A SAR interference suppression method based on learnable time-frequency feature separation

Abstract

This invention discloses a SAR interference suppression method based on learnable time-frequency feature separation. First, a SAR interference suppression problem model based on learnable time-frequency feature separation is established. A learnable and invertible nonlinear transformation is introduced into the low-rank sparse decomposition model framework. Then, a SAR interference suppression network is constructed and trained. The SAR echo containing interference to be processed undergoes time-frequency transformation and is cropped before being input into the trained network. The network outputs the SAR echo time spectrum and the interference time-frequency map. The SAR echo time spectrum output by the network is then reassembled into complete time-frequency data according to the cropping method to obtain the interference-suppressed SAR echo time spectrum. This spectrum is then restored to the time domain echo using inverse short-time Fourier transform. Finally, the interference-suppressed time domain echo is processed by SAR imaging to obtain the interference-suppressed SAR image. This invention solves the problem of SAR image quality degradation or inability to image under interference environments, providing reliable performance in interference suppression and echo fidelity preservation in both the time-frequency and image domains.

Description

Technical Field

[0001] This invention belongs to the field of SAR interference suppression technology, specifically relating to a SAR interference suppression method based on learnable time-frequency feature separation. Background Technology

[0002] Synthetic Aperture Radar (SAR), as an important remote sensing technology, possesses unique capabilities to penetrate clouds and fog and to image continuously day and night. It can accurately capture subtle surface features of land and ocean, playing a vital role in many fields such as earth mapping, oil spill detection, iceberg detection, disaster monitoring, and surveillance and reconnaissance.

[0003] However, with the increasing number of electromagnetic devices, broadband SAR systems are inevitably affected by radio frequency interference (RFI). Strong external electromagnetic signals from the same frequency band can form large areas of stripes or bright patches on SAR images, seriously hindering image interpretation. In particular, the forms of interference are becoming increasingly complex, and the echoes recorded by SAR pulse acquisition may exhibit diverse signal forms and time-varying signal components, posing a greater challenge to interference suppression. Therefore, it is necessary to design signal processing techniques with interference suppression capabilities to effectively suppress interference in SAR images.

[0004] In recent years, deep learning technology, with its powerful data learning and representation capabilities, has demonstrated outstanding performance in tasks such as high-precision SAR imaging, target enhancement, and interference detection, enabling it to uncover complex nonlinear relationships between data. The paper "Fan, W., Zhou, F., Rong, P., & Yao, X. (2019). Interference Mitigation for Synthetic Aperture Radar Using Deep Learning. 2019 6th Asia-Pacific Conference on Synthetic Aperture Radar (APSAR). IEEE" proposes an end-to-end interference suppression network (IMN) based on ResNet, which utilizes data-driven learning to transform the contaminated time-frequency spectrum to the interference-free echo time-frequency spectrum. The paper “Wang, S., Du, J., Fan, W., & Zhou, F. (2023). Interference Suppression for Synthetic ApertureRadar Using Dual-path Residual Network with Attention Mechanism. IGARSS2023-2023IEEE International Geoscience and Remote Sensing Symposium.IEEE” proposes a dual-path residual network that incorporates an attention mechanism to achieve end-to-end mapping of the Comb Spectrum Modulation Jamming (CSMJ) suppression problem. The paper "Shen, J., Han, B., Pan, Z., Li, G., Hu, Y., & Ding, C. (2022). Learning Time-frequency Information with Prior for SAR Radio Frequency Interference Suppression. IEEE Transactions on Geoscience and Remote Sensing. IEEE" introduces low-rank sparse prior knowledge into data-driven approaches. Based on the low-rank sparse characteristics of SAR echoes and interference in the time-frequency domain, it proposes a network PIS-Net guided by time-frequency feature clustering and a low-rank sparse loss function.

