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

Abstract

The present invention relates to a harmonic wavelet inverse synthetic aperture radar imaging method and device based on ADMM. The method comprises: acquiring range unit signals, constructing a discrete Fourier transform matrix based on the range unit signals; determining a window function, processing each time point of the range unit signals according to a sliding window, and determining the signal within the local time window; constructing a local harmonic wavelet basis matrix based on the discrete Fourier transform matrix and the window function; then constructing an optimization model based on 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 final harmonic wavelet coefficients; calculating local energy distribution based on the harmonic wavelet coefficients, constructing a time-frequency matrix based on the local energy distribution, and reconstructing the target image based on the time-frequency matrix to obtain the final ISAR image. The present invention can improve resolution, reduce cross-term interference, and achieve high imaging accuracy.

Description

Technical Field

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

[0002] Inverse synthetic aperture radar (ISAR) technology is a key method for acquiring two-dimensional target imaging in modern radar systems. ISAR utilizes the relative motion between the radar and the target to generate an equivalent synthetic aperture. By performing time-frequency analysis on the radar echo data, it reconstructs a two-dimensional reflection distribution image of the target. Traditional ISAR imaging primarily 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, targets often exhibit complex motions, such as rotation, pitch, and roll. This causes the Doppler frequency of the echo signal to vary over time, resulting in non-stationary characteristics. This, in turn, can cause images generated by traditional RD algorithms to exhibit problems such as defocus, blur, and cross-term interference.

[0003] To address the problem of non-stationary signal processing, researchers have proposed a variety of improved methods, which can be mainly divided into three categories: motion compensation techniques, 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 between time and frequency resolution, making it difficult to simultaneously achieve good time and frequency resolution. While PWVD has high time-frequency focusing performance, it produces significant cross-term interference. SPWVD reduces cross-term interference by smoothing PWVD, but also reduces time-frequency resolution. Summary of the Invention

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

[0005] A harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM, the method comprising:

[0006] Acquire a range unit signal, and construct a discrete Fourier transform matrix based on the range unit signal;

[0007] Determine a window function, process each time point of the range unit signal according to the sliding window, and determine a signal within a local time window;

[0008] 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 in the local time window;

[0009] Introducing auxiliary variables and dual variables to iteratively update the optimization model to obtain final harmonic wavelet coefficients;

[0010] The local energy distribution is calculated based on the harmonic wavelet coefficients, a time-frequency matrix is constructed through the local energy distribution, and a target image is reconstructed according to the time-frequency matrix to obtain a final ISAR image.

[0011] A harmonic wavelet inverse synthetic aperture radar imaging device based on ADMM, the device comprising:

[0012] A Fourier transform module, configured to obtain a range unit signal and construct a discrete Fourier transform matrix based on the range unit signal;

[0013] A signal determination module within a local time window is used to determine a window function, process each time point of the range unit signal according to a sliding window, and determine the signal within the local time window;

[0014] An optimization model construction module is used to construct a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; and then construct an optimization model according to the local harmonic wavelet basis matrix and the signal in the local time window;

[0015] A harmonic wavelet coefficient calculation module is used to introduce auxiliary variables and dual variables to iteratively solve the optimization model to obtain harmonic wavelet coefficients;

[0016] An imaging module is used to calculate local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, reconstruct a target image according to the time-frequency matrix, and obtain a final ISAR image.

[0017] The above-mentioned ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method and device obtains range unit signals and constructs a discrete Fourier transform matrix based on the range unit signals; determines a window function, processes each time point of the range unit signal according to a sliding window, and determines the signal in the local time window; constructs a local harmonic wavelet basis matrix according to the discrete Fourier transform matrix and the window function; then constructs an optimization model based on the local harmonic wavelet basis matrix and the signal in the local time window; introduces auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients; calculates the local energy distribution based on the harmonic wavelet coefficients, constructs a time-frequency matrix through the local energy distribution, and reconstructs the target image according to the time-frequency matrix to obtain the final ISAR image.

