High-resolution range profile feature preserving enhancement method based on iterative weighted sparse decomposition

Abstract

The application discloses a high-resolution range profile feature preserving enhancement method based on iterative weighted sparse decomposition, and comprises the following steps: obtaining radar echo data collected by a radar receiver in a coherent processing time, constructing a two-dimensional radar echo matrix composed of a distance unit number and a pulse sequence array after distance matching filtering; expressing the two-dimensional radar echo matrix as a superposition relationship of a low-rank clutter component matrix and a sparse target component matrix; based on the superposition relationship, constructing an optimization model, and a target function of the optimization model is a sum of a weighted nuclear norm of the low-rank clutter component matrix and an L1 norm of the sparse target component matrix. The method of the application realizes effective suppression of clutter in a strong clutter background by applying adaptive weights to singular values, and meanwhile, key structural features such as the number, position distribution and relative amplitude relationship of scattering points in a target high-resolution range profile are maintained.

Description

Technical Field

[0001] This invention relates to the field of radar target recognition technology, and in particular to a high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition. Background Technology

[0002] As radar technology continues to develop towards wider bandwidth and higher resolution, high-resolution range profiles (HRRPs) acquired by radar are increasingly widely used in the field of target recognition. HRRPs reflect the distribution of scattering centers of a target along the radar line of sight, containing important physical features such as the target's fine geometric structure, the location of key scattering points, and their relative amplitude relationships. They serve as a crucial data foundation for achieving automatic radar target identification and classification.

[0003] However, in practical radar applications, such as ground surveillance, sea surface detection, or low-altitude target monitoring, the radar echo signals typically contain strong clutter interference from background objects such as ground features, sea surfaces, vegetation, or buildings. Especially for radar systems lacking multi-antenna arrays or spatial diversity capabilities (such as some single-antenna radars or low-cost radar platforms), target echoes and background clutter often severely overlap in both the range dimension (time domain) and the Doppler dimension (frequency domain), leading to a significant reduction in the signal-to-clutter ratio. Under these conditions, effectively suppressing clutter energy while maximally preserving the scattering point structure characteristics (including the number, precise location, and relative amplitude relationships of scattering points) inherent in the high-resolution range image of the target becomes a key technical bottleneck for improving radar target recognition performance.

[0004] Currently, common clutter suppression techniques can be broadly categorized into two types. The first type is filtering methods, represented by Moving Target Indication (MTI) and Moving Target Detection (MTD). These methods primarily utilize the difference in Doppler frequencies between the target and clutter to suppress zero-frequency or low-speed clutter by designing frequency-domain filters. However, they are essentially band-stop filters based on fixed or adaptive thresholds. When the target and clutter overlap in the Doppler domain (e.g., with slow-moving targets or platform motion), the filtering operation inevitably weakens the target signal energy, leading to peak attenuation in high-resolution range images, blurred scattering point positions, and even overall structural distortion, thus losing crucial details essential for identification.

[0005] The second category comprises subspace methods or low-rank sparse decomposition methods based on signal decomposition. Robust Principal Component Analysis (RPCA) is a representative technique that has gained attention in recent years. This method models the radar echo data matrix as the sum of a low-rank clutter component and a sparse target component, and achieves separation between the two by minimizing a convex optimization model that minimizes the kernel norm (to constrain low rank) and the L1 norm (to constrain sparsity). Compared to filtering methods, RPCA reduces the dependence on target Doppler information to some extent. However, traditional RPCA methods apply a uniform kernel norm to all singular values ​​of the matrix with the same shrinkage penalty. This "one-size-fits-all" approach fails to distinguish between small singular values ​​dominated by clutter and large singular values ​​that may contain target structural information, easily leading to over-compression of principal singular values ​​related to strong target scattering points. The consequence is that, under conditions of strong clutter or low signal-to-clutter ratio, the high-resolution range image of the target obtained by RPCA processing may have its scattering point amplitude inappropriately weakened and its relative relationship may be destroyed, resulting in "feature distortion". This makes it impossible to provide stable and reliable structural feature input for subsequent recognition algorithms, thus limiting its performance in application scenarios that require high-precision feature preservation.

[0006] Therefore, there is an urgent need in this field for a signal processing method that can effectively suppress clutter interference and accurately maintain the inherent structural features of the target's high-resolution range image in a strong clutter background, so as to solve the problems of insufficient feature preservation capability, target energy loss and structural distortion in the existing technology, thereby providing higher quality and more robust feature data for radar automatic target identification. Summary of the Invention

[0007] To address the technical problems existing in the background art, this invention proposes a high-resolution distance image feature preservation enhancement method based on iterative weighted sparse decomposition.

[0008] The high-resolution range image feature preservation and enhancement method proposed in this invention based on iterative weighted sparse decomposition includes the following steps:

[0009] S1. Acquire radar echo data collected by the radar receiver within one coherent processing time, and after range-direction matched filtering, construct a two-dimensional radar echo matrix composed of the number of range elements and the number of pulse sequences.

