfied, the iteration can be terminated in advance to further reduce the computational amount.

[0039] In the specific implementation process of step 205, for each time window, the squared modulus of the final harmonic wavelet coefficient is extracted as the local energy distribution, and the expression is: ; And the vector is used as a column in the output matrix. A time-frequency matrix is constructed through the local energy distribution, and this time-frequency matrix constitutes the energy mapping of the signal in the time-frequency domain, and the expression is: ; A time-frequency matrix is constructed for each range cell to obtain the final time-frequency representation of the ISAR image, which is defined as: ; In the formula, represents the time-frequency matrix; represents the number of sampling points in the azimuth unit; represents the time-frequency distribution of the ISAR image; the matrix represents the number of sampling points in the range cell.

[0040] It should be noted that for the signal of each time window, a local harmonic wavelet basis matrix can be independently constructed and iteratively updated. That is, the method proposed in this embodiment supports parallel computing. For the signal of each time window, steps 202 to 204 are simultaneously run on a multi-core processor or a parallel computing platform, so as to meet the requirements of real-time signal processing.

[0041] In one of the embodiments, the method provided by the present invention is verified.

[0042] As Figure 2 shows, the imaging result obtained by using the traditional RD algorithm is shown. It can be seen that there are obvious blurs and noise interferences in the target contour, the distribution of scattering centers is not concentrated enough, resulting in difficulty in identifying the target structure details, and the image contrast is low.

[0043] As Figure 3As shown, the imaging results obtained by the STFT algorithm are presented. Compared with the RD algorithm, the target contour has been improved to a certain extent, but there are still problems of cross-term interference and limited resolution, and the definition of the target edge is not clear enough.

[0044] As Figure 4 shown, the imaging results obtained by the SPWVD algorithm are presented. The focusing effect of the target scattering center has been improved, but certain artifacts can still be seen around the target contour, and the distribution of scattering points in some parts of the target is uneven.

[0045] As Figure 5 shown, the imaging results obtained by the method proposed in the present invention are presented. It can be seen that the distribution of target scattering points is more concentrated, the edge contour is clearer, the background noise is effectively suppressed, and the structural details of the target are retained more completely, which reflects the advantages of the present invention.

[0046] Although each step in this embodiment Figure 1 is displayed in sequence according to the indication of the arrow, these steps are not necessarily executed in the order indicated by the arrow. Unless there is a clear description in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, Figure 1 at least a part of the steps in this embodiment may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0047] Embodiment 2 Based on the ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method in Embodiment 1, this embodiment discloses an ADMM-based harmonic wavelet inverse synthetic aperture radar imaging device. As Figure 6 shown, the ADMM-based harmonic wavelet inverse synthetic aperture radar imaging device includes: a Fourier transform module 401, a signal determination module 402 within a local time window, an optimization model construction module 403, a harmonic wavelet coefficient calculation module 404, and an imaging module 405, where: The Fourier transform module 401 is used to obtain range cell signals and construct a discrete Fourier transform matrix based on the range cell signals.

[0048] The signal determination module 402 within a local time window is used to determine a window function, process each time point of the range cell signals according to a sliding window, and determine the signals within the local time window.

[0049] The optimization model construction module 403 is used to construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then, an optimization model is constructed according to the local harmonic wavelet basis matrix and the signal within the local time window.

[0050] The harmonic wavelet coefficient calculation module 404 is used to introduce auxiliary variables and dual variables to iteratively solve the optimization model to obtain harmonic wavelet coefficients.

[0051] The imaging module 405 is used to calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, and reconstruct the target image according to the time-frequency matrix to obtain the final ISAR image.

[0052] In this embodiment, the specific working processes and working principles of the Fourier transform module 401, the local time window signal determination module 402, the optimization model construction module 403, the harmonic wavelet coefficient calculation module 404, and the imaging module 405 are the same as those of the method in Embodiment 1, so they will not be elaborated herein. Each of these unit modules can be implemented in whole or in part by software, hardware, and their combination. Each unit module can be embedded in the processor of the computer device in hardware form or be independent of it, or can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to each of these unit modules.

[0053] Those of ordinary skill in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to the memory, storage, database, or other media used in the various embodiments provided in the present application can include non-volatile and / or volatile memories. The non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. The volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0054] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0055] The above-described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the appended claims.