[0005] The aforementioned interference suppression network designs suffer from drawbacks such as data quality dependence, poor interpretability, residual image interference, and insufficient low-rank sparse representation capabilities under complex interference conditions, resulting in poor interference suppression performance in such environments. Compared to purely data-driven end-to-end networks, model-driven networks offer stronger interpretability. Furthermore, deep networks possess strong nonlinear representation capabilities, overcoming the limitations of existing low-rank sparse features and improving the separation of interference and echoes. Therefore, designing a model-data jointly driven network that combines interpretability and representational capabilities is of great significance. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a SAR interference suppression method based on learnable time-frequency feature separation, which solves the problem of difficulty in separating echo and interference components in the time spectrum of SAR contaminated by interference.

[0007] The technical solution adopted in this invention is: a SAR interference suppression method based on learnable time-frequency feature separation, the specific steps of which are as follows:

[0008] S1. Establish a SAR interference suppression problem model based on learnable time-frequency feature separation, and introduce learnable and invertible nonlinear transformation into the low-rank sparse decomposition model framework to enhance the feature representation capability of interference and echo.

[0009] Based on the time-frequency domain distribution characteristics of SAR echoes and interference, a basic model for interference suppression based on low-rank and sparse decomposition is established, with the following expression:

[0010]

[0011] Among them, ||·|| * Let ||·||1 represent the nuclear norm, ||·||1 represent the l1 norm, λ represent the weighting factor, L represent the low-rank component, S represent the sparse component, and X represent the data to be processed.

[0012] Then, based on the low-rank sparse decomposition model, two learnable nonlinear transformations are introduced. and The feature representations of SAR echoes and interference are enhanced respectively, and the SAR interference suppression problem is modeled as a low-rank sparse decomposition model based on learnable transformation, as shown in the following expression:

[0013]

[0014] The solution for the augmented Lagrange function is reconstructed as follows:

[0015]

[0016] Where ρ represents the penalty factor, Λ represents the Lagrange multiplier, and <·> represents the inner product, which is the sum of the corresponding element-wise products of the matrix.

[0017] Then, the ADMM algorithm is used to solve the problem, decomposing equation (3) into three subproblems. In each step, only one variable is updated while the other variables are fixed, and the updates are repeated alternately. For the number of iterations k = 1, 2, 3, ..., the expressions for the three iterative subproblems are as follows:

[0018]

[0019] S2. Based on step S1, construct a SAR interference suppression network based on learnable time-frequency feature separation, including: a deep unfolding network of the overall iterative algorithm and a reversible nonlinear transformation learning network.

[0020] S21, Deep Unfolding Network of the Overall Iterative Algorithm;

[0021] The iterative process of solving equation (4) is expanded into a deep learning scheme with P iterative layers. The three sub-problems correspond to three network modules: LM, SM and ΛM. L, S and Λ are updated respectively, and the hyperparameters ρ and λ are set as learnable parameters.

[0022] Specifically, the network modules corresponding to L, S, and Λ are updated as follows:

[0023] 1) The update module LM for the low-rank component L in layer p p The expression is as follows:

[0024]

[0025] in, This represents an invertible nonlinear transformation that enhances the characterization of interference. It is its inverse transformation, p = 1, 2, ..., P represents the number of layers of the unfolded network, corresponding to the number of iterations k in equation (4). The proximal operator representing the nuclear norm is defined as follows: W=UΣV H That is, the singular value decomposition of matrix W, where U represents the left singular vector, V represents the right singular vector, H represents the conjugate transpose of the matrix, and Σ=diag(σ1,σ2,...,σ r ) represents a diagonal matrix consisting of singular values, and r represents the rank of matrix W. Used to filter out singular values ​​that exceed a threshold; α p The parameter representing the singular value threshold is designed as a learnable network parameter, and α increases with the number of iterations. p Decreasing layer by layer, then α p The specific expression is as follows:

[0026]

[0027] Where, ω α θ represents the learnable coefficient factor. α Used to control α p The degree of variation with the number of layers p is set to θ α >1 to constrain α p Decrease layer by layer.

[0028] 2) The update module SM for the sparse component S in the p-th layer p The expression is as follows:

[0029]

[0030] in, This represents the reversible nonlinear transformation that enhances the time-frequency characterization of SAR echoes. It is its inverse transformation. This represents the soft thresholding operator, where β controls the soft threshold. p The expression is as follows:

[0031]

[0032] Where, ω β and θ β θ represents the learnable parameters. β Used to control β p The degree of variation with the number of layers p is set to θ β >1 to constrain β p It decreases as p increases.

[0033] 3) The update module ΛM of the Lagrange multipliers Λ in the p-th layer p The expression is as follows:

[0034] Λ (p) =Λ (p-1) +γ p (L (p) +S (p) -X) (9)

[0035] Among them, the learnable penalty factor γ p The expression is as follows:

[0036]

[0037] Where, ω γ and θ γ This represents the learnable parameter, where the exponent p is greater than 1, then when θ γ When γ > 1, p It increases with the number of layers p.

[0038] S22, Invertible Nonlinear Transformation Learning Network;

[0039] The reversible nonlinear transform learning network divides the input into two parts and constructs the transform through cross-coupling between the two parts, processing complex time-spectral data. First, a reconstruction operator is used. Combine the real and imaginary parts of X, and... Reorganized into a tensor with two channels The expression is as follows:

[0040]

[0041] in, Represents the field of complex numbers. Let m represent the real number field, q represent the discrete time sampling points, and N represent the discrete frequency sampling points. m N represents the number of time sampling points. q This indicates the number of frequency sampling points.

[0042] Then along the channel dimension Divided into two parts During the forward transform, a forward process is performed, and the two components pass through the learned function. Cross-coupling is achieved. The forward process expression for the i-th coupled layer is as follows:

[0043]

[0044] Here, ψ(·) represents the invertible downsampling operator, used to transform the spatial dimension into the channel dimension while maintaining the equality of the dimensions of the two parts being summed. The invertibility of the coupling layer and and Regardless, a convolutional neural network (CNN) module is used to extract effective deep features through linear and nonlinear operations in the network.

[0045] The operations on X1 and X2 in a coupled layer are not symmetrical. Constructing l coupled layers together forms an invertible transformation network module, i.e., an invertible nonlinear transformation learning network. After the coupled layers, the two output components are merged along the channel dimension as the result of the forward transformation.

[0046] Where l>3.

[0047] The inverse process is performed during the inverse transformation, and the expression for the inverse process of the i-th coupling layer is as follows:

[0048]

[0049] S3. The SAR echo data containing interference to be processed is transformed into the time-frequency domain pulse by pulse using short-time Fourier transform, and then the time-frequency domain data is cropped to the size that the SAR interference suppression network constructed in step S2 can process.

[0050] Short-Time Fourier Transform (STFT) is used to realize time-frequency data analysis and processing, and the local time-frequency characteristics X of signal x[n] are obtained. tf The expression for [m,q] is as follows:

[0051]

[0052] Where w[n] represents the time-domain analysis window, x[n] represents the echo to be processed for a pulse, n represents the discrete time variable, i.e. the position of the analysis window on the time axis, and R represents the step size.

[0053] After the short-time Fourier transform, the time-frequency domain data is cropped to a uniform network-processable size.

[0054] S4. Train a SAR interference suppression network based on learnable time-frequency feature separation;

[0055] Supervised training was conducted, using the time spectra of SAR echoes in different scenarios and the time spectra of interference of different types and parameters as the ground truth values ​​of the separation results to construct training and validation datasets.

[0056] Spectrum of interference contamination in the dataset Echo Spectrum Interference Time Spectrum Amplitude normalization is performed. The maximum-minimum normalization method is chosen, and since the frequency axis range is greater than the signal bandwidth, the minimum amplitude in the time-frequency graph is 0. This ensures that the normalized triplet satisfies... Maximum value adopted If the maximum amplitude is found, the normalization expression is as follows:

[0057]

[0058] Then, the normalized time-frequency data is segmented into complex time-frequency graphs of uniform size and saved as triples. As training input.