[0010] S2. The two-dimensional radar echo matrix is ​​represented as the superposition of the low-rank clutter component matrix and the sparse target component matrix.

[0011] S3. Based on the superposition relationship, an optimization model is constructed. The objective function of the optimization model is the sum of the weighted nuclear norm of the low-rank clutter component matrix and the L1 norm of the sparse objective component matrix. The weight of the weighted nuclear norm is adaptively adjusted according to the singular values ​​of the low-rank clutter component matrix.

[0012] S4. The optimization model is solved iteratively using the alternating direction multiplier method framework. During the iterative solution process, the low-rank clutter component matrix, the sparse target component matrix, and the Lagrange multiplier matrix and penalty parameters introduced by the alternating direction multiplier method are updated alternately.

[0013] S5. When the iteration process meets the preset termination condition, stop the iteration and output the currently updated sparse target component matrix as a high-resolution range image of the target after clutter suppression and preservation of structural features.

[0014] Preferably, the superposition relationship is specifically expressed as follows: the two-dimensional radar echo matrix is ​​equal to the sum of the low-rank clutter component matrix and the sparse target component matrix.

[0015] Preferably, the objective function of the optimization model is:

[0016] ;

[0017] in, Denotes the L1 norm of a matrix. For sparse regularization weights, The parameters are non-convex penalty function parameters; It is a two-dimensional radar echo matrix; This is the low-rank clutter component matrix; The sparse target component matrix; For the first matrix One singular value; It is a non-convex penalty function.

[0018] Preferably, the non-convex penalty function is one of a logarithmic function, an exponential function, or a piecewise concave function.

[0019] Preferably, the iterative solution of the optimization model using the alternating direction multiplier method framework specifically includes:

[0020] The sparse target component matrix, Lagrange multiplier matrix and penalty parameter are fixed, the first intermediate matrix is ​​constructed and singular value decomposition is performed on the first intermediate matrix, and the low-rank clutter component matrix is ​​updated by weighted singular value thresholding operation based on adaptive weights.

[0021] By fixing the low-rank clutter component matrix, the Lagrange multiplier matrix, and the penalty parameter, a second intermediate matrix is ​​constructed and the sparse target component matrix is ​​updated through element-wise soft thresholding.

[0022] Based on the updated low-rank clutter component matrix and sparse target component matrix, the constraint residuals are calculated and the Lagrange multiplier matrix is ​​updated. At the same time, the penalty parameters are adaptively updated according to the changes in the constraint residuals.

[0023] Preferably, the weighted singular value thresholding operation specifically involves subtracting half of the product of the corresponding adaptive weight and the current penalty parameter from each element in the singular value vector of the first intermediate matrix, and setting any values ​​less than zero in the result to zero.

[0024] Preferably, the element-wise soft thresholding operation specifically involves subtracting the ratio of the sparse regularization parameter to the current penalty parameter from each element in the second intermediate matrix, setting elements whose absolute value is less than the ratio to zero, and retaining the value after subtracting the ratio and the original sign of the remaining elements.

[0025] Preferably, the preset termination condition is: the relative error of the Frobenius norm between the sum of the low-rank clutter component matrix and the sparse target component matrix and the two-dimensional radar echo matrix in the current iteration is less than a set threshold, or the number of iterations reaches the preset maximum number.

[0026] Preferably, step S1 specifically includes:

[0027] Range-direction matched filtering is performed on the radar echo data of multiple pulses acquired by the radar receiver within one coherent processing time to obtain a high-resolution one-dimensional range profile corresponding to each pulse.

[0028] The high-resolution one-dimensional range image corresponding to each pulse is arranged in pulse time order to construct a two-dimensional radar echo matrix with the number of rows equal to the number of range cells and the number of columns equal to the number of pulse sequences.

[0029] Preferably, the range-oriented matched filtering is implemented using a matched filter for the radar transmitted signal, and the cell resolution of the high-resolution one-dimensional range image is determined by the bandwidth of the radar transmitted signal.

[0030] This invention presents a high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition. By introducing an adaptive weighting mechanism and a non-convex optimization model, this method overcomes the inherent defect of traditional methods in damaging target structural features during strong clutter suppression. This method can more precisely characterize and separate low-rank clutter from sparse targets, effectively suppressing clutter while preserving key identification features such as the number, location distribution, and relative amplitude relationships of scattering points in the high-resolution range image to the greatest extent possible. It does not rely on multiple antennas or spatial diversity information, exhibiting good platform applicability and scenario robustness. It provides structurally complete, stable, and reliable feature inputs for subsequent radar target identification, thereby significantly improving the overall performance and reliability of automatic radar target identification in low signal-to-clutter and complex clutter environments. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the workflow of the high-resolution distance image feature preservation and enhancement method based on iterative weighted sparse decomposition proposed in this invention.