Claims

1. An inverse synthetic aperture radar imaging method based on ADMM harmonic wavelet, characterized in that The method includes: Obtaining a range cell signal and constructing a discrete Fourier transform matrix based on the range cell signal; Determining a window function, processing each time point of the range cell signal according to a sliding window, and determining the signal within a local time window; Constructing a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then constructing an optimization model according to the local harmonic wavelet basis matrix and the signal within the local time window; Introducing auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients; Calculating the local energy distribution based on the harmonic wavelet coefficients, constructing a time-frequency matrix through the local energy distribution, and reconstructing the target image according to the time-frequency matrix to obtain the final ISAR image.

2. The method for inverse synthetic aperture radar imaging based on ADMM harmonic wavelet according to claim 1, wherein Determining a window function, processing each time point of the range cell signal according to a sliding window, and determining the signal within a local time window, includes: Determining a window function, the expression of which is: ； In the formula, represents a window function; represents the index variable of the window function; represents the window function length; Based on the window function length , process each time point of the distance cell signal according to the sliding window to determine a local time window; Determining the signal within the local time window according to the local time window, the expression of the signal within the local time window is: ； In the formula, represents the signal within the local time window; represents the range cell signal; represents the starting index; represents the ending index.

3. The harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM according to claim 1, wherein The expression of the local harmonic wavelet basis matrix is: ； In the formula, represents the local harmonic wavelet basis matrix; represents the window function; represents the discrete Fourier transform matrix.

4. The harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM according to claim 1, characterized in that, The expression of the optimization model is: ； In the formula, represents the local harmonic wavelet basis matrix; represents the harmonic wavelet coefficients to be solved; represents the signal within the local time window; represents the regularization parameter.

5. The method for inverse synthetic aperture radar imaging based on ADMM harmonic wavelet according to any one of claims 1 to 4, characterized in that, Introducing auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients, includes: Introduce auxiliary variables and dual variables ; Based on the auxiliary variables , transform the optimization model into a constraint model; Based on the constraint model, for the harmonic wavelet coefficients to be solved , the auxiliary variables , and the dual variables are iteratively updated. When the iteration termination condition is satisfied, the final harmonic wavelet coefficients are obtained.

6. The harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM according to claim 5, wherein Converting the optimization model into a constraint model, the expression of the constraint model is: ； subject to: ; In the formula, represents the local harmonic wavelet basis matrix; represents the harmonic wavelet coefficients to be solved; represents the signal within the local time window; represents the regularization parameter.

7. The harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM according to claim 6, wherein For the harmonic wavelet coefficients to be solved perform iterative update, including: Constructing an update model for the harmonic wavelet coefficients, the expression of which is: ； Writing out the first-order optimal condition of the update model to obtain a regularized linear function, the expression of which is: ； Let be a lower triangular matrix such that ; By solving the triangular matrix twice, the -th harmonic wavelet coefficient is obtained; In the formula, represents the step auxiliary variable; represents the step dual variable; represents the penalty parameter; represents the time-frequency distribution of the ISAR image; represents vector transpose, where represents a replaceable variable.

8. The method for inverse synthetic aperture radar imaging based on ADMM harmonic wavelet according to claim 6, wherein Iteratively update the auxiliary variable as follows: Through the step harmonic wavelet coefficients and the step dual variables iteratively update the auxiliary variable The expression is: ； Wherein, the definition of the soft threshold operator is: ； In the formula, represents the step auxiliary variable; represents the penalty parameter; , represent the replacement variables.

9. The method for inverse synthetic aperture radar imaging based on ADMM and harmonic wavelet according to claim 6, wherein Iteratively update the dual variables including: Through harmonic wavelet coefficients and auxiliary variables to iteratively update the dual variable The expression is as follows: ； In the formula, represents the step dual variable; represents the step dual variable.

10. An ADMM-based harmonic wavelet inverse synthetic aperture radar imaging device, characterized in that, The device includes: A Fourier transform module, configured to obtain a range cell signal and construct a discrete Fourier transform matrix based on the range cell signal; A module for determining the signal within a local time window, configured to determine a window function, process each time point of the range cell signal according to a sliding window, and determine the signal within a local time window; An optimization model construction module, configured to construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then construct an optimization model according to the local harmonic wavelet basis matrix and the signal within the local time window; A harmonic wavelet coefficient calculation module, configured to introduce auxiliary variables and dual variables to iteratively solve the optimization model to obtain harmonic wavelet coefficients; An imaging module, configured to calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, and reconstruct the target image according to the time-frequency matrix to obtain the final ISAR image.

Images