[0018] 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, avoiding repeated calculation of the Fourier transform in the subsequent iterative process, greatly reducing the complexity of the 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. 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 this 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 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 calculation time and accuracy in traditional time-frequency analysis, can improve resolution, reduce cross-term interference, and have high imaging accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

[0020] Figure 1 Schematic diagram of the flow of the ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method provided in Example 1;

[0021] Figure 2 Schematic diagram of the imaging results of the RD method provided in Example 1;

[0022] Figure 3 Schematic diagram of the imaging results of the STFT method provided in Example 1;

[0023] Figure 4 Schematic diagram of the imaging results of the SPWVD method provided in Example 1;

[0024] Figure 5 Schematic diagram of the imaging results of the method of the present invention provided in Example 1;

[0025] Figure 6 This is a structural block diagram of the ADMM-based harmonic wavelet inverse synthetic aperture radar imaging device provided in Example 2.

[0026] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0027] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0028] 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 this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0029] The following describes the implementation of the present invention in detail with reference to the accompanying drawings in the embodiments of the present invention.

[0030] Example 1

[0031] 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 constructed once, avoiding repeated calculation of the Fourier transform in subsequent iterative processes and greatly reducing the complexity of the calculation. At the same time, such processing can also ensure energy conservation, making subsequent transformations based on this matrix more numerically stable.

[0032] 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. 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 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.

[0033] By introducing auxiliary and dual variables, decomposition and efficient iteration are achieved. Artifacts and cross-terms in the time-frequency distribution are also avoided, allowing energy to be concentrated solely on the true signal components. This method effectively overcomes the contradiction between computational time and accuracy in traditional time-frequency analysis, improving resolution, reducing cross-term interference, and achieving high imaging accuracy.

[0034] like Figure 1 As shown in FIG, the harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM provided in this embodiment includes the following steps:

[0035] Step 201: Acquire a range unit signal, and construct a discrete Fourier transform matrix based on the range unit signal.

[0036] Step 202: determine a window function, process each time point of the range unit signal according to the sliding window, and determine the signal within the local time window.

[0037] 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 according to the local harmonic wavelet basis matrix and the signal in the local time window.

[0038] Step 204 : introducing auxiliary variables and dual variables to iteratively update the optimization model to obtain the final harmonic wavelet coefficients.

[0039] Step 205 : Calculate the local energy distribution based on the harmonic wavelet coefficients, construct a time-frequency matrix through the local energy distribution, reconstruct the target image according to the time-frequency matrix, and obtain the final ISAR image.

[0040] In the specific implementation process of step 201, the echo signal received by each distance unit is recorded as the distance unit signal , the number of distance unit sampling points is . Constructing a discrete Fourier transform matrix based on the distance unit signal ,matrix Each element in is defined as:

[0041] ;

[0042] Where, Represents the elements in the discrete Fourier transform matrix; represents an imaginary unit; Represents the row index of the matrix; Represents the column index of the matrix.

[0043] As you can understand, this constructed matrix exhibits the properties of a unitary matrix, namely, energy conservation. This makes subsequent transformations based on this matrix more numerically stable and facilitates matrix multiplication and transformation calculations. By precalculating the matrix once, it can be reused in multiple subsequent time steps, avoiding the redundant overhead of repeated calculations and reducing computational complexity.

[0044] In the specific implementation process of step 202, the window function is first determined, and the expression is:

[0045] ;

[0046] Where, represents the window function; The index variable representing the window function; Indicates the length of the window function;

[0047] Then, based on the window function length , in this embodiment, it is set to 4. According to the sliding window, each time point of the distance unit signal , select a local time window for processing. The local time window is determined by the start index and the end index. The expression of the start index is:

[0048] ;

[0049] The expression for the end index is:

[0050] ;

[0051] The signal in the local time window is determined according to the local time window. The expression of the signal in the local time window is:

[0052] ;

[0053] Where, Represents the signal in the local time window; Indicates the distance unit signal; Indicates the starting index; Indicates the end index; Indicates the number of sampling points in the orientation unit.

[0054] It can be understood that in the signal extraction and window selection process, this embodiment uses the start index and end index to perform boundary protection, and adopts a strategy of dynamically adjusting the window length at the start and end of the signal to avoid the adverse impact of edge effects on signal reconstruction.

[0055] By using the signal within the local time window, local features can be fully captured, the blurring of time-varying features caused by global transformation can be avoided, the non-stationarity of the signal can be broken, and high-purity and high-resolution feature input can be provided for subsequent high-precision imaging.

[0056] In the specific implementation process of step 203, a local harmonic wavelet basis matrix is constructed according to the discrete Fourier transform matrix and the window function. The expression of the local harmonic wavelet basis matrix is:

[0057] ;

[0058] Where, represents the local harmonic wavelet basis matrix; represents the window function; represents the discrete Fourier transform matrix.

[0059] It can be understood that based on the pre-built discrete Fourier transform matrix , through the window function By weighting the Fourier basis matrix, a local harmonic wavelet basis matrix suitable for describing local signals can be constructed in a very short time. The local harmonic wavelet basis matrix can better adapt to changes in the frequency domain distribution of the signal within a local time. Because the Fourier basis matrix has been pre-calculated, the operation of extracting a specific row can be completed in constant time, significantly improving the efficiency of basis matrix construction.

[0060] In constructing the local harmonic wavelet basis matrix Finally, for the local problem, considering that the actual signal usually has sparse representation characteristics, an optimization model with sparse constraints is constructed, which is expressed as:

[0061] ;

[0062] Where, represents the local harmonic wavelet basis matrix; represents the harmonic wavelet coefficients to be solved; Represents the signal in the local time window; represents the regularization parameter.

[0063] It can be understood that in the optimization model, the first term is the data fidelity term, which is used to ensure that the reconstructed signal has a high consistency with the original observation signal; the second term is the regularization term, which is used to apply Norm constraint forces the absolute values of most harmonic wavelet coefficients to approach zero, thereby achieving sparse representation while retaining the key features of the signal; regularization parameter Used to balance the relationship between data error and sparsity.

[0064] In the specific implementation process of step 204, in order to split the complex optimization problem into sub-problems that are easier to solve, thereby ensuring convergence to a better solution within a smaller number of iterations, the ADMM method is adopted and the auxiliary variable is introduced. With dual variables ; Based on the auxiliary variables , transform the optimization model into a constraint model; the constraint model expression is:

[0065] ;

[0066] subject to: ;

[0067] Based on the constraint model, the harmonic wavelet coefficients are solved , auxiliary variables With dual variables Perform iterative updates, and when the iteration termination condition is met, the final harmonic wavelet coefficients are obtained .

[0068] Specifically, we first solve the harmonic wavelet coefficients Perform iterative updates, including:

[0069] Construct the update model of harmonic wavelet coefficients, the expression is:

[0070] ;

[0071] Write down the first-order optimal condition of the updated model and obtain the regularized linear function, which is expressed as:

[0072] ;

[0073] Since the matrix It usually has a good condition number and can be solved efficiently by Cholesky decomposition. is a lower triangular matrix, so ; Then, by solving the triangular matrix twice, we can quickly get the Step-harmonic wavelet coefficients .

[0074] Where, Indicates the step auxiliary variables; Indicates the step-dual variables; represents the penalty parameter; represents the vector transpose, where Indicates a replaceable variable.

[0075] For auxiliary variables Perform iterative updates, including:

[0076] Through the Step-harmonic wavelet coefficients With the Step-dual variables For the auxiliary variable Perform iterative update, the expression is:

[0077] ;

[0078] Among them, the soft threshold operator is defined as:

[0079] ;

[0080] Where, Indicates the step auxiliary variables; represents the penalty parameter; 、 Represents a replacement variable, where , .

[0081] It is understandable that in the auxiliary variable During the iterative update process, The sub-problem of the regularization term is solved by using a vectorized soft threshold operation, which can process each component separately to ensure the sparsity of the solution.

[0082] Dual variables Perform iterative updates, including:

[0083] By using harmonic wavelet coefficients With auxiliary variables For the dual variable Perform iterative update, the expression is:

[0084] ;

[0085] Where, Indicates the step-dual variables; Indicates the Step dual variable.

[0086] It can be understood that in the entire iterative update process, the Cholesky decomposition is used to solve the positive quadratic optimization subproblem, and then combined with the vectorized soft threshold operation, the entire iterative process is efficient and stable. When setting the iterative termination condition, in addition to setting the number of iterations, you can also pre-set the convergence threshold , after each certain number of iterations, check the updated variables and The difference between When , the iteration can be terminated early to further reduce the amount of calculation.

[0087] In the specific implementation process of step 205, for each time window, the final harmonic wavelet coefficients are extracted. The square of the modulus is used as the local energy distribution, and the expression is:

[0088] ;

[0089] And the vector As a column in the output matrix. The time-frequency matrix is constructed through the local energy distribution. The time-frequency matrix constitutes the energy mapping of the signal in the time-frequency domain, and the expression is:

[0090] ;

[0091] The time-frequency matrix is constructed for each distance unit to obtain the final ISAR image time-frequency representation, which is defined as:

[0092] ;

[0093] Where, represents the time-frequency matrix; Indicates the number of sampling points of the orientation unit; Represents the time-frequency distribution of ISAR images; the matrix Indicates the number of distance unit sampling points.

[0094] It is worth noting that for each time window signal, a local harmonic wavelet basis matrix can be independently constructed and iteratively updated. In other words, the method proposed in this embodiment supports parallel computing. For each time window signal, steps 202 to 204 are run simultaneously on a multi-core processor or parallel computing platform, thereby meeting the requirements of real-time signal processing.

[0095] In one embodiment, the method provided by the present invention is verified.

[0096] like Figure 2 As shown in the figure, the imaging results obtained by using the traditional RD algorithm are shown. It can be seen that the target contour is obviously blurred and noisy, and the scattering center distribution is not concentrated enough, which makes the target structure details difficult to identify and the image contrast is low.

[0097] like Figure 3 As shown in FIG, the imaging results obtained by using the STFT algorithm are shown. Compared with the RD algorithm, the target contour is improved to a certain extent, but there are still problems of cross-term interference and limited resolution, and the target edge definition is not clear enough.

[0098] like Figure 4 As shown in FIG, the imaging results obtained by using the SPWVD algorithm are shown. The focusing effect of the target scattering center is improved, but certain artifacts are still visible around the target outline, and the scattering points of some parts of the target are unevenly distributed.

[0099] like Figure 5 As shown in FIG, the imaging results obtained by the method proposed in the present invention are shown. It can be seen that the target scattering points are more concentrated, the edge contour is clearer, the background noise is effectively suppressed, and the target structure details are more completely retained, which reflects the advantages of the present invention.

[0100] Although this embodiment Figure 1 The steps in the diagram are shown in the order indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1At least part of the steps 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. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0101] Example 2

[0102] Based on the harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM in Example 1, this embodiment discloses a harmonic wavelet inverse synthetic aperture radar imaging device based on ADMM, such as Figure 6 As shown, the harmonic wavelet inverse synthetic aperture radar imaging device based on ADMM includes: a Fourier transform module 401, a signal determination module 402 in a local time window, an optimization model construction module 403, a harmonic wavelet coefficient calculation module 404 and an imaging module 405, wherein:

[0103] The Fourier transform module 401 is used to obtain the range unit signal and construct a discrete Fourier transform matrix based on the range unit signal.

[0104] The signal determination module 402 in the local time window is used to determine a window function, and processes each time point of the range unit signal according to the sliding window to determine the signal in the local time window.

[0105] 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; and then construct an optimization model according to the local harmonic wavelet basis matrix and the signal in the local time window.

[0106] 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.

[0107] 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, reconstruct the target image according to the time-frequency matrix, and obtain the final ISAR image.

[0108] In this embodiment, the specific working process and working principle of the Fourier transform module 401, the signal determination module 402 within the local time window, the optimization model construction module 403, the harmonic wavelet coefficient calculation module 404 and the imaging module 405 are the same as those in the method of Example 1, and therefore are not described in detail in this embodiment. Each unit module can be implemented in whole or in part by software, hardware or a combination thereof. Each unit module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above unit modules.

[0109] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the 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-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0110] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, 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, they should be considered to be within the scope of this specification.

[0111] The above-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that a person skilled in the art would be able to make numerous modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A harmonic wavelet inverse synthetic aperture radar imaging method based on ADMM, characterized in that: The method comprises: Acquire a range unit signal, and construct a discrete Fourier transform matrix based on the range unit signal; Determine a window function, process each time point of the range unit signal according to the sliding window, and determine a 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 in the local time window; Introducing auxiliary variables and dual variables to iteratively update the optimization model to obtain final harmonic wavelet coefficients; The local energy distribution is calculated based on the harmonic wavelet coefficients, a time-frequency matrix is constructed through the local energy distribution, and a target image is reconstructed according to the time-frequency matrix to obtain a final ISAR image.

2. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to claim 1, characterized in that: Determining a window function, processing each time point of the range unit signal according to the sliding window, and determining a signal within a local time window, including: Determine the window function, the expression is: ； Where, represents the window function; The index variable representing the window function; Indicates the length of the window function; Based on the window function length , processing each time point of the range unit signal according to the sliding window to determine a local time window; The signal in the local time window is determined according to the local time window, and the expression of the signal in the local time window is: ； Where, Represents the signal in the local time window; Indicates the distance unit signal; Indicates the starting index; Indicates the ending index.

3. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to claim 1, characterized in that: The local harmonic wavelet basis matrix expression is: ； Where, represents the local harmonic wavelet basis matrix; represents the window function; represents the discrete Fourier transform matrix.

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

5. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to any one of claims 1 to 4, characterized in that: Auxiliary variables and dual variables are introduced to iteratively update the optimization model to obtain the final harmonic wavelet coefficients, including: Introducing auxiliary variables With dual variables ; Based on the auxiliary variables , converting the optimization model into a constraint model; Based on the constraint model, the harmonic wavelet coefficients to be solved , the auxiliary variable With the dual variable Perform iterative updates, and when the iteration termination condition is met, the final harmonic wavelet coefficients are obtained .

6. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to claim 5, characterized in that: The optimization model is converted into a constraint model, and the constraint model expression is: ； subject to: ; Where, represents the local harmonic wavelet basis matrix; represents the harmonic wavelet coefficients to be solved; Represents the signal in the local time window; represents the regularization parameter.

7. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to claim 6, characterized in that: The harmonic wavelet coefficients to be solved Perform iterative updates, including: Construct the update model of harmonic wavelet coefficients, the expression is: ； The first-order optimal condition of the update model is written out to obtain the regularized linear function, which is expressed as: ； set up is a lower triangular matrix, so ; Solve the triangular matrix twice and get Step-harmonic wavelet coefficients ; Where, Indicates the step auxiliary variables; Indicates the step-dual variables; represents the penalty parameter; Represents the time-frequency distribution of ISAR images; represents the vector transpose, where Indicates a replaceable variable.

8. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to claim 6, characterized in that: For the auxiliary variable Perform iterative updates, including: Through the Step-harmonic wavelet coefficients With the Step-dual variables For the auxiliary variable Perform iterative update, the expression is: ； Among them, the soft threshold operator is defined as: ； Where, Indicates the step auxiliary variables; represents the penalty parameter; 、 Indicates a replacement variable.

9. The ADMM-based harmonic wavelet inverse synthetic aperture radar imaging method according to claim 6, characterized in that: For the dual variable Perform iterative updates, including: By using harmonic wavelet coefficients With auxiliary variables For the dual variable Perform iterative update, the expression is: ； Where, Indicates the step-dual variables; Indicates the Step dual variable.

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

Images