[0032] Figure 2 The figure shows the comparison of the relative root mean square error between the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition and the clutter suppression method based on robust principal component analysis under different signal-to-clutter ratios.

[0033] Figure 3 The figure shows the correlation coefficient comparison between the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition and the clutter suppression method based on robust principal component analysis under different signal-to-clutter ratios.

[0034] Figure 4 The figure shows a comparison of the error in the number of scattering points between the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition and the clutter suppression method based on robust principal component analysis under different signal-to-clutter ratios.

[0035] Figure 5 The echo (distance-pulse map) after processing using the traditional robust principal component analysis (RPCA) method.

[0036] Figure 6 The echo (range-pulse map) after processing by the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition proposed in this invention.

[0037] Figure 7 This is a magnified comparison of a high-resolution range image processed using the traditional RPCA method.

[0038] Figure 8 This is a magnified comparison of a high-resolution range image after processing using the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition proposed in this invention.

[0039] Figure 9 This image shows a comparison of the identification results of the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition proposed in this invention and the method based on robust principal component analysis under clutter-free conditions. Detailed Implementation

[0040] Reference Figures 1-9 ,in Figure 1 This is a flowchart of the method of the present invention. Figures 2 to 4 This is a comparison between the method of the present invention and the prior art. Figure 5 and Figure 7 The processing results are from the existing RPCA method. Figure 6 , Figure 8 and Figure 9 The result is shown in the accompanying drawings. The invention will now be described in detail with reference to the accompanying drawings. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition proposed in this invention includes the following steps:

[0041] S1. Acquire radar echo data collected by the radar receiver within one coherent processing time. After range-direction matched filtering, construct a two-dimensional radar echo matrix composed of the number of range elements and the number of pulse sequences.

[0042] In this embodiment, step S1 specifically includes:

[0043] Range-direction matched filtering is performed on the radar echo data of multiple pulses acquired by the radar receiver within one coherent processing time to obtain a high-resolution one-dimensional range profile corresponding to each pulse.

[0044] The high-resolution one-dimensional range image corresponding to each pulse is arranged in pulse time order to construct a two-dimensional radar echo matrix with the number of rows equal to the number of range cells and the number of columns equal to the number of pulse sequences.

[0045] Specifically, range-oriented matched filtering is implemented using a matched filter on the radar transmitted signal, and the cell resolution of the high-resolution one-dimensional range image is determined by the bandwidth of the radar transmitted signal.

[0046] Specifically, radar echo data acquired by the radar receiver within one coherent processing time is obtained, range-direction matched filtering is performed on the radar echo data, and a range-pulse two-dimensional radar echo matrix is ​​constructed according to the arrangement of range cells and pulse sequences. ,in, , This indicates the number of echo sequences within a coherent processing time. Indicates the number of range cells contained within the observation window; two-dimensional radar echo matrix. It includes both target echo components and clutter components.

[0047] S2. The two-dimensional radar echo matrix is ​​represented as the superposition of the low-rank clutter component matrix and the sparse target component matrix.

[0048] In this embodiment, the superposition relationship is specifically expressed as follows: the two-dimensional radar echo matrix is ​​equal to the sum of the low-rank clutter component matrix and the sparse target component matrix.

[0049] Specifically, based on the physical characteristics that radar clutter has strong correlation in the pulse dimension and target echoes exhibit sparse distribution in the range dimension, the two-dimensional radar echo matrix is... Modeled as low-rank clutter components With sparse target components Superposition relationship:

[0050] ;

[0051] in, The low-rank clutter component is used to characterize clutter and background echo. It has a strong correlation in the pulse dimension and satisfies the low-rank characteristic. The sparse target component is used to characterize the high-resolution range image echo of the target, which exhibits a sparse distribution in the range dimension; express Complex matrix space.

[0052] S3. Based on the superposition relationship, an optimization model is constructed. The objective function of the optimization model is the sum of the weighted nuclear norm of the low-rank clutter component matrix and the L1 norm of the sparse objective component matrix. The weight of the weighted nuclear norm is adaptively adjusted according to the singular values ​​of the low-rank clutter component matrix.

[0053] In this embodiment, to avoid the weakening of the target structure caused by the traditional nuclear norm's uniform penalty for singular values, a non-convex penalty function is introduced. A low-rank constraint is modeled, and an iterative weighted low-rank sparse decomposition optimization model is constructed. By applying adaptive weights to singular values, an accurate characterization of the low-rank structure of clutter is achieved. The objective function of the optimization model is as follows:

[0054] ;

[0055] in, Denotes the L1 norm of a matrix. For sparse regularization weights, The parameters are non-convex penalty function parameters; It is a two-dimensional radar echo matrix; This is the low-rank clutter component matrix; The sparse target component matrix; For the first matrix One singular value; It is a non-convex penalty function; the above parameters can be set according to the dimension of the echo matrix, the noise level, or empirical rules.