[0059] The network output consists of separate SAR echo time spectra and interference time spectra. Considering the interference in the network output and the reconstruction error of the SAR echo time spectra, a loss function is defined. The expression is as follows:

[0060]

[0061] Where L′ and S′ represent the spectral decomposition results of the network output interference and SAR echo, respectively, and σ represents the parameter for adjusting the weights, ||·|| F This represents the F-norm of the matrix. Since the data processed is all complex, the F-norm is calculated as the sum of the squared moduli of the differences between the complex pixel values ​​of the network output data and the labels.

[0062] S5. Perform time-frequency transformation and cropping on the SAR echo containing interference to be processed according to step S3. Then input the cropped time-frequency data into the SAR interference suppression network trained in step S4 for processing to obtain the SAR echo time spectrum and interference time-frequency map output by the network.

[0063] S6. The SAR echo time spectrum obtained from the network output in step S5 is reassembled into complete time-frequency data according to the cropping method to obtain the SAR echo time spectrum after interference suppression. The time-domain echo is then restored by inverse short-time Fourier transform, i.e., the time-domain echo after interference suppression.

[0064] S7. Perform SAR imaging processing on the time-domain echo after interference suppression in step S6 to obtain the SAR image after interference suppression.

[0065] The beneficial effects of this invention are as follows: First, the method of this invention establishes a SAR interference suppression problem model based on learnable time-frequency feature separation. A learnable and invertible nonlinear transformation is introduced into the low-rank sparse decomposition model framework. Then, a SAR interference suppression network is constructed and trained. The interference-laden SAR echo to be processed undergoes time-frequency transformation and is cropped before being input into the trained network. The network outputs the SAR echo time spectrum and the interference time-frequency map. The SAR echo time spectrum output by the network is then reassembled into complete time-frequency data according to the cropping method to obtain the interference-suppressed SAR echo time spectrum. This is then restored to the time-domain echo through inverse short-time Fourier transform. Finally, the interference-suppressed time-domain echo is processed by SAR imaging to obtain the interference-suppressed SAR image. This invention solves the problem of SAR image quality degradation or inability to image under interference environments. It combines data-driven and model-driven approaches, introducing a learnable nonlinear transformation network based on low-rank sparse decomposition theory to enhance the features of interference and SAR echoes, achieving effective separation of interference and echoes. Simultaneously, the iterative solution process is expanded into a parameter-learnable network, avoiding manual parameter tuning. This provides reliable performance in interference suppression and echo fidelity in both the time-frequency and image domains. Attached Figure Description

[0066] Figure 1 This is a flowchart of a SAR interference suppression method based on learnable time-frequency feature separation according to the present invention.

[0067] Figure 2 This is a schematic diagram of the reversible nonlinear transformation network module structure in an embodiment of the present invention.

[0068] Figure 3 This is a schematic diagram of the downsampling operator in the reversible network in an embodiment of the present invention.

[0069] Figure 4 This is a structural diagram of the convolutional neural network module in an embodiment of the present invention.

[0070] Figure 5 This is a schematic diagram of the training data triples used in the embodiments of the present invention.

[0071] Figure 6 This is a comparison chart of the time-frequency domain interference suppression effects of different methods in the embodiments of the present invention.

[0072] Figure 7 This is a comparison chart of the image domain interference suppression effects of different methods in the embodiments of the present invention. Detailed Implementation

[0073] To facilitate understanding of the technical content of the present invention by those skilled in the art, the method of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0074] like Figure 1 The flowchart of a SAR interference suppression method based on learnable time-frequency feature separation according to the present invention is shown below. The specific steps are as follows:

[0075] S1. Establish a SAR interference suppression problem model based on learnable time-frequency feature separation, and introduce learnable and invertible nonlinear transformation into the low-rank sparse decomposition model framework to enhance the feature representation capability of interference and echo.

[0076] Based on the time-frequency domain distribution characteristics of SAR echoes and interference, a basic model for interference suppression based on low-rank and sparse decomposition is established, with the following expression:

[0077]

[0078] Among them, ||·|| * Let ||·||1 represent the nuclear norm, ||·||1 represent the l1 norm, λ represent the weighting factor, L represent the low-rank component, S represent the sparse component, and X represent the data to be processed.

[0079] Analysis revealed a coupling between the low-rank and sparsity of the time-spectral frequencies of SAR echoes and ideal interference signals, making it difficult to accurately separate the echo and interference components using only low-rank and sparse decomposition models. Therefore, this embodiment introduces two learnable nonlinear transformations based on the low-rank sparse decomposition model. and The feature representations of SAR echoes and interference are enhanced respectively, and the SAR interference suppression problem is modeled as a low-rank sparse decomposition model based on learnable transformation, as shown in the following expression:

[0080]

[0081] The solution for the augmented Lagrange function is reconstructed as follows:

[0082]

[0083] Where ρ represents the penalty factor, Λ represents the Lagrange multiplier, and <·> represents the inner product, which is the sum of the corresponding element-wise products of the matrix.

[0084] Then, the ADMM algorithm is used to solve the problem, decomposing equation (3) into three subproblems. In each step, only one variable is updated while the other variables are fixed, and the updates are repeated alternately. For the number of iterations k = 1, 2, 3, ..., the expressions for the three iterative subproblems are as follows:

[0085]

[0086] Low-rank and sparse models have limited ability to characterize time-frequency domain interference and SAR echoes, and iterative methods suffer from difficulties in setting hyperparameters and high computational costs. This embodiment enhances the characteristic characterization of time-frequency domain interference and echoes by introducing data assistance into the model-driven scheme, and learns a more robust and efficient parameter scheme from the data.

[0087] S2. Based on step S1, construct a SAR interference suppression network based on learnable time-frequency feature separation, including: a deep unfolding network of the overall iterative algorithm and a reversible nonlinear transformation learning network.

[0088] S21, Deep Unfolding Network of the Overall Iterative Algorithm;

[0089] The iterative process of solving equation (4) is expanded into a deep learning scheme with P iterative layers. The three sub-problems correspond to three network modules: LM, SM and ΛM. L, S and Λ are updated respectively, and the hyperparameters ρ and λ are set as learnable parameters.

[0090] Specifically, the network modules corresponding to L, S, and Λ are updated as follows:

[0091] 1) The update module LM for the low-rank component L in layer p p The expression is as follows:

[0092]

[0093] in, This represents an invertible nonlinear transformation that enhances the characterization of interference. It is its inverse transformation, p = 1, 2, ..., P represents the number of layers of the unfolded network, corresponding to the number of iterations k in equation (4). The proximal operator representing the nuclear norm is defined as follows: W=UΣV H That is, the singular value decomposition of matrix W, where U represents the left singular vector, V represents the right singular vector, H represents the conjugate transpose of the matrix, and Σ=diag(σ1,σ2,...,σ r ) represents a diagonal matrix consisting of singular values, and r represents the rank of matrix W. Used to filter out singular values ​​that exceed a threshold; α p The parameter representing the singular value threshold is designed as a learnable network parameter, and α increases with the number of iterations. p Decreasing layer by layer, then α p The specific expression is as follows:

[0094]

[0095] Where, ω α θ represents the learnable coefficient factor. α Used to control α p The degree of variation with the number of layers p is set to θ α >1 to constrain α p Decrease layer by layer.

[0096] 2) The update module SM for the sparse component S in the p-th layer p The expression is as follows:

[0097]

[0098] in, This represents the reversible nonlinear transformation that enhances the time-frequency characterization of SAR echoes. It is its inverse transformation. This represents the soft thresholding operator, where β controls the soft threshold. p The expression is as follows:

[0099]

[0100] Where, ω β and θ β θ represents the learnable parameters. β Used to control β p The degree of variation with the number of layers p is set to θ β >1 to constrain β p It decreases as p increases.

[0101] 3) The update module ΛM of the Lagrange multipliers Λ in the p-th layer p The expression is as follows:

[0102] Λ (p) =Λ (p-1) +γ p (L (p) +S (p) -X) (9)

[0103] Among them, the learnable penalty factor γ p The expression is as follows:

[0104]

[0105] Where, ω γ and θ γ This represents the learnable parameter, where the exponent p is greater than 1, then when θ γ When γ > 1, p It increases with the number of layers p.

[0106] S22, Invertible Nonlinear Transformation Learning Network;

[0107] The reversible nonlinear transform network constructs a nonlinear transform through data fitting, enhancing the characterization of interference and SAR echoes. In this embodiment, the nonlinear transform... and It exhibits good reversibility, enabling lossless information conversion between the feature domain and the time-frequency domain. The reversible transformation network structure of this invention is as follows: Figure 2 As shown, the core of this structure is to divide the input into two parts, namely... Figure 2 X1 and X2 in the network construct the transformation through cross-coupling between the two parts, with superscripts 1, 2, ..., I indicating the number of coupling layers. This network processes complex time-frequency spectral data.

[0108] First, use the reconstruction operator. Combine the real and imaginary parts of X, and... Reorganized into a tensor with two channels The expression is as follows:

[0109]

[0110] in, Represents the field of complex numbers. Let m represent the real number field, q represent the discrete time sampling points, and N represent the discrete frequency sampling points. m N represents the number of time sampling points. q This indicates the number of frequency sampling points.

[0111] Then along the channel dimension Divided into two parts The forward process is executed during the forward transformation, such as... Figure 2 As shown in (a), the two components are learned through the function. Cross-coupling is achieved. The forward process expression for the i-th coupled layer is as follows:

[0112]

[0113] Wherein, ψ(·) represents the invertible downsampling operator, used to convert the spatial dimension into the channel dimension while maintaining the equality of the two dimensions in the summation. Its operation diagram is shown below. Figure 3 As shown.

[0114] Thanks to the special nature of the structure, the reversibility of the coupling layer and and Irrelevant. and It can be implemented by any deep neural network module; this embodiment uses, for example... Figure 4 The Convolutional Neural Network (CNN) module shown is used to extract effective deep features through linear and nonlinear operations in the network.

[0115] Since the operations on X1 and X2 in a single coupling layer are not symmetrical, this embodiment constructs a combination of four coupling layers as a reversible transformation network module, i.e., a reversible nonlinear transformation learning network, to ensure that all dimensions influence each other. After the four coupling layers, the two output components are merged along the channel dimension as the result of the forward transformation.

[0116] Perform the following during the inverse transformation: Figure 2 (b) shows the reverse process, where the expression for the reverse process of the i-th coupling layer is as follows:

[0117]

[0118] No calculation is required during the reverse process. and The inverse. Therefore, it can be constructed flexibly. and The structural reinforcement features are characterized without affecting the transformation. and The reversibility of the transform. Without performing any additional operations, a forward transform plus an inverse transform achieves perfect reversibility, i.e.

[0119] S3. The SAR echo data containing interference to be processed is transformed into the time-frequency domain pulse by pulse using short-time Fourier transform, and then the time-frequency domain data is cropped to the size that the SAR interference suppression network constructed in step S2 can process.

[0120] In processing, the SAR echo data containing interference is first transformed pulse-by-pulse into the time-frequency domain using Short-Time Fourier Transform (STFT). The time-frequency domain, as a two-dimensional feature domain, can provide instantaneous time and frequency information of the signal, making it suitable for revealing comprehensive information about non-stationary signals. This embodiment uses Short-Time Fourier Transform (STFT) to achieve time-frequency data analysis and processing, and the local time-frequency characteristics X of signal x[n] are... tf The expression for [m,q] is as follows:

[0121]

[0122] Where w[n] represents the time-domain analysis window, x[n] represents the echo to be processed for a pulse, n represents the discrete time variable, i.e. the position of the analysis window on the time axis, and R represents the step size.

[0123] After the short-time Fourier transform, the time-frequency domain data is cropped to a uniform network-processable size, which is 256*256 in this embodiment.

[0124] S4. Train a SAR interference suppression network based on learnable time-frequency feature separation;

[0125] Supervised training is performed, using the SAR echo time spectra of different scenarios and the interference time spectra of different types and parameters from the simulation data of this embodiment as the ground truth of the separation results to construct training and validation datasets. To ensure the comparability of echo data from different scenarios and signal-to-interference ratios, it is necessary to remove interference-contaminated time spectra from the dataset. Echo Spectrum Interference Time Spectrum Amplitude normalization is performed. The maximum-minimum normalization method is chosen because the frequency axis range is greater than the signal bandwidth, and the minimum amplitude value in the time-frequency graph is 0. To ensure that the normalized triplet satisfies... Maximum value adopted If the maximum amplitude is found, the normalization expression is as follows:

[0126]

[0127] Then, the normalized time-frequency data is segmented into complex time-frequency plots of uniform size (256*256) and saved as triples. As training input. Figure 5 The training data triples used in this embodiment

[0128] The network output consists of separate SAR echo time spectra and interference time spectra. Considering the interference in the network output and the reconstruction error of the SAR echo time spectra, a loss function is defined. The expression is as follows:

[0129]

[0130] Where L′ and S′ represent the spectral decomposition results of the network output interference and SAR echo, respectively, and σ represents the parameter for adjusting the weights, ||·|| F This represents the F-norm of the matrix. The data processed is all complex data, and the F-norm is calculated as the sum of the squared moduli of the differences between the complex pixel values ​​of the network output data and the labels. During the iteration process, due to the constraint L+S=X, the reconstruction error losses of interference and echo components can mutually restrict and promote each other.

[0131] S5. Perform time-frequency transformation and cropping on the SAR echo containing interference to be processed according to step S3. Then input the cropped time-frequency data into the SAR interference suppression network trained in step S4 for processing to obtain the SAR echo time spectrum and interference time-frequency map output by the network.

[0132] S6. The SAR echo time spectrum obtained from the network output in step S5 is reassembled into complete time-frequency data according to the cropping method to obtain the SAR echo time spectrum after interference suppression. The time-domain echo is then restored by inverse short-time Fourier transform, i.e., the time-domain echo after interference suppression.

[0133] S7. Perform SAR imaging processing on the time-domain echo after interference suppression in step S6 to obtain the SAR image after interference suppression.

[0134] To verify the performance of the method of the present invention, this embodiment conducted experiments on the suppression effect of narrowband and broadband interference with different parameters and combinations. The differences between the interference-suppressed image and the interference-free ground truth image were calculated using three indicators: NMSE, SSIM, and PSNR, in order to evaluate the interference suppression performance of the method.

[0135] Figure 6 The time-frequency domain interference suppression performance of the method of this invention is compared with other methods, including frequency domain filtering, time-frequency domain filtering, RPCA, and two aforementioned network methods in this field, IMN and PIS-Net. The time-frequency domain interference suppression performance is shown in Table 1.

[0136] Table 1

[0137]

[0138] Experimental comparisons show that the method of this invention has superior time-frequency domain interference suppression and echo fidelity, and also exhibits better adaptability to multi-type combined interference scenarios not present in the training data. Furthermore, the method of this invention can directly obtain the suppressed complex time-frequency spectrum, and can simultaneously recover the desired echo amplitude and phase.

[0139] To verify the interference suppression and image fidelity performance of the method of this invention in SAR images, time-varying narrowband and broadband combined interference were set, and the image domain interference suppression performance of several methods was compared, such as... Figure 7 As shown. Among them, Figure 7 (a) is a simulated SAR image under interference. Figure 7 (b)-(f) show the imaging results after interference suppression for five comparison methods: frequency domain filtering, time-frequency domain filtering, RPCA, IMN, and PIS-Net, respectively. Figure 7 (g) shows the imaging result after interference suppression in this embodiment. Figure 7 (h) is a simulated interference-free SAR image. Table 2 gives the data containing... Figure 7 Comparison of SAR image domain interference suppression performance in three different imaging scenarios and interference settings.

[0140] Table 2

[0141]

[0142] Because the bandwidth and duration of interference contained in different pulses vary, the comparative methods lose useful echoes to varying degrees after removing the interference. This results in inconsistent residual echo energy from different pulses during imaging, causing regional variations in brightness in the image. In summary, the method of this invention provides the most stable performance when facing complex time-varying interference, effectively removing interference with varying durations, bandwidths, and intensities. While removing interference, the energy of the real scene echoes is preserved as much as possible, and the image does not exhibit significant amplitude distortion due to fluctuations in the interference distribution range. Experiments (Table 2) demonstrate that, compared to the comparative methods and other network-based methods, the method of this invention improves SSIM and PSNR by more than 0.014 and 6.22 dB, respectively, showing advantages in interference suppression and image fidelity. Furthermore, it exhibits good suppression performance in complex interference environments such as time-varying and multi-signal combinations, providing a feasible solution for SAR suppression in complex environments.

[0143] In summary, the method of this invention enhances the time-frequency representation of SAR echoes and interference by constructing learnable transformations, thereby improving their separability. By expanding the existing iterative solution process into a network computing architecture and setting the hyperparameters that require manual adjustment in existing methods as network learnable parameters, a more robust and efficient parameter setting scheme is provided. The processing network is a data-model jointly driven network, which takes into account interpretability while utilizing the representation capabilities of deep networks.

[0144] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A SAR interference suppression method based on learnable time-frequency feature separation, the specific steps being as follows: S1. Establishing a SAR interference suppression problem model based on learnable time-frequency feature separation, introducing a learnable reversible nonlinear transformation in a low-rank sparse decomposition model framework, and enhancing the feature representation capability of interference and echoes; According to the time-frequency domain distribution characteristics of SAR echoes and interference, a basic model of interference suppression problem based on low-rank and sparse decomposition is set, and the expression is as follows: wherein ||·|| * Let ||·||1 represent the nuclear norm, ||·||1 represent the l1 norm, λ represent the weighting factor, L represent the low-rank component, S represent the sparse component, and X represent the data to be processed. Then, two learnable nonlinear transforms are introduced to enhance the feature representation of SAR echoes and jamming, respectively and The SAR jamming suppression problem is modeled as a low-rank sparse decomposition model based on the learnable transforms, which is expressed as follows: Then, an augmented Lagrange function is constructed to solve the equation, and the expression is as follows: Wherein, ρ represents a penalty factor, Λ represents a Lagrange multiplier, and <·> represents an inner product, that is, the sum of the products of corresponding elements of matrices; Then, the ADMM algorithm is used to solve, and equation (3) is decomposed into three sub-problems, each step only updates one variable while fixing the remaining variables, and the update is repeated alternately; for iteration number k = 1, 2, 3, …, the expressions of the three iteration sub-problems are as follows: S2. Based on step S1, a SAR interference suppression network based on learnable time-frequency feature separation is constructed, including: a deep unfolding network of the overall iterative algorithm and a reversible nonlinear transformation learning network; S21. Deep unfolding network of the overall iterative algorithm; The iteration process of solving equation (4) is unfolded as a deep learning scheme containing P iteration layers, and the three sub-problems correspond to three network modules: LM, SM and ΛM, respectively updating L, S and Λ, and setting the hyperparameters ρ and λ as learnable parameters; Wherein, the network modules corresponding to the update of L, S and Λ are as follows: 1) Update module LM of the low-rank component L in the p-th layer p The expression is as follows: wherein, denotes a reversible nonlinear transformation that enhances the interference characterization, is its inverse transformation, p = 1, 2,..., P denotes the number of layers of the unfolding network, corresponding to the iteration number k in equation (4); denotes the proximal operator of the nuclear norm, defined as W = UΣV H i.e. the singular value decomposition of the matrix W, U denotes the left singular vectors, V denotes the right singular vectors, H denotes the conjugate transpose of the matrix, Σ = diag(σ1, σ2,..., σ r ) denotes a diagonal matrix composed of singular values, r denotes the rank of the matrix W; is used to filter out the singular values that exceed the threshold; a p denotes a parameter that controls the singular value threshold, is designed as a learnable network parameter, and as the iteration number increases, a p decreases layer by layer, then a p The specific expression is as follows: where ω α represents a learnable coefficient factor, θ α is used to control α p with the degree of change in the layer number p, θ α > 1 is set to constrain α p decreases layer by layer; 2) update module SM of the sparse component S in the pth layer p The expression is as follows: wherein, denