Inverse synthetic aperture radar imaging method and system with phase distortion and two-dimensional compression sampling, terminal equipment and medium

Abstract

The invention discloses an inverse synthetic aperture radar imaging method and system with phase distortion and two-dimensional compression sampling, terminal equipment and a medium, and relates to the technical field of radar imaging. The method comprises the following steps: constructing a sparse recovery model containing phase error correction based on a low-rank and sparsity principle; wherein the sparse recovery model is adapted to an inverse synthetic aperture radar echo signal which is subjected to two-dimensional compression sampling and has phase distortion; and based on a unified alternating direction multiplier method framework, solving the sparse recovery model to complete sparse recovery and phase error correction of the two-dimensional compressed sampling signal, and outputting an inverse synthetic aperture radar image. According to the method, the problems that phase errors are ignored in existing inverse synthetic aperture radar imaging and phase correction fails during down-sampling are solved, a clear image can be generated, and the calculation complexity is reduced.

Description

Technical Field

[0001] This invention relates to the field of radar imaging technology, and in particular to an inverse synthetic aperture radar imaging method, system, terminal equipment, and medium with phase distortion and two-dimensional compressed sampling. Background Technology

[0002] Sparse reconstruction technology can effectively reconstruct signals with limited sampling and is widely used in high-resolution radar imaging, medical imaging and other fields.

[0003] For Inverse Synthetic Aperture Radar (ISAR), existing sparse imaging techniques such as compressed sensing, matrix completion, and hybrid methods only consider the incoherence of compressed sampling and ignore the influence of phase error. However, phase distortion will destroy the sparsity of the image and the low rank of the radar data, reducing imaging accuracy. Although there are phase correction techniques such as main / multiple scatterer autofocus and phase gradient autofocus (PGA), these techniques will fail when directly processing downsampled radar data due to the lack of pulse coherence. In addition, although deep learning-based hybrid methods can alleviate parameter sensitivity, their generalization ability is insufficient when processing new radar systems or new target data.

[0004] Therefore, there is an urgent need for a method that can combine sparse recovery of two-dimensional downsampled signals with phase error correction of inverse synthetic aperture radar imaging to fill the gap in existing technologies. Summary of the Invention

[0005] The technical problem this invention aims to solve is that, in the field of radar imaging, existing inverse synthetic aperture radar (INS) sparse imaging techniques ignore the influence of phase errors, existing phase correction techniques fail with downsampled radar data, and deep learning hybrid methods lack generalization ability, making it difficult to generate clear INS images in scenarios with two-dimensional compressed sampling and phase distortion. Therefore, an effective solution is urgently needed to address the aforementioned technical problems.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides an inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling, the method comprising: Based on the principles of low rank and sparsity, a sparse recovery model including phase error correction is constructed; wherein, the sparse recovery model is adapted to two-dimensional compressed sampling and inverse synthetic aperture radar echo signals with phase distortion. Based on the unified alternating direction multiplier method framework, the sparse recovery model is solved to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal, and output the inverse synthetic aperture radar image.

[0007] In one implementation, the construction of a sparse recovery model including phase error correction based on the principles of low rank and sparsity includes: Define the matrix form of the inverse synthetic aperture radar signal model with all sampled measurements; The matrix form of the inverse synthetic aperture radar signal model is subjected to two-dimensional compression sampling to obtain the downsampled signal model; Since the phase error matrix is ​​a diagonal matrix, the downsampled signal model is rewritten. For two-dimensional downsampled radar data with phase distortion, we define an inverse synthetic aperture radar imaging problem with low-rank and sparsity constraints.

[0008] In one implementation, the matrix form of the inverse synthetic aperture radar signal model with fully sampled measurements is expressed as:

[0009] in, This represents fully sampled radar data. This represents an inverse synthetic aperture radar image. This represents additive white Gaussian noise from the full sample. Denotes the Fourier matrix of the distance dimension. Represents the Fourier matrix in the azimuth direction (lateral distance dimension). This represents the phase error matrix of the full sampling. This indicates the conjugate transpose operation.

[0010] In one implementation, a two-dimensional compression sampling operation is performed on the matrix form of the inverse synthetic aperture radar signal model to obtain the downsampled signal model, which is represented as:

[0011] in, This indicates a downsampling operation.

[0012] In one implementation, since the phase error matrix is ​​a diagonal matrix, the downsampled signal model is rewritten as follows:

[0013] in, , and .

[0014] In one implementation, the inverse synthetic aperture radar (ISAR) imaging problem with low-rank and sparsity constraints for two-dimensional downsampled radar data with phase distortion is expressed as:

[0015] in, The nuclear norm is denoted by , which represents the rank of a matrix and is equal to the sum of its singular values. Representing a matrix Norm, Describing the Frobenius norm, The regularization coefficient is used to determine the low-rank degree of the recovered radar data. is the regularization coefficient used to determine the sparsity of the reconstructed inverse synthetic aperture radar image.

[0016] In one implementation, the sparse recovery model is solved based on a unified alternating direction multiplier method framework to complete the sparse recovery and phase error correction of the two-dimensional compressed sampled signal, and output an inverse synthetic aperture radar image, including: Construct the augmented Lagrangian function; Using an alternating direction multiplier solver, several minimization subproblems are solved iteratively, and inverse synthetic aperture radar images are output.

[0017] In one implementation, the constructed augmented Lagrangian function is expressed as:

[0018] in, Represents the Lagrange multipliers. This represents the penalty parameter.

[0019] In one implementation, the plurality of minimization subproblems include:

[0020]

[0021]

[0022]

[0023] in, Indicates the first iteration Represents image entropy. It is the phase vector to be compensated.

[0024] In one implementation, the sparse mode of the two-dimensional compressed sampling includes at least one of the following: root mean square mode, separable root mean square mode, Gaussian random mask mode, and mixed sparse mode.

[0025] In one implementation, the noise in the data of the inverse synthetic aperture radar echo signal is additive white Gaussian noise, and the sparse recovery model suppresses the noise through Frobenius norm constraints.

[0026] Secondly, embodiments of the present invention also provide an inverse synthetic aperture radar imaging system with phase distortion and two-dimensional compressed sampling, the system comprising: A sparse recovery model construction module is used to construct a sparse recovery model including phase error correction based on the principles of low rank and sparsity; wherein, the sparse recovery model is adapted to two-dimensional compressed sampling and inverse synthetic aperture radar echo signals with phase distortion; The inverse synthetic aperture radar (ISAR) image output module is used to solve the sparse recovery model based on a unified alternating direction multiplier method framework to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal and output an ISAR image.

[0027] In one implementation, the sparse recovery model construction module includes: The signal model matrix definition unit is used to define the matrix form of the inverse synthetic aperture radar signal model with full sampled measurements; The signal model matrix downsampling unit is used to perform two-dimensional compression sampling on the matrix form of the inverse synthetic aperture radar signal model to obtain the downsampled signal model. The signal model matrix rewriting unit is used to rewrite the downsampled signal model since the phase error matrix is ​​a diagonal matrix; The imaging problem definition unit is used to define the inverse synthetic aperture radar imaging problem with low-rank and sparsity constraints for two-dimensional downsampled radar data with phase distortion.

[0028] In one implementation, the inverse synthetic aperture radar image output module includes: Augmented Lagrangian function building unit, used to construct augmented Lagrangian functions; The alternating direction multiplier method solver unit is used to iteratively solve several minimization subproblems using the alternating direction multiplier method solver, and output inverse synthetic aperture radar images.

[0029] Thirdly, embodiments of the present invention also provide a terminal device, the terminal device including a memory, a processor, and an inverse synthetic aperture radar imaging program with phase distortion and two-dimensional compressed sampling stored in the memory and executable on the processor. When the processor executes the inverse synthetic aperture radar imaging program with phase distortion and two-dimensional compressed sampling, it implements the steps of the inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling as described in any of the above schemes.

[0030] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing an inverse synthetic aperture radar (INS) imaging program with phase distortion and two-dimensional compressed sampling. When the INS imaging program with phase distortion and two-dimensional compressed sampling is executed by a processor, it implements the steps of the INS imaging method with phase distortion and two-dimensional compressed sampling described in any of the above schemes.

[0031] Beneficial Effects: This invention discloses an inverse synthetic aperture radar (InSAR) imaging method, system, terminal device, and medium with phase distortion and two-dimensional compressed sampling, relating to the field of radar imaging technology. The method first constructs a sparse recovery model including phase error correction based on the principles of low rank and sparsity; wherein the sparse recovery model is adapted to two-dimensional compressed sampling and phase-distorted InSAR echo signals. Subsequently, based on a unified alternating direction multiplier method framework, the sparse recovery model is solved to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal, outputting an InSAR image. Compared with existing technologies, this invention can effectively suppress noise and sidelobes in two-dimensional compressed sampling and phase-distortion scenarios, preserve the target contour of the InSAR image, solve the problem of target identification difficulties in existing methods, and avoid the matrix vectorization and nested iteration of multi-task alternating direction multiplier methods, reducing computational complexity. It is robust to different phase errors, signal-to-noise ratios, and sampling modes, and can generate clearer InSAR images. Attached Figure Description

[0032] Figure 1 A flowchart illustrating a specific implementation of the inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling provided in this invention.

[0033] Figure 2 This is a flowchart illustrating the sparse recovery model construction steps of a specific implementation of the inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling provided in this invention.

[0034] Figure 3 This is a flowchart illustrating the sparse recovery model solution steps for a specific implementation of the inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling provided in this invention.

[0035] Figure 4 The inverse synthetic aperture radar (InSAR) images under different sparse modes with a sampling rate of 20% provided in the embodiment of the present invention are provided in the inverse synthetic aperture radar (InSAR) imaging method with phase distortion and two-dimensional compressed sampling.

[0036] Figure 5 This is a schematic diagram of the inverse synthetic aperture radar imaging device with phase distortion and two-dimensional compressed sampling provided in the embodiments of the present invention.

[0037] Figure 6 This is a block diagram illustrating the internal structure of the terminal device provided in an embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0039] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content, operations, or steps, nor does it require execution in the described order. For example, some operations or steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0040] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0041] It should be understood that, in order to clearly describe the technical solutions of the embodiments of the present invention, the terms "first" and "second" are used in the embodiments of the present invention to distinguish identical or similar items with essentially the same function and effect. For example, "first control information" and "second control information" are only used to distinguish different control information and do not limit their order.

[0042] Those skilled in the art will understand that the words "first" and "second" do not limit the quantity or the order of execution, and that the words "first" and "second" do not necessarily imply that they are different.

[0043] It should also be understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0044] Sparse reconstruction technology, with its advantage of effectively reconstructing signals under limited sampling conditions, has been widely applied in various key scenarios in modern measurement fields, including but not limited to high-resolution radar imaging, medical imaging, communication signal processing, and Earth observation. In these applications, accurate signal recovery is crucial for subsequent target identification and information extraction, especially in scenarios requiring precise recovery of target details such as target contours and scattering point distribution in radar imaging. The effectiveness of sparse reconstruction technology directly impacts the overall system performance.

[0045] However, in practical engineering applications, signal measurement often faces two major challenges. First, the inherent phase distortion of the signal itself; second, the uncertainty of the sparse pattern and degree of sparsity. These two problems together lead to a decrease in signal reconstruction accuracy, becoming a bottleneck restricting the further application of sparse reconstruction technology. Taking the field of Inverse Synthetic Aperture Radar (ISAR) imaging as an example, existing sparse imaging technologies can be clearly divided into three categories based on their data processing methods: Compressed Sensing (CS), Matrix Completion (MC), and hybrid methods that combine the advantages of both. The design of these methods revolves around the need to reduce sampling by utilizing signal sparsity, focusing only on the data incoherence caused by compressed sampling, while generally neglecting the impact of phase error on the imaging process. Phase distortion directly destroys the sparsity characteristics of the image to be reconstructed, and also changes the low-rank nature of the processed radar data, leading to a significant increase in the complexity of the image reconstruction process. Ultimately, this severely weakens the effectiveness of the aforementioned sparse recovery methods, making it impossible to obtain clear and usable ISAR images.

[0046] To address phase error issues, various phase correction techniques have been developed, including: main / multiple scatterer autofocus, which corrects overall phase error by identifying the main scatterer or multiple key scatterers in the imaging region and using their phase as a reference; Doppler Centroid Tracking (DCT), which assumes a central Doppler frequency shift in the radar echo signal and eliminates some phase deviation by adjusting this shift to zero; Phase Gradient Autofocus (PGA), which first performs a coarse phase correction and then refines the phase accuracy through windowing and cyclic shifting operations in multiple iterations; and phase correction techniques based on image quality metrics, which estimate and correct phase errors by optimizing image quality metrics (such as image contrast and image entropy). However, all of the above phase correction techniques share a common flaw: due to the lack of sufficient coherence between pulses in the radar data after two-dimensional compressed sampling, these autofocus algorithms completely fail when directly used to process downsampled radar data, failing to achieve effective phase error compensation and thus failing to generate ISAR images that meet the accuracy requirements.

[0047] With the development of deep learning technology, hybrid methods combining model-based approaches with data-driven training have emerged to alleviate the limitations of traditional model-based sparse reconstruction algorithms. These methods utilize deep unrolling techniques to transform traditional iterative algorithms such as Alternating Direction Method of Multipliers (ADMM), Iterative Soft-Thresholding Algorithm (ISTA), and Approximate Message Passing (AMP) into trainable neural network layers. By adjusting the hyperparameters of the algorithms using small datasets, they alleviate the parameter sensitivity problem of traditional model-based algorithms to some extent. However, these hybrid methods still have significant shortcomings. Their generalization ability heavily relies on the training dataset. When processing data from new radar systems or new targets not included in the training set, model performance drops sharply, making it difficult to stably output high-quality ISAR images and adapt to the complex and ever-changing application scenarios in real-world engineering.

[0048] Therefore, existing ISAR imaging technologies generally suffer from low imaging accuracy, phase correction failure, and insufficient generalization ability when faced with composite scenarios of two-dimensional compressed sampling and phase distortion. They cannot meet the requirements of practical applications for ISAR image quality and stability, and there is an urgent need for an imaging method that can solve the above-mentioned technical problems.

[0049] This embodiment provides an inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling, such as... Figure 1 As shown, the specific steps include the following: Step S100: Based on the principles of low rank and sparsity, a sparse recovery model including phase error correction is constructed; wherein, the sparse recovery model is adapted to two-dimensional compressed sampling and inverse synthetic aperture radar echo signals with phase distortion.

[0050] In this embodiment, the principles of low rank and sparsity are core theories in signal processing that utilize the inherent structural characteristics of signals to simplify problem-solving. By mining the low-rank or sparse properties of signals in specific transform domains or representation spaces, the computational complexity of signal recovery or reconstruction is reduced and accuracy is improved. Low-rank properties are characterized by singular values ​​of the matrix concentrated in a few large values, with most singular values ​​close to zero. Sparsity properties are characterized by the extremely low proportion of non-zero elements in the signal. Specifically, this can be based on the sparsity of target scattering point distribution and the low-rank correlation of radar data in the azimuth and range dimensions. Sparsity is characterized by target scattering points in ISAR images typically concentrated in a few regions, with most regions being background noise. Low-rank correlation is characterized by strong correlation between adjacent pulses of radar echoes from the same target, resulting in a matrix with low-rank characteristics.

[0051] Phase error correction is a technique used to compensate for and calibrate the phase shift caused by factors such as system errors and motion errors during the transmission, reception, or processing of radar echo signals. Specifically, it can be achieved by estimating the phase error matrix and correcting the phase of the signal to eliminate the negative impact of phase distortion on imaging quality and ensure the phase consistency of the target scattering points.

[0052] Sparse recovery models are mathematical models built upon the principles of low rank and sparsity. They are used to recover the original sparse or low-rank signals from undersampled or noisy observation signals. Specifically, they can be optimization models with regularization constraints, guiding the model output to conform to the sparse or low-rank characteristics. The sparse recovery model used in this embodiment incorporates phase error correction into its framework, rather than focusing solely on sparse recovery or handling phase correction separately as in traditional models. Existing techniques often ignore the destructive effects of phase errors on sparsity and low rank, leading to blurred images. By embedding phase error correction into the model, phase distortion can be compensated simultaneously during signal recovery, fundamentally ensuring the effectiveness of the model's constraints on sparsity and low rank, and significantly improving imaging accuracy.

[0053] Two-dimensional compressed sampling refers to using a sampling method with a lower sampling rate than Nyquist in both the range and azimuth dimensions of the radar signal, in order to reduce the amount of data collected and reduce storage and transmission pressure. Specifically, it can selectively collect the full sampled signal according to a preset sparse mode such as root mean square mode or Gaussian random mask mode, retaining only some key observation values.

[0054] Inverse synthetic aperture radar (ISAR) echo signals with phase distortion refer to signals received by ISAR radar that have undergone phase shift after being scattered and propagated by the target. Specifically, these signals may be echo signals whose phase deviates from the ideal value due to factors such as unstable target motion, radar system phase noise, and atmospheric refraction. These types of signals are common observation objects in practical engineering and are also the objects of processing in this embodiment.

[0055] The sparse restoration model, adapted to 2D compressed-sampled ISAR echo signals with phase distortion, clearly defines its input characteristics and applicable scenarios, avoiding the limitations of traditional models that are only applicable to fully sampled or phase-distortion-free signals. By combining low-rank and sparsity principles with phase error correction, the model can simultaneously utilize the structural characteristics of the signal and compensate for phase distortion, providing a foundation for subsequent solutions and high-quality imaging. Even with reduced sampling rates, it can effectively preserve key target information, avoiding target contour blurring or loss due to phase distortion and undersampling.

[0056] In one implementation, such as Figure 2As shown, the sparse recovery model, which incorporates phase error correction based on the principles of low rank and sparsity, specifically includes the following steps: Step S110: Define the matrix form of the inverse synthetic aperture radar signal model with full sampled measurements; Step S120: Perform a two-dimensional compression sampling operation on the matrix form of the inverse synthetic aperture radar signal model to obtain the downsampled signal model; Step S130: Since the phase error matrix is ​​a diagonal matrix, the downsampled signal model is rewritten; Step S140: For two-dimensional downsampled radar data with phase distortion, define an inverse synthetic aperture radar imaging problem with low-rank and sparsity constraints.

[0057] In this embodiment, the matrix form of the inverse synthetic aperture radar signal model with fully sampled measurements is first defined. Fully sampled measurements refer to the raw radar data acquired at the Nyquist sampling rate without compressed sampling. The purpose is to first establish the mathematical relationship between the signal, image, and phase error under ideal sampling conditions, providing a benchmark for the subsequent model derivation in compressed sampling scenarios. In practical applications, although fully sampled data provides the most complete signal information, the data volume is enormous and is only used for theoretical modeling and benchmark verification. Subsequent compressed sampling can significantly reduce the data volume, adapting it to actual engineering needs.

[0058] Subsequently, a two-dimensional compression sampling operation is performed on the matrix form of the fully sampled signal model to obtain the downsampled signal model. This adapts the ideal model to the actual engineering scenario. Two-dimensional compression sampling reduces the sampling rate simultaneously in the distance and azimuth dimensions, reducing the pressure on data acquisition, storage, and transmission. Specifically, the sampling operation can be performed by filtering elements of the fully sampled matrix according to a preset sparse pattern, such as root mean square mode or Gaussian random mask mode, retaining only observations at certain locations and discarding the remaining redundant data. This reduces the data volume while ensuring that key signal information is not lost, solving the problem of high processing costs for fully sampled data, and simultaneously providing undersampled observation data for subsequent sparse recovery.

[0059] Subsequently, since the phase error matrix is ​​a diagonal matrix, the downsampled signal model is rewritten. The diagonal characteristic of the phase error matrix is ​​determined by the physical principles of ISAR imaging. Phase errors mainly originate from target motion or system errors, and their effects are independent in each range cell; therefore, the phase error matrix exhibits a diagonal structure. Utilizing this characteristic to rewrite the model simplifies complex matrix multiplication operations to the product of a diagonal matrix and a regular matrix. Specifically, it integrates the product of the downsampling operation matrix, the Fourier matrix, and the phase error matrix into a simplified matrix, reducing the computational load in subsequent solution processes. By simplifying the model structure, the solution complexity of the optimization problem is reduced, providing a foundation for efficient iterative solutions.

[0060] Finally, for 2D downsampled radar data with phase distortion, an ISAR imaging problem with low-rank and sparsity constraints is defined. By introducing low-rank and sparsity constraints, the model is guided to recover high-quality ISAR images from undersampled, phase-distorted observation data. The low-rank constraint corresponds to the correlation between the azimuth and range dimensions of the radar data, while the sparsity constraint corresponds to the scattering point distribution characteristics of the ISAR image. The combination of the two can fully utilize the inherent structure of the signal and improve the recovery accuracy. The imaging problem is transformed into a solvable optimization problem, clarifying the objective function and constraints of the model, providing a mathematical framework for subsequent ADMM solving, and at the same time, the synergistic effect of the two constraints resists the negative impact of phase distortion and undersampling.

[0061] The modeling process transitions from ideal full-sampling scenarios to actual compressed sampling scenarios, and from unconstrained models to optimization problems with dual constraints. While ensuring the theoretical rigor of the model, it also takes into account its engineering practicality. The constructed sparse recovery model can adapt to the composite scenario of two-dimensional compressed sampling and phase distortion, thus overcoming the limitations of existing models.

[0062] In one implementation, the matrix form of the inverse synthetic aperture radar signal model with fully sampled measurements is expressed as:

[0063] in, This represents fully sampled radar data. This represents an inverse synthetic aperture radar image. This represents additive white Gaussian noise from the full sample. Denotes the Fourier matrix of the distance dimension. Represents the Fourier matrix in the azimuth direction (lateral distance dimension). This represents the phase error matrix of the full sampling. This indicates the conjugate transpose operation.

[0064] In this embodiment, the matrix form of the inverse synthetic aperture radar signal model with full sampling measurements serves to quantify the mathematical relationship between radar echo signals, ISAR images, phase errors, and noise under full sampling conditions, providing a theoretical basis for subsequent compressed sampling modeling and signal recovery.

[0065] In this matrix form, the fully sampled radar data matrix It is the original signal matrix collected by the radar receiver. Its dimensions are determined by the number of sampling points in the range and azimuth dimensions. Specifically, it can be a matrix with the number of rows equal to the number of sampling points in the range dimension and the number of columns equal to the number of pulses in the azimuth dimension. Each element corresponds to the radar echo amplitude and phase information of a specific range cell and a specific pulse time.

[0066] Inverse synthetic aperture radar image matrix It is the target image matrix to be reconstructed, with the same dimensions as the fully sampled radar data matrix. Each element corresponds to the scattering intensity of the target at a specific distance and azimuth unit. Its non-zero elements are concentrated at the target scattering point, exhibiting significant sparsity characteristics.

[0067] Fully sampled additive white Gaussian noise This is the inherent noise of the radar system, and its distribution follows a Gaussian distribution with zero mean and constant variance. Specifically, it can be... For random matrices of the same dimension, the presence of noise can interfere with the purity of the signal, causing deviations between the observed data and the ideal signal, which is a factor affecting image quality.

[0068] Fourier matrix of distance dimension Fourier matrix of orientation It is an orthogonal matrix used for signal domain transformation, specifically a unit orthogonal matrix constructed based on the Fast Fourier Transform (FFT). Its function is to transform the ISAR image matrix from the range and azimuth domain to the frequency domain of the radar echo, realizing the Fourier transform operation of the signal, where the conjugate transpose operation... Used to perform inverse or orthogonal transformations.

[0069] Phase error matrix of full sampling It is a diagonal matrix, whose diagonal elements correspond to the phase error value of each azimuth pulse, used to characterize the phase distortion caused by target motion, system errors, etc.

[0070] In this matrix form, the ideal noise-free and phase-distortion-free radar echo signal is obtained by multiplying the ISAR image by the phase error matrix after performing range and azimuth Fourier transforms. The actual observed fully sampled radar data is the superposition of the ideal signal and additive white Gaussian noise. Establishing this relationship clarifies the quantitative correlation between various physical quantities, providing a theoretical basis for subsequent phase error correction. The phase error matrix can be separated from the observation data through reverse derivation. Furthermore, it provides a basic framework for constructing a compressed sampling model. Subsequent implementations only require introducing downsampling operations based on this model to adapt to compressed sampling scenarios in actual engineering, without needing to reconstruct a completely new mathematical model, thus ensuring the consistency and rigor of the technical solution.

[0071] In one implementation, a two-dimensional compression sampling operation is performed on the matrix form of the inverse synthetic aperture radar signal model to obtain the downsampled signal model, which is represented as:

[0072] in, This indicates a downsampling operation.

[0073] In this embodiment, a two-dimensional compression sampling operation is performed on the matrix form of the inverse synthetic aperture radar signal model. This simulates the data acquisition process of downsampling in actual engineering. By reducing the amount of observation data, the storage, transmission and processing costs are reduced, while the key information of the signal is preserved to support subsequent recovery and reconstruction.

[0074] In the downsampled signal model, variable downsampling operation It is a selection matrix with a dimension lower than the full sampling matrix. Its elements are 1 only at the corresponding sampling position and 0 at the rest. Its function is to select from the full sampling radar data matrix. A subset of observations is selected to form a downsampled radar data matrix. The downsampling operation can be implemented using a preset sparse pattern, such as sampling at fixed intervals in the range and azimuth dimensions, or randomly selecting sampling points using a random mask pattern. The specific sampling pattern can be selected according to engineering requirements.

[0075] In this downsampling operation, the downsampled radar data is the fully sampled data. After downsampling operation The result is obtained by extracting a subset of rows or columns (corresponding to sampling points in the range or azimuth dimension) from the fully sampled matrix using matrix multiplication or tensor multiplication, resulting in a lower-dimensional observation matrix. The technical benefits of this downsampling operation are threefold: First, it reduces the amount of data. Through two-dimensional compressed sampling, the data volume can be significantly reduced proportionally to the sampling rate, lowering storage and transmission pressure. Second, it adapts to practical acquisition systems. Actual radar systems are limited by hardware performance and cannot achieve full sampling; two-dimensional compressed sampling meets the engineering requirements of low power consumption and low cost. Third, it preserves key information. The downsampling operation is designed based on sparse reconstruction theory. The sampling mode ensures incoherence between the observed data and the original signal, providing the possibility of recovering the original signal from the undersampled data. If the sampling mode meets the constraints of compressed sensing, the original signal can be recovered with high precision from the downsampled signal model using a sparse recovery algorithm. This allows for the reconstruction of ISAR images.

[0076] The sparse mode of downsampling is not unique and can be adjusted according to the actual scenario. For example, a higher sampling rate can be used in areas with dense target scattering points and a lower sampling rate can be used in background areas to further reduce the amount of data while ensuring recovery accuracy.

[0077] In one implementation, since the phase error matrix is ​​a diagonal matrix, the downsampled signal model is rewritten as follows:

[0078] in, , and .

[0079] In this embodiment, due to the phase error matrix It is a diagonal matrix that rewrites the downsampled signal model. It uses the operational properties of diagonal matrices to simplify the model structure, reduce the complexity of subsequent optimization and solution, and at the same time keep the physical meaning of the model unchanged.

[0080] The model is rewritten using the characteristics of a diagonal matrix. The essence of a diagonal matrix is ​​that only the main diagonal has non-zero elements, and when multiplied by other matrices, it only affects the elements in the corresponding dimension and does not introduce cross-dimensional coupling. Specifically, in this model... It is the phase error diagonal matrix of the full sampling, and its conjugate transpose Maintaining the same diagonal structure, this characteristic makes With downsampling operation The order of operations can be adjusted, but will not change. The physical meaning of the signal terms after the azimuth and range Fourier transform of the ISAR image.

[0081] Based on the above characteristics, the technical disclosure document first defines new variables. , indicating the ISAR image matrix The signal matrix after sequentially performing azimuth-dimensional Fourier transform and range-dimensional Fourier transform is physically represented by the ISAR image in the frequency domain, simplifying and encapsulating the transformation process from image to frequency domain signal.

[0082] Subsequently, new observation and noise matrices are defined based on the results of the downsampling operation. Let... That is, the downsampled radar data, and let This is the downsampled additive white Gaussian noise matrix. At this point, the downsampled signal model is rewritten as... .

[0083] Rewriting simplifies the model structure, clarifies the relationships between physical quantities, and lays the foundation for sparse recovery modeling. Specifically, the multi-layered coupling relationships of downsampling operations, phase errors, and frequency domain signals in the original model are reorganized into a structure of phase error, downsampling operations, and frequency domain signals, avoiding redundant expressions involving continuous multiplication of multiple matrices, making the model easier to understand and for subsequent derivation. Furthermore, by defining... By fixing the transformation relationship between ISAR images and frequency domain signals, subsequent optimization problems only need to focus on... Expanding allows for indirect manipulation of ISAR images. The reconstruction was performed. Simultaneously, after rewriting, the phase error term, downsampled signal term, and noise term were separated; subsequent steps only require... By introducing low-rank, sparse constraints, a complete sparse recovery model can be formed without having to decompose the complex coupling relationships of the original model.

[0084] The calculations are simplified and rewritten by utilizing the diagonal properties of the phase error matrix. At the same time, the physical relationships are clarified through variable definition, providing a mathematical foundation for the subsequent construction and solution of the sparse recovery model.

[0085] In one implementation, the inverse synthetic aperture radar (ISAR) imaging problem with low-rank and sparsity constraints for two-dimensional downsampled radar data with phase distortion is expressed as:

[0086] in, The nuclear norm is denoted by , which represents the rank of a matrix and is equal to the sum of its singular values. Representing a matrix Norm, Describing the Frobenius norm, The regularization coefficient is used to determine the low-rank degree of the recovered radar data. is the regularization coefficient used to determine the sparsity of the reconstructed inverse synthetic aperture radar image. Here, the Frobenius norm is the square root of the sum of the squares of all elements in the matrix, used to measure the overall deviation between the observed data and the model output.

[0087] In this embodiment, for 2D downsampled radar data with phase distortion, the inverse synthetic aperture radar (ISAR) imaging problem with low-rank and sparsity constraints essentially transforms the imaging problem into an optimization problem with regularization constraints. The constraint terms guide the model to output results that conform to physical properties, thereby recovering high-quality ISAR images from undersampled, noisy, and phase-distorted observation data. The objective function of this optimization problem consists of three parts: the Frobenius norm term, the kernel norm term, and... Normative terms.

[0088] Among them, the Frobenius norm term It is a data fitting term used to constrain the downsampled radar data. With phase error corrected signal terms To minimize discrepancies and ensure that the optimization results closely match the actual observation data. It is downsampled radar data. It is the conjugate transpose of the full-sample phase error matrix. It is a downsampling operation. This is the frequency domain signal representation of the ISAR image after azimuth and range Fourier transform.

[0089] Secondly, several nuclear items Used for characterization matrix Due to the low-rank property of low-rank matrices, the nuclear norm is the sum of the singular values ​​of the matrix. Since the nuclear norm of a low-rank matrix is ​​relatively small, this constraint term guides the model to recover the low-rank frequency domain signal matrix by minimizing the nuclear norm. This constraint fits the physical characteristics of radar data, namely that radar echoes of the same target have strong correlation between adjacent pulses, and its frequency domain representation naturally has low-rank properties. Extracting low-rank components can effectively suppress noise and sidelobe interference.

[0090] at last, Normative terms Used to characterize the ISAR image matrix sparsity property The norm is the sum of the absolute values ​​of the elements of a matrix; it is the norm of a sparse matrix. The norm value is small, so this constraint term is minimized. The norm guides the model to output sparse ISAR images. This constraint corresponds to the actual scene of ISAR imaging, where target scattering points are usually concentrated in a few areas, while most areas are background noise. The sparsity constraint can highlight the target scattering points and eliminate background interference.

[0091] Constraints The frequency domain signal was defined. With ISAR images The connection, It is the Fourier matrix in the azimuth direction. It is a Fourier matrix in the range dimension. Together, they transform the ISAR image from the range and orientation domain to the frequency domain, ensuring the logical consistency between frequency domain signal recovery and image reconstruction during the optimization process.

[0092] Regularization coefficient and It is a key parameter for balancing the weights of various constraint terms. The lower rank of the recovered radar data is determined by the value; the larger the value, the more the model tends to output a higher rank. . Determine the sparsity of the reconstructed ISAR image; the larger the value, the more the model tends to output a more sparsity-oriented image. The values ​​of both need to be adjusted according to the actual scenario. They are usually determined adaptively based on parameters such as the signal-to-noise ratio and sampling rate of radar data to achieve an optimal balance between low-rank constraints and sparsity constraints.

[0093] By leveraging the synergistic effect of low-rank and sparsity constraints, the inherent structural characteristics of radar signals and ISAR images are fully utilized. At the same time, phase error correction is embedded into the signal term, avoiding the error accumulation of traditional step-by-step processing, and providing a mathematical foundation for subsequent efficient solution and high-quality imaging.

[0094] Step S200: Based on the unified alternating direction multiplier method framework, solve the sparse recovery model to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal, and output the inverse synthetic aperture radar image.

[0095] In this embodiment, the unified alternating direction multiplier (ADMM) framework integrates the two major tasks of sparse recovery and phase error correction into a single ADMM iterative process, avoiding the use of multiple independent frameworks. Specifically, it can be achieved by constructing a unified augmented Lagrangian function, transforming the multi-objective optimization problem into multiple single-variable subproblems, and solving them iteratively in a fixed order. This framework design differs from the matrix vectorization and nested iteration commonly used in existing multi-task ADMM methods. Matrix vectorization refers to converting matrices into vectors for computation, and nested iteration refers to an iteration process containing another sub-iteration within itself. This unified framework directly performs matrix operations and uses a single-level iteration, eliminating the need for data format conversion and nested loops, thus reducing computational complexity. Matrix vectorization increases data storage and computational dimensionality, and nested iteration leads to an exponential increase in the number of iterations. The unified framework, by simplifying the process, improves computational efficiency and shortens imaging time while maintaining accuracy.

[0096] Solving the sparse restoration model refers to solving an optimization problem based on low-rank and sparsity constraints through iterative computation within the ADMM framework. Specifically, it involves updating each optimization variable sequentially according to a pre-defined iterative step until the convergence condition is met, at which point the result is output. During the solution process, sparse restoration and phase error correction are performed simultaneously, unlike the distributed steps of traditional methods where restoration precedes correction or vice versa. This synchronous processing avoids the error accumulation caused by step-by-step processing. In step-by-step processing, errors from previous steps propagate to subsequent steps, leading to a decrease in final image quality. Synchronous processing, however, optimizes both signal restoration and phase correction accuracy in each iteration, achieving mutual constraints and improvements.

[0097] Outputting an inverse synthetic aperture radar (ISAR) image refers to converting the solved sparse image matrix into a visualized ISAR image. Specifically, this can be achieved by processing the matrix elements through amplitude normalization, grayscale mapping, and other methods to generate an image that clearly shows the target outline and scattering point distribution. By simultaneously processing sparse recovery and phase error correction, the noise and sidelobe levels of the image are significantly reduced, and the target outline is clearer. The simplified design of the unified ADMM framework enables the imaging speed to meet the real-time requirements of practical engineering, making it particularly suitable for ISAR applications that are sensitive to processing delays, such as real-time target monitoring and rapid identification.

[0098] In one implementation, such as Figure 3As shown, the method based on the unified alternating direction multiplier method, which solves the sparse recovery model to complete the sparse recovery and phase error correction of the two-dimensional compressed sampled signal and outputs an inverse synthetic aperture radar image, specifically includes the following steps: Step S210: Construct the augmented Lagrangian function; Step S220: Use the alternating direction multiplier method solver to iteratively solve several minimization subproblems and output the inverse synthetic aperture radar image.

[0099] In this embodiment, the sparse recovery model is solved based on a unified alternating direction multiplier method framework. The complex constrained optimization problem is decomposed into multiple simple single-variable subproblems, and the global optimum is achieved through iterative solution. At the same time, the efficiency and stability of the solution process are guaranteed. This process mainly includes two steps: constructing the augmented Lagrangian function and iteratively solving the minimization subproblems.

[0100] Constructing the augmented Lagrangian function is fundamental to the ADMM method. Its purpose is to transform constrained optimization problems into unconstrained optimization problems, while introducing a penalty term to improve the iterative convergence speed. Traditional Lagrangian functions handle constraints by introducing Lagrange multipliers, but their convergence speed is relatively slow. The augmented Lagrangian function, by adding a quadratic penalty term to the traditional Lagrangian function, effectively accelerates convergence and enhances the stability of the iterative process, avoiding oscillations.

[0101] The alternating direction multiplier method solver iteratively solves several minimization subproblems. In each iteration, other variables are fixed, and only one variable is optimized. This process is repeated cyclically to update all variables until the convergence condition is met. The alternating optimization approach decomposes the original problem into multiple easily solvable single-variable subproblems, such as low-rank matrix updates, sparse matrix updates, and phase error matrix updates. Each subproblem can be solved quickly using mature algorithms such as singular value thresholding and soft thresholding, significantly reducing computational complexity.

[0102] By decomposing the problem and iteratively solving subproblems, the following advantages are achieved: First, the difficulty of the solution can be reduced by breaking down the original complex multivariate constrained optimization problem into simpler subproblems, avoiding the computational bottleneck of direct solution and making the problem feasible in engineering. Second, the solution efficiency can be improved. The design of alternating iteration and augmented Lagrangian function accelerates the convergence speed. Compared with traditional optimization algorithms such as gradient descent, it requires fewer iterations and converges faster, meeting the requirements of real-time imaging. Third, the stability of the solution can be guaranteed. The ADMM method is robust to parameter changes. Even if there are small deviations in the settings of regularization coefficients, penalty parameters, etc., it can still converge stably to the vicinity of the optimal solution, avoiding the parameter sensitivity problem of traditional algorithms.

[0103] The ADMM framework used employs a unified single-level iteration, rather than the nested iteration of traditional multi-task ADMM, further simplifying the process. Nested iteration requires multiple inner iterations within each outer iteration, leading to an exponential increase in the number of iterations. In contrast, single-level iteration updates all variables in a fixed order, without inner loops, significantly improving computational efficiency. Furthermore, the framework directly operates on matrices without needing to vectorize them, avoiding redundant data format conversions, reducing storage and computational load, and further lowering computational complexity.

[0104] In one implementation, the constructed augmented Lagrangian function is expressed as:

[0105] in, Represents the Lagrange multipliers. This represents the penalty parameter.

[0106] In this embodiment, the Lagrange multiplier It is the dual variable used to measure the degree of constraint violation, and its dimension is the same as... Consistency. When the constraints are met. The value tends to stabilize; when the constraint is violated, It will be adjusted iteratively to guide subsequent optimizations towards convergence in a direction that satisfies the constraints. Penalty parameter. This is a positive real number that controls the severity of the penalty for constraint violations. A larger value results in a heavier penalty for violation and faster convergence, but an excessively large value may lead to iterative oscillations; conversely, an excessively small value will delay convergence. An adaptive adjustment strategy is typically adopted: a smaller value is taken in the early stage of the iteration, and the value is gradually increased as the number of iterations increases, in order to balance the convergence speed and stability.

[0107] The first three terms of the augmented Lagrangian function are consistent with the objective function of the imaging problem, preserving the core requirements of low-rank constraints, sparse constraints, and data fitting. The fourth term is a penalty term for the constraints, which transforms the constraints into iteratively optimizeable terms by penalizing the square of the constraint violation. This design avoids the complexity of directly dealing with hard constraints while ensuring that the constraints are gradually satisfied during the iteration process.

[0108] The effect of the augmented Lagrangian function is that, by introducing Lagrange multipliers and penalty terms, it transforms the original constrained optimization problem into an unconstrained iterative alternation problem, while simultaneously decomposing... and The coupling relationship ensures that each subsequent subproblem involves the optimization of only one variable, which greatly reduces the difficulty of solving the problem and provides a foundation for efficient iteration.

[0109] In one implementation, the plurality of minimization subproblems include:

[0110]

[0111]

[0112]

[0113] in, Indicates the first iteration Represents image entropy. It is the phase vector to be compensated.

[0114] In this embodiment, the alternating direction multiplier method framework completes optimization by iteratively solving four minimization subproblems. The four minimization subproblems include the frequency domain signal matrix update subproblem, the phase vector to be compensated update subproblem, the ISAR image matrix update subproblem, and the Lagrange multiplier update subproblem.

[0115] Specifically, the first subproblem of updating the frequency domain signal matrix... In the next iteration The update expression is:

[0116] This subproblem is in the fixed (No. (ISAR image matrix of the next iteration) and (No. Given the Lagrange multipliers of the next iteration, minimize the augmented Lagrange function with respect to... The objective function contains nuclear norm terms and quadratic terms, and its optimal solution can be obtained using the singular value thresholding algorithm. In solving this minimization subproblem, singular value thresholding preserves... Its low-rank characteristics meet the needs of data fitting and ensure the accuracy of frequency domain signal recovery.

[0117] The first subproblem of updating the phase vector to be compensated In the next iteration The update expression is:

[0118] in Represents image entropy. This is the phase vector to be compensated. Image entropy reflects the uniformity of image grayscale distribution; the lower the entropy value, the higher the image contrast and the clearer the target contour. By minimizing the entropy value of the image after the inverse transformation of the frequency domain signal, the phase vector is indirectly estimated and updated. In solving this minimization subproblem, the quality assessment characteristics of image entropy are utilized to achieve accurate correction of phase error, and the phase vector... The update will synchronously adjust the phase error matrix to ensure the phase consistency of the radar signal and solve the problem of existing phase correction technology failing at low sampling rates.

[0119] The first subproblem of ISAR image matrix update In the next iteration The update expression is:

[0120] This subproblem is in the fixed and Under the premise of minimizing the augmented Lagrange function with respect to The part. Because the objective function contains The optimal solutions for the norm and quadratic terms can be obtained using a soft thresholding algorithm. In solving this minimization subproblem, the sparsity constraint of the ISAR image is achieved through soft thresholding, eliminating background noise and false scattering points, and highlighting the true outline of the target, with the aim of generating a clear ISAR image.

[0121] The first subproblem of the Lagrange multiplier update subproblem In the next iteration The update expression is:

[0122] This is the standard multiplier update step of the ADMM method, adjusting based on the amount of constraint violation in the current iteration. This ensures that subsequent iterations converge in the direction that satisfies the constraints. During the solution of this minimization subproblem, the convergence of the iteration process is maintained by gradually adjusting the multipliers, so that the constraints are gradually satisfied during iteration, ultimately achieving logical consistency between the frequency domain signal and the ISAR image.

[0123] The termination condition for the entire iterative process can be set as follows: the number of iterations reaches a preset maximum, the difference between the ISAR image matrices of two adjacent iterations is less than a preset error threshold, or the image entropy is less than a preset entropy threshold. Through the iterative process, sparse recovery, phase error correction, and low-rank extraction can be completed simultaneously, ultimately outputting a clear ISAR image.

[0124] In one implementation, the sparse mode of the two-dimensional compressed sampling includes at least one of the following: root mean square mode, separable root mean square mode, Gaussian random mask mode, and mixed sparse mode.

[0125] In this embodiment, the sparse mode of two-dimensional compressed sampling refers to the specific distribution method of the observation points when performing compressed sampling in the distance and azimuth dimensions. Different sparse modes are adapted to different engineering scenarios and target characteristics. The technical solution of this embodiment can support multiple sparse modes to improve the flexibility and robustness of the technical solution. Specifically, it includes root mean square mode, separable root mean square mode, Gaussian random mask mode and hybrid sparse mode.

[0126] The Root Mean Square (RMS) mode selects sampling points according to the root mean square distribution. Specifically, it determines the sampling positions in both the range and azimuth dimensions based on the distribution of the signal's RMS values. The higher the concentration of signal energy in a region, the higher the sampling point density; conversely, the lower the sampling point density in a region with more dispersed signal energy. The advantage of this mode is its adaptive signal energy distribution, maximizing the reduction of the sampling rate while ensuring no loss of critical information. It is suitable for scenarios with concentrated target scattering energy and uniform background noise. Even at low sampling rates, it can retain high-energy scattering point information of the target, avoiding the loss of critical information or redundant sampling caused by uniform sampling.

[0127] Separable RMS mode is an extension of the root mean square (RMS) mode. Its key feature is that the sampling modes for the range and azimuth dimensions are independent. Sampling strategies can be designed separately based on the signal energy distribution in each dimension. Specifically, the range dimension can be sampled using the RMS mode, while the azimuth dimension can be sampled at fixed intervals, or vice versa. The advantage of this mode is its greater flexibility, allowing for optimization of the sampling mode for different signal characteristics in different dimensions. For example, it is suitable for signals with concentrated energy in the range dimension and dispersed energy in the azimuth dimension, making it applicable to fields where the target has different structural characteristics in different dimensions. This mode further enhances the targeting of sampling, reduces invalid sampling, and lowers the complexity of sampling mode design, facilitating engineering implementation.

[0128] Gaussian Random Mask (GMS) mode refers to the random selection of sampling points according to a Gaussian distribution. Specifically, it can generate a random index matrix that conforms to a Gaussian distribution, where positions with 1 represent sampling points and positions with 0 represent non-sampling points. The mean of the Gaussian distribution corresponds to the signal energy center, and the variance controls the dispersion of the sampling points. The advantage of this mode is its strong randomness in the distribution of sampling points, satisfying the finite isometry condition of compressed sensing, ensuring the accuracy of sparse recovery, and making it suitable for scenarios with uncertain target scattering point distribution and complex signal structures. This mode has strong adaptability to unknown targets or complex scenarios; even if the target scattering point distribution changes, it can still retain sufficient information for recovery through random sampling, exhibiting strong robustness.

[0129] Hybrid sparse mode refers to a composite sampling mode designed by combining the characteristics of two or more individual sparse modes. Specifically, it can be a combination of root mean square (RMS) mode and Gaussian random mask mode (e.g., using RMS mode for the range dimension and Gaussian random mask mode for the orientation dimension), or a combination of separable RMS mode and Gaussian random mask mode, etc. The combination ratio can be adjusted according to the actual scenario. The advantage of this mode is that it combines the advantages of multiple individual modes, such as the energy adaptive characteristics of RMS mode and the robustness of Gaussian random mask mode. It is suitable for complex and variable engineering scenarios, such as scenarios where the target's motion state is unstable and the signal energy distribution changes dynamically. This mode can maintain high sampling efficiency and recovery accuracy under different scenarios, further expanding the applicability of the technical solution.

[0130] The choice of different sparsity modes can be adjusted according to actual engineering needs. For example, when imaging known targets in a laboratory environment, the root mean square mode or separable root mean square mode can be selected to minimize the sampling rate. When imaging unknown targets in complex environments, the Gaussian random mask mode or mixed sparsity mode can be selected to improve robustness. This imaging method can adapt to different application scenarios without redesigning the sampling system due to changes in the scenario, thus improving the practicality and engineering value of the technical solution.

[0131] In one implementation, the noise in the data of the inverse synthetic aperture radar echo signal is additive white Gaussian noise, and the sparse recovery model suppresses the noise through Frobenius norm constraints.

[0132] In this embodiment, the noise in the inverse synthetic aperture radar echo signal is fully sampled additive white Gaussian noise. Originating from electronic thermal noise and external electromagnetic interference in the radar receiver, its probability density function follows a Gaussian distribution with zero mean and constant variance. It manifests as a linear superposition of noise signal and radar echo signal, introducing random disturbances only into the observation data.

[0133] The noise matrix after downsampling is Its dimension is the same as that of the downsampled radar data matrix. It is consistent and also follows the distribution characteristics of additive white Gaussian noise.

[0134] Sparse recovery models utilize Frobenius norm terms This achieves noise suppression. The Frobenius norm, the square root of the sum of squares of matrix elements, comprehensively measures matrix-level bias. The primary function of this norm term is to minimize the sum of squared errors between noisy observations and the noise-free signal. Since additive white Gaussian noise has a zero mean, this minimization process automatically filters out random noise disturbances, making model predictions closer to the true signal.

[0135] Furthermore, the noise suppression effect is further enhanced by combining the low-rank and sparsity constraints in the model. Since noise typically exhibits high-rank characteristics at the matrix level, the low-rank constraint extracts the low-rank components of the signal, eliminating high-rank disturbances from the noise. Moreover, because the non-zero elements of noise are randomly distributed, they do not satisfy the concentrated sparsity characteristic of the target scattering points. Therefore, the sparsity constraint highlights the sparse scattering points of the target, eliminating spurious sparse components caused by noise.

[0136] Through noise suppression mechanisms, even under low signal-to-noise ratio conditions, noise interference can still be suppressed and key target information can be preserved, thus solving the problem of sharp decline in imaging quality under low signal-to-noise ratio conditions in traditional methods.

[0137] Appendix Figure 4 This is a comparison of ISAR images under different sparse modes when the sampling rate is 20% in this embodiment. This figure verifies the technical effect of the method (i.e., the LRSP method) in this embodiment through experiments.

[0138] In this experiment, the sampling rate was specifically set to 20%, meaning that the number of sampling points in both the distance and azimuth dimensions was 20% of the total number of sampling points, simulating a real-world engineering scenario of two-dimensional compressed sampling. Four typical sparsity modes were employed: Root Mean Square (RMS) mode, Separable RMS mode, Gaussian Random Mask (GMS) mode, and Hybrid mode, covering both single and composite modes to comprehensively verify the method's adaptability. Two existing mainstream methods were selected for comparison: Structural Low-Rank and Sparse with Phase Compensation (SLRS-PC) and ADMM-Downsampling in Fast Time Dimension (ADMM-DF). Both methods (Fast-time) are designed for ISAR sparse imaging or phase correction scenarios and are representative; the radar echo signal contains phase distortion and additive white Gaussian noise, and the signal-to-noise ratio is set to 10dB, which is close to the medium noise level in actual engineering. The phase error is generated by the target motion error simulation, which is consistent with the error source of actual ISAR imaging; the displayed color range is [-35,0]dB, which can clearly present the target scattering intensity distribution, highlight the difference between the main lobe and the side lobes, and facilitate intuitive comparison of imaging quality.

[0139] The experimental procedure begins with data acquisition and preprocessing. A fully sampled echo signal containing phase distortion and additive white Gaussian noise is generated using an ISAR radar simulation system. The signal dimension is 100×100, with 100 sampling points in the range dimension and 100 pulses in the azimuth dimension. Subsequently, two-dimensional compressed sampling is performed, downsampling the fully sampled signal at a 20% sampling rate according to four sparse modes, resulting in four sets of downsampled observation data. Image reconstruction is then performed using the LRSP (Low-Rank and Sparsity Priors-based) method, SLRS-PC method, and ADMM-DF method proposed in this embodiment to reconstruct the images from the four sets of downsampled data. The LRSP method utilizes the sparse recovery model and ADMM solution framework of this embodiment, while the SLRS-PC and ADMM-DF methods are set with parameters according to their original technical schemes. Finally, image post-processing is performed, including amplitude normalization and grayscale mapping of the reconstructed image, generating a visualization image within a color range of [-35, 0] dB. Finally, the results were compared, with the imaging results of the three methods compared in three dimensions: target contour sharpness, noise level, and sidelobe level.

[0140] The experimental results can be found in the appendix. Figure 4 It is clear that the sparse pattern part represents the sparse mode, which is used to define the distribution rules of observation points of radar signals in the range and azimuth dimensions during the two-dimensional compressed sampling process. By controlling the position and density of sampling points, the key information of the signal is preserved while reducing the amount of data collected, thus providing effective observation data for ISAR image restoration based on sparsity.

[0141] In the imaging results of the SLRS-PC method, the target outline is blurred, noise and sidelobes are high, and there are many bright spots in the background area. It is difficult to accurately identify the shape of the target in all four sparse modes. This is because although the method considers low rank and sparsity, phase compensation and sparse recovery are performed step by step, and the phase error correction accuracy is insufficient, resulting in the failure of sparsity constraints and the inability to effectively suppress noise and sidelobes. The imaging results of the ADMM-DF method also have the problem of unclear target outline, high sidelobes, and severe confusion between target scattering points and noise. In some sparse modes such as GMS mode, it is even impossible to distinguish the target from the background. This is because the method only performs downsampling processing in the fast time dimension or range dimension, does not fully consider the incoherence of two-dimensional compressed sampling, and the phase error correction is not integrated with the ADMM framework, resulting in limited imaging accuracy.

[0142] The LRSP method of this invention exhibits excellent imaging performance in all four sparse modes. The target outline is clear and complete, accurately representing the target's shape and scattering point distribution; the noise level is significantly lower than that of the comparison method, the background area is clean, and there are no obvious false bright spots; the main lobe and side lobes are clearly distinguished, and the scattering point is accurately located.

[0143] The above results validate the advantages of this method. By incorporating phase error correction into the sparse recovery model and achieving synchronous optimization through the unified ADMM framework, and by combining low rank and sparsity constraints, noise and sidelobes are effectively suppressed. Even at a low sampling rate of 20%, the key information of the target can still be preserved, thus solving the problem of poor imaging quality in existing methods under two-dimensional compressed sampling and phase distortion scenarios.

[0144] In addition, Figure 4 The invention also verified the strong adaptability of the method to different sparse modes. Under four sparse modes with significant differences, the imaging quality remained stable without significant fluctuations, further demonstrating the robustness of the method and providing experimental basis for the flexible selection of sparse modes in practical engineering.

[0145] In summary, this invention discloses an inverse synthetic aperture radar (ISAR) imaging method with phase distortion and two-dimensional compressed sampling, which is used for sparse recovery of two-dimensional downsampled signals and phase error correction in ISAR imaging. Under various phase error, signal-to-noise ratio, and compressed sampling modes, it can generate clearer ISAR images with lower noise and sidelobes.

[0146] like Figure 5 As shown in the figure, this embodiment of the invention provides an inverse synthetic aperture radar imaging system with phase distortion and two-dimensional compressed sampling. The system includes: a sparse recovery model construction module 10 and an inverse synthetic aperture radar image output module 20.

[0147] Specifically, the sparse recovery model construction module 10 is used to construct a sparse recovery model including phase error correction based on the principles of low rank and sparsity; wherein, the sparse recovery model is adapted to two-dimensional compressed sampling and inverse synthetic aperture radar echo signals with phase distortion; the inverse synthetic aperture radar image output module 20 is used to solve the sparse recovery model based on a unified alternating direction multiplier method framework to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal and output an inverse synthetic aperture radar image.

[0148] In one implementation, the sparse recovery model construction module includes: The signal model matrix definition unit is used to define the matrix form of the inverse synthetic aperture radar signal model with full sampled measurements; The signal model matrix downsampling unit is used to perform two-dimensional compression sampling on the matrix form of the inverse synthetic aperture radar signal model to obtain the downsampled signal model. The signal model matrix rewriting unit is used to rewrite the downsampled signal model since the phase error matrix is ​​a diagonal matrix; The imaging problem definition unit is used to define the inverse synthetic aperture radar imaging problem with low-rank and sparsity constraints for two-dimensional downsampled radar data with phase distortion.

[0149] In one implementation, the inverse synthetic aperture radar image output module includes: Augmented Lagrangian function building unit, used to construct augmented Lagrangian functions; The alternating direction multiplier method solver unit is used to iteratively solve several minimization subproblems using the alternating direction multiplier method solver, and output inverse synthetic aperture radar images.

[0150] Based on the above embodiments, the present invention also provides a terminal device, the principle block diagram of which can be as follows: Figure 6 As shown, the terminal device includes a processor, memory, network interface, display screen, and temperature sensor connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements an inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling. The display screen can be a liquid crystal display (LCD) or an e-ink display. The temperature sensor is pre-installed inside the terminal device to detect the operating temperature of the internal components.

[0151] Those skilled in the art will understand that Figure 6 The schematic diagram shown is only a partial structural diagram related to the present invention and does not constitute a limitation on the terminal device to which the present invention is applied. The specific terminal device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0152] In one embodiment, a terminal device is provided, including a memory and one or more programs, wherein one or more programs are stored in the memory and configured to be executed by one or more processors, the one or more programs including instructions for performing operations as described in the embodiments of the methods above.

[0153] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. 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), dual 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.

[0154] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0155] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. An inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling, characterized in that, The method includes: Based on the principles of low rank and sparsity, a sparse recovery model including phase error correction is constructed; wherein, the sparse recovery model is adapted to two-dimensional compressed sampling and inverse synthetic aperture radar echo signals with phase distortion. Based on the unified alternating direction multiplier method framework, the sparse recovery model is solved to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal, and output the inverse synthetic aperture radar image.

2. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 1, characterized in that, The sparse recovery model, based on the principles of low rank and sparsity, and including phase error correction, is constructed as follows: Define the matrix form of the inverse synthetic aperture radar signal model with all sampled measurements; The matrix form of the inverse synthetic aperture radar signal model is subjected to two-dimensional compression sampling to obtain the downsampled signal model; Since the phase error matrix is ​​a diagonal matrix, the downsampled signal model is rewritten. For two-dimensional downsampled radar data with phase distortion, we define an inverse synthetic aperture radar imaging problem with low-rank and sparsity constraints.

3. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 2, characterized in that, The matrix form of the inverse synthetic aperture radar signal model with fully sampled measurements is expressed as: in, This represents fully sampled radar data. This represents an inverse synthetic aperture radar image. This represents additive white Gaussian noise from the full sample. Denotes the Fourier matrix of the distance dimension. Represents the Fourier matrix in the azimuth direction (lateral distance dimension). This represents the phase error matrix of the full sampling. This indicates the conjugate transpose operation.

4. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 3, characterized in that, Performing a two-dimensional compression sampling operation on the matrix form of the inverse synthetic aperture radar signal model, the resulting downsampled signal model is expressed as: in, This indicates a downsampling operation.

5. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 4, characterized in that, Since the phase error matrix is ​​a diagonal matrix, the downsampled signal model can be rewritten as follows: in, , and .

6. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 5, characterized in that, For two-dimensional downsampled radar data with phase distortion, the inverse synthetic aperture radar (ISAR) imaging problem with low-rank and sparsity constraints is expressed as: in, The nuclear norm is denoted by , which represents the rank of a matrix and is equal to the sum of its singular values. Representing a matrix Norm, Denotes the Frobenius norm. The regularization coefficient is used to determine the low-rank degree of the recovered radar data. is the regularization coefficient used to determine the sparsity of the reconstructed inverse synthetic aperture radar image.

7. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 5, characterized in that, The unified alternating direction multiplier method framework is used to solve the sparse recovery model to complete the sparse recovery and phase error correction of the two-dimensional compressed sampled signal, and output an inverse synthetic aperture radar image, including: Construct the augmented Lagrangian function; Using an alternating direction multiplier solver, several minimization subproblems are solved iteratively, and inverse synthetic aperture radar images are output.

8. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 7, characterized in that, The constructed augmented Lagrangian function is expressed as: in, Represents the Lagrange multipliers. This represents the penalty parameter.

9. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 8, characterized in that, The aforementioned minimization subproblems include: in, Indicates the first iteration Represents image entropy, It is the phase vector to be compensated.

10. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 1, characterized in that, The sparse mode of the two-dimensional compressed sampling includes at least one of the following: root mean square mode, separable root mean square mode, Gaussian random mask mode, and mixed sparse mode.

11. The inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling according to claim 1, characterized in that, The noise in the inverse synthetic aperture radar echo signal data is additive white Gaussian noise, and the sparse recovery model suppresses the noise through Frobenius norm constraints.

12. An inverse synthetic aperture radar imaging system with phase distortion and two-dimensional compressed sampling, characterized in that, The system includes: A sparse recovery model construction module is used to construct a sparse recovery model including phase error correction based on the principles of low rank and sparsity; wherein, the sparse recovery model is adapted to two-dimensional compressed sampling and inverse synthetic aperture radar echo signals with phase distortion; The inverse synthetic aperture radar (ISAR) image output module is used to solve the sparse recovery model based on a unified alternating direction multiplier method framework to complete the sparse recovery and phase error correction of the two-dimensional compressed sampling signal and output an ISAR image.

13. The inverse synthetic aperture radar imaging system with phase distortion and two-dimensional compressed sampling according to claim 12, characterized in that, The sparse recovery model construction module includes: The signal model matrix definition unit is used to define the matrix form of the inverse synthetic aperture radar signal model with full sampled measurements; The signal model matrix downsampling unit is used to perform two-dimensional compression sampling on the matrix form of the inverse synthetic aperture radar signal model to obtain the downsampled signal model. The signal model matrix rewriting unit is used to rewrite the downsampled signal model since the phase error matrix is ​​a diagonal matrix; The imaging problem definition unit is used to define the inverse synthetic aperture radar imaging problem with low-rank and sparsity constraints for two-dimensional downsampled radar data with phase distortion.

14. The inverse synthetic aperture radar imaging system with phase distortion and two-dimensional compressed sampling according to claim 12, characterized in that, The inverse synthetic aperture radar image output module includes: Augmented Lagrangian function building unit, used to construct augmented Lagrangian functions; The alternating direction multiplier method solver unit is used to iteratively solve several minimization subproblems using the alternating direction multiplier method solver, and output inverse synthetic aperture radar images.

15. A terminal device, characterized in that, The terminal device includes a memory, a processor, and an inverse synthetic aperture radar imaging program with phase distortion and two-dimensional compressed sampling stored in the memory and executable on the processor. When the processor executes the inverse synthetic aperture radar imaging program with phase distortion and two-dimensional compressed sampling, it implements the steps of the inverse synthetic aperture radar imaging method with phase distortion and two-dimensional compressed sampling as described in any one of claims 1-11.

16. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an inverse synthetic aperture radar (INS) imaging program with phase distortion and two-dimensional compressed sampling. When the INS MRI program with phase distortion and two-dimensional compressed sampling is executed by a processor, it implements the steps of the INS MRI method with phase distortion and two-dimensional compressed sampling as described in any one of claims 1-11.

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