[0056] Specifically, an example of a non-convex penalty function is as follows:

[0057] ;

[0058] in, It is a non-convex penalty function; is the independent variable, representing the parameter to be estimated; This is the regularization threshold parameter, which controls the shape and saturation point of the penalty function; For the quadratic correction term, make the function in The segment grows in a concave shape; The denominator for scaling is determined by the threshold parameter. It consists of twice the amount of; For when The saturation constant value of the time function.

[0059] In this embodiment, the non-convex penalty function is one of a logarithmic function, an exponential function, or a piecewise concave function. Alternatively, the non-convex penalty function can be any other function that satisfies the property of weak penalty for large singular values ​​and strong penalty for small singular values.

[0060] S4. The optimization model is solved iteratively using the alternating direction multiplier method framework. During the iterative solution process, the low-rank clutter component matrix, the sparse target component matrix, and the Lagrange multiplier matrix and penalty parameters introduced by the alternating direction multiplier method are updated alternately.

[0061] In this embodiment, the alternating direction multiplier method framework is used to iteratively solve the optimization model, specifically including:

[0062] The sparse target component matrix, Lagrange multiplier matrix and penalty parameter are fixed, the first intermediate matrix is ​​constructed and singular value decomposition is performed on the first intermediate matrix, and the low-rank clutter component matrix is ​​updated by weighted singular value thresholding operation based on adaptive weights.

[0063] By fixing the low-rank clutter component matrix, the Lagrange multiplier matrix, and the penalty parameter, a second intermediate matrix is ​​constructed and the sparse target component matrix is ​​updated through element-wise soft thresholding.

[0064] Based on the updated low-rank clutter component matrix and sparse target component matrix, the constraint residuals are calculated and the Lagrange multiplier matrix is ​​updated. At the same time, the penalty parameters are adaptively updated according to the changes in the constraint residuals.

[0065] In this embodiment, the weighted singular value thresholding operation is specifically as follows: for each element in the singular value vector of the first intermediate matrix, subtract half of the product of the corresponding adaptive weight and the current penalty parameter, and set any values ​​less than zero in the result to zero.

[0066] In this embodiment, the element-wise soft thresholding operation is specifically as follows: subtract the ratio of the sparse regularization parameter to the current penalty parameter from each element in the second intermediate matrix, set the absolute value of the result to zero for elements whose absolute value is less than the ratio, and retain the value after subtracting the ratio and the original sign for the remaining elements.

[0067] Specifically, for the low-rank sparse decomposition optimization model, a Lagrange multiplier matrix is ​​introduced. and penalty parameters Construct the augmented Lagrangian function:

[0068] ;

[0069] in, To augment the Lagrange function; To sum over all values; Low-rank clutter component matrix The One singular value; It is a Lagrange multiplier matrix; For Lagrange linear terms, i.e., Lagrange multiplier matrices The inner product of the matrix with the constraint residuals; Represents the inner product of matrices; The coefficient for the augmentation penalty term; The squared Frobenius norm measures the fitting error between matrices. To constrain the residuals, measure the deviation of the decomposition; To constrain the squared Frobenius norm of the residuals, let Then there is ; For matrix No. Line 1 Column elements; For matrix number of rows; For matrix The number of columns; For elements The square of the modulus.

[0070] Under the current iteration conditions, the sparse target component matrix is ​​fixed. With Lagrange multiplier matrix Based on the weighting property of the non-convex penalty function on singular values, singular value decomposition is performed on the two-dimensional echo matrix, and the singular values ​​are weighted and thresholded according to the current iteration weights, thereby updating the low-rank clutter component matrix. In the first In the next iteration, the fixed and Please solve:

[0071] ;

[0072] in, For the first The low-rank clutter component matrix after the next iteration; For the low-rank clutter component matrix Find the solution that minimizes the objective function; For the first The sparse target component matrix is ​​fixed in the next iteration; For the first The Lagrange multiplier matrix is ​​fixed in each iteration; For the first The penalty parameter for the next iteration; The coefficient for the augmentation penalty term; To broaden the range of penalties; This is the residual matrix after removing the current sparse target component matrix from the observation matrix; The scaling term for the Lagrange multipliers is used to correct the optimization objective.

[0073] because For a non-convex / concave function, perform a first-order approximation at the current singular point:

[0074] ;

[0075] in, The non-convex penalty function in the low-rank clutter component matrix The Function values ​​at singular values; For the first The corresponding iteration is the 1st iteration Weighting coefficients for each singular value; This is the deviation of the current singular value from the expansion point, i.e., the increment term of the linear approximation.

[0076] Among them, weight Defined as:

[0077] ;

[0078] in, For the first During the nth iteration The weights corresponding to the singular values; Non-convex penalty function For the first A singular value The derivative; The weight expression is given when the singular values ​​are small, and it follows... It increases and then decreases linearly.

[0079] Specifically, the process of solving the weighted singular value threshold includes:

[0080] set up:

[0081] ;

[0082] in, For the first The auxiliary matrix for the low-rank subproblem in the next iteration is used to simplify the expression of the low-rank subproblem.

[0083] The low-rank matrix is ​​then updated as follows:

[0084]

[0085] in, For the first The low-rank clutter component matrix updated in the next iteration; For A weighted singular value shrinkage operator for a threshold; Auxiliary matrix for low-rank subproblems The left singular vector matrix in singular value decomposition; This is a diagonal matrix with the vectors inside the brackets as its diagonal elements; This is a soft threshold shrinkage function, where the threshold is... ; Auxiliary matrix for low-rank subproblems The One singular value; Auxiliary matrix for low-rank subproblems The transpose of the right singular vector matrix in singular value decomposition; To take the maximum of the two values; This is the explicit expression of the soft thresholding function, which takes non-negative values ​​after applying soft thresholding to each singular value.

[0086] With a fixed low-rank clutter component matrix With Lagrange multipliers Under the given conditions, the subproblems corresponding to the target components are solved, and the sparse target component matrix is ​​updated through element-wise soft thresholding operations. To enhance the ability of the target echo to express the sparse structure in the range dimension.

[0087] In maintaining and Solve the following problem while keeping the original conditions unchanged:

[0088] ;

[0089] in, For the first The sparse target component matrix is ​​updated in the next iteration; To Find the solution that minimizes the objective function; This is the residual matrix after removing the current low-rank clutter component matrix.

[0090] set up

[0091] ;

[0092] in, For the first The auxiliary matrix for the sparse subproblem in the next iteration is used to simplify the expression of the sparse subproblem.

[0093] Its closed-form solution is an element-wise soft thresholding operation:

[0094] ;

[0095] in, For the first The sparse target component matrix after the next iteration update; For The complex field soft thresholding operator for the threshold; Auxiliary matrix for sparse subproblems The phase of each element is used to preserve the directional information of the complex elements; Auxiliary matrix for sparse subproblems The modulus of each element; Auxiliary matrix for sparse subproblems The magnitude of each element is taken as a non-negative value after applying a soft threshold to shrink it, which is the shrunk magnitude.

[0096] Based on the low-rank clutter component matrix in the current iteration With sparse target component matrix The updated results are used to calculate the constraint residuals and update the Lagrange multiplier matrix accordingly. At the same time, the penalty parameter is adaptively adjusted according to the changes in the residuals to improve the convergence stability of the algorithm.

[0097] Based on the low-rank clutter component matrix With sparse target component matrix Calculate the Lagrange multiplier matrix :

[0098] ;

[0099] in, For the first The Lagrange multiplier matrix after the next iteration; For the first The Lagrange multiplier matrix at the next iteration; This represents the constraint residual for the current iteration.

[0100] The penalty parameters are adaptively updated based on the changes in residuals. :

[0101] ;

[0102] in, For the first The penalty parameter for the next iteration; The growth factor for the penalty parameter ( ), used to accelerate convergence; For the first The penalty parameter for the next iteration; The Frobenius norm is the change in the sparse matrix between two consecutive iterations. The Frobenius norm of the observation matrix, i.e. ; To find the square root, take the radical sign for the entire denominator. For matrix No. Line 1 Column elements; and Two-dimensional radar echo matrix The number of rows and columns; The penalty parameter remains unchanged when the increase condition is not met.

[0103] S5. When the iteration process meets the preset termination condition, stop the iteration and output the currently updated sparse target component matrix as a high-resolution range image of the target after clutter suppression and preservation of structural features.

[0104] In this embodiment, the preset termination condition is: the relative error of the Frobenius norm between the sum of the low-rank clutter component matrix and the sparse target component matrix and the two-dimensional radar echo matrix in the current iteration is less than a set threshold, or the number of iterations reaches the preset maximum number.

[0105] Specifically, iteration stops when the following equation is satisfied:

[0106] ;

[0107] in, It is the Frobenius norm; This is a preset convergence threshold; iteration stops when the relative residual is less than this value. It is the same parameter as the penalty parameter update.

[0108] At this point, the sparse target component matrix is ​​the target echo matrix after clutter suppression.

[0109] Example 1:

[0110] To verify the technical effects of the present invention, experimental verification was conducted using simulation data and measured radar data.

[0111] The simulation experimental environment is set up as follows:

[0112] Computing platform: Intel(R) Core(TM) i7-14650HX (2.20GHz), 24.0GB RAM;

[0113] Operating system: 64-bit Windows 11;

[0114] Software environment: MATLAB 2024b;

[0115] The simulation platform is used to generate radar echo data and complete the low-rank sparse decomposition and high-resolution range image feature extraction processes.

[0116] To measure the effect of clutter suppression on the preservation of high-resolution range image structure, three parameters are used to quantitatively evaluate the loss of high-resolution range image structure.

[0117] The relative root mean squared error (RMSE) is a standardized form of the root mean square error (RMSE). It provides a dimensionless error metric by comparing the model's prediction error with a reference value of the actual observations, thus overcoming the comparability problem across different data scales. The formula is as follows:

[0118] ;

[0119] in, The relative root mean square error is used to measure the relative error of the recovery result. Root mean square error represents the absolute error between the recovered matrix and the true matrix; and These are the original high-resolution range image and the high-resolution range image after clutter suppression processing, respectively, in the support region. The amplitude value of each distance unit; ; For high-resolution distance images The mean; This refers to either the total length or the number of samples. For high resolution distance The Each element.

[0120] Correlation coefficient:

[0121] The Pearson correlation coefficient is usually expressed by the symbol... The linear relationship between two continuous variables is a core indicator in statistics used to quantify the strength and direction of the linear relationship. Essentially, it measures the degree to which a change in one variable tends to cause the other variable to change along a best-fit line (linear trend). The range of values ​​is limited to The Pearson correlation coefficient is calculated by standardizing the covariance and standard deviation of the variable data to make it a dimensionless quantity, as shown in the following formula:

[0122] ;

[0123] in, Pearson correlation coefficient; and For the first High-resolution distance image data points and The range; and To support high-resolution range image data points within the region and The mean; For data points and Length; It is the element-wise product of the two sets of data after removing the mean, which is the numerator of the covariance; For the second term in the denominator, the subscript is... from arrive Summation; The square of the first set of data after removing the mean is used to calculate its variance; The square of the second set of data after removing the mean is used to calculate its variance. When the coefficient... A coefficient of 1 indicates a perfect positive linear correlation between the two variables, meaning that an increase in one variable will necessarily lead to a proportional increase in the other variable; when the coefficient is 1... A coefficient of -1 indicates a perfect negative linear correlation, meaning that an increase in one variable necessarily leads to a proportional decrease in the other; when the coefficient is -1... A value of 0 indicates that there is no linear correlation between the two variables (but a nonlinear relationship may exist). The correlation coefficient can directly quantify the fidelity of the overall waveform shape, the consistency of amplitude variation trends, and capture the macroscopic distortion of the target's outline.

[0124] Scattering Point Count Consistency (SPCC) in high-resolution range images can be represented as the difference between the number of scattering points in the original high-resolution range image and the number of scattering points after clutter suppression processing. It reflects the loss of detail in the high-resolution range image during clutter suppression. If the number of scattering points is too low, some details on the target surface may not be captured, resulting in the loss of some feature information in the target's high-resolution range image. Too many scattering points will blur the target outline, while too few will lead to incomplete features, both reducing target distinguishability. For example, too many scattering points may cause the target outline to be blurred, while too few scattering points may result in incomplete reflection features of the target, as shown in the following formula:

[0125] ;

[0126] in, Error due to the number of scattering points; To take the absolute value; This represents the number of scattering points in the original high-resolution range image. This represents the number of scattering points in the high-resolution range image after clutter suppression. This represents the difference in the number of scattering points.

[0127] The number of scattering points error, relative root mean square error, and correlation coefficient are used as quantitative indicators of recovery capability. The smaller the number of scattering points error and relative root mean square error, and the closer the correlation coefficient is to 1, the higher the fidelity of the recovery of the target's high-resolution range image structure.

[0128] In the simulation, the radar transmitted signal uses a linear frequency modulated (LFM) pulse signal, the target echo consists of several strong scattering points, and clutter is simulated using a generalized K-distribution model. By adjusting the power ratio of the target echo to the clutter, echo matrices under different signal-to-clutter ratios are constructed. The method of this invention is used for processing, and the results are compared with the traditional robust principal component analysis method. Evaluation indicators include relative root mean square error, correlation coefficient, and error in the number of scattering points. The results show that the method of this invention can achieve lower errors and higher correlation coefficients under all signal-to-clutter ratio conditions, effectively preserving the structural characteristics of the high-resolution range image.

[0129] Table 1 summarizes four quantitative evaluation metrics for the RPCA method and the high-resolution range image feature-preserving enhancement method based on iterative weighted sparse decomposition (IRNN-RPCA) after clutter suppression, including the improvement factor. The relative mean square error, correlation coefficient, and number of scattering points are used to facilitate a direct comparison of the overall performance differences between the two methods. The IRNN-RPCA method outperforms the traditional RPCA method in all the evaluation dimensions set, verifying the effect of introducing iterative reweighted nuclear norm penalty on improving the performance of low-rank sparse decomposition. This method can better preserve the characteristic information of the target HRRP while suppressing clutter.

[0130] Table 1 Comparison of Clutter Suppression Quantization Indicators of Different Methods

[0131]

[0132] Combined with Table 1, Figures 3-8 It can be seen that the method of the present invention can effectively suppress low-rank clutter components in the echo matrix, while maintaining the number, position distribution and relative amplitude relationship of target scattering points in the high-resolution range image, thus avoiding the structural distortion problem of the high-resolution range image.

[0133] Specifically, Figure 2 This is a comparison curve of the relative root mean square error (RMSE) of the IRNN-RPCA method and the RPCA method after processing simulation data under different signal-to-noise ratios (SNRs). The horizontal axis represents the SNR, and the vertical axis represents the relative RMSE; a smaller value indicates better feature preservation. The curves marked with squares represent the RPCA method results, and the curves marked with diamonds represent the IRNN-RPCA method results. As the SNR increases, the errors of both methods decrease monotonically, and the IRNN-RPCA method consistently outperforms the RPCA method across the entire range, indicating that the IRNN-RPCA method has superior amplitude structure recovery capability.

[0134] Specifically, Figure 3 This is a comparison curve of the correlation coefficients between the IRNN-RPCA method and the RPCA method after processing simulation data under different signal-to-clutter ratios. The horizontal axis represents the signal-to-clutter ratio, and the vertical axis represents the correlation coefficient. The closer the value is to 1, the better the target scattering structure is preserved. The square markings represent the RPCA method, and the diamond markings represent the IRNN-RPCA method. The IRNN-RPCA method consistently outperforms the RPCA method within the experimentally set signal-to-clutter ratio range, indicating that the IRNN-RPCA method has a greater advantage in preserving the overall structure, especially under low signal-to-clutter ratio conditions.

[0135] Specifically, Figure 4This is a comparison curve showing the error in the number of scattering points under different signal-to-clutter ratios (SCRs) after processing simulation data using the IRNN-RPCA method and the RPCA method of this invention. The horizontal axis represents the SCR, and the vertical axis represents the error in the number of scattering points; a smaller value indicates better preservation of the number of target scattering centers. Squares indicate the RPCA method, and diamonds indicate the IRNN-RPCA method. The IRNN-RPCA method consistently performs worse than the RPCA method within the experimentally set SCR range, indicating that the IRNN-RPCA method can more accurately retain the number of target scattering centers, providing more reliable feature support for subsequent target identification.

[0136] Specifically, Figure 5 and Figure 6 The figures show two-dimensional amplitude diagrams of the range cell-pulse sequence extracted from the low-rank sparse decomposition of simulated cluttered radar echoes using the RPCA method and the IRNN-RPCA method of this invention, respectively. The horizontal and vertical axes and color codes have the same meaning in both figures. (Comparison) Figure 5 and Figure 6 It can be seen that, Figure 5 There are low-amplitude, light blue horizontal stripe-like residues in the mid-background area, while Figure 6 The background region amplitude value is close to zero, the background color is uniformly dark blue, and there is no obvious clutter residue, indicating that the IRNN-RPCA method achieves more thorough clutter suppression.

[0137] Specifically, Figure 7 , Figure 8 The RPCA method and the method of this invention are used to perform low-rank sparse decomposition on simulated cluttered radar echoes, extract sparse components, and then perform range migration correction and coherent accumulation to obtain the high-resolution target range image. (Comparison) Figure 7 and Figure 8 It can be seen that both methods can preserve the location of the main scattering center, but Figure 7 The blue dashed line has false scattering components in the background area and does not fit well with the black solid line. Figure 8 The blue dashed line and the black solid line have a significantly higher degree of agreement, the relative position and amplitude relationship of the main scattering peak are well restored, and there are no false scattering components in the background area, indicating that the IRNN-RPCA method of this invention achieves higher quality HRRP feature preservation.

[0138] Specifically, Figure 9This graph compares the target recognition accuracy of the IRNN-RPCA method and the RPCA method under different signal-to-clutter ratios (SCRs) after processing measured data from an X-band broadband radar of one embodiment. The horizontal axis represents the SCR, and the vertical axis represents the recognition accuracy. The red curve marked with a circle represents the baseline method, i.e., direct recognition of data under no clutter interference conditions, serving as the upper limit of performance. The black curve marked with a solid circle represents the result of the IRNN-RPCA method, and the blue curve marked with a square represents the result of the RPCA method. Figure 9 It can be seen that the IRNN-RPCA method outperforms the RPCA method within the experimental signal-to-clutter ratio range, indicating that the method of the present invention can better preserve the key discrimination features of the target after processing the measured data, and effectively improve the target recognition performance in complex clutter environments.

[0139] Therefore, the high-resolution range image feature preservation enhancement method based on iterative weighted sparse decomposition proposed in this invention first models the clutter-containing radar echo data matrix as the sum of a low-rank matrix and a sparse matrix. The low-rank matrix represents the main clutter component, and the sparse matrix represents the target echo. Next, an iterative weighted nuclear norm is introduced to replace the traditional nuclear norm to impose a non-convex penalty on the low-rank matrix. By applying adaptive weights to different singular values, a more compact approximation of the true rank function is achieved. Finally, the alternating direction multiplier method is used to iteratively solve the optimization problem, and the resulting sparse component is the target echo estimate after clutter suppression. Compared with existing RPCA methods, the method of this invention exhibits superior overall performance in both simulation and measured data: lower relative root mean square error, higher correlation coefficient, smaller error in the number of scattering points, less residual background clutter, and a higher degree of agreement between the recovered HRRP and the original target. Experiments show that the method of this invention can more accurately preserve key features such as the position, number, and amplitude of the target scattering center while effectively suppressing clutter.

[0140] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A high resolution range profile feature preserving enhancement method based on iterative weighted sparse decomposition, characterized in that, Includes the following steps: S1. Acquire radar echo data collected by the radar receiver within one coherent processing time, and after range-direction matched filtering, construct a two-dimensional radar echo matrix composed of the number of range elements and the number of pulse sequences. S2. The two-dimensional radar echo matrix is ​​represented as the superposition of the low-rank clutter component matrix and the sparse target component matrix. S3. Based on the superposition relationship, an optimization model is constructed. The objective function of the optimization model is the sum of the weighted nuclear norm of the low-rank clutter component matrix and the L1 norm of the sparse objective component matrix. The weight of the weighted nuclear norm is adaptively adjusted according to the singular values ​​of the low-rank clutter component matrix. S4. The optimization model is solved iteratively using the alternating direction multiplier method framework. During the iterative solution process, the low-rank clutter component matrix, the sparse target component matrix, and the Lagrange multiplier matrix and penalty parameters introduced by the alternating direction multiplier method are updated alternately. S5. When the iteration process meets the preset termination condition, stop the iteration and output the currently updated sparse target component matrix as a high-resolution range image of the target after clutter suppression and preservation of structural features. The objective function of the optimization model is specifically: ； in, Denotes the L1 norm of a matrix. For sparse regularization weights, The parameters are non-convex penalty function parameters; It is a two-dimensional radar echo matrix; This is the low-rank clutter component matrix; The sparse target component matrix; For the first matrix One singular value; It is a non-convex penalty function; The method of iteratively solving the optimization model using the alternating direction multiplier method specifically includes: The sparse target component matrix, Lagrange multiplier matrix and penalty parameter are fixed, the first intermediate matrix is ​​constructed and singular value decomposition is performed on the first intermediate matrix, and the low-rank clutter component matrix is ​​updated by weighted singular value thresholding operation based on adaptive weights. By fixing the low-rank clutter component matrix, the Lagrange multiplier matrix, and the penalty parameter, a second intermediate matrix is ​​constructed and the sparse target component matrix is ​​updated through element-wise soft thresholding. Based on the updated low-rank clutter component matrix and sparse target component matrix, the constraint residuals are calculated and the Lagrange multiplier matrix is ​​updated. At the same time, the penalty parameters are adaptively updated according to the changes in the constraint residuals.

2. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 1, characterized in that, The superposition relationship is specifically expressed as follows: the two-dimensional radar echo matrix is ​​equal to the sum of the low-rank clutter component matrix and the sparse target component matrix.

3. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 1, characterized in that, The non-convex penalty function is one of a logarithmic function, an exponential function, or a piecewise concave function.

4. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 1, characterized in that, The weighted singular value thresholding operation specifically involves subtracting half of the product of the corresponding adaptive weight and the current penalty parameter from each element in the singular value vector of the first intermediate matrix, and setting any values ​​less than zero in the result to zero.

5. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 1, characterized in that, The element-wise soft thresholding operation is specifically as follows: subtract the ratio of the sparse regularization parameter to the current penalty parameter from each element in the second intermediate matrix, set the absolute value of the result to zero for elements whose absolute value is less than the ratio, and retain the value after subtracting the ratio and the original sign for the remaining elements.

6. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 1, characterized in that, The preset termination condition is: the relative error of the Frobenius norm between the sum of the low-rank clutter component matrix and the sparse target component matrix and the two-dimensional radar echo matrix in the current iteration is less than a set threshold, or the number of iterations reaches the preset maximum number.

7. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 1, characterized in that, Step S1 specifically includes: Range-direction matched filtering is performed on the radar echo data of multiple pulses acquired by the radar receiver within one coherent processing time to obtain a high-resolution one-dimensional range profile corresponding to each pulse. The high-resolution one-dimensional range image corresponding to each pulse is arranged in pulse time order to construct a two-dimensional radar echo matrix with the number of rows equal to the number of range cells and the number of columns equal to the number of pulse sequences.

8. The high-resolution range image feature preservation and enhancement method based on iterative weighted sparse decomposition according to claim 7, characterized in that, The range-oriented matched filtering is implemented using a matched filter for the radar transmitted signal, and the cell resolution of the high-resolution one-dimensional range image is determined by the bandwidth of the radar transmitted signal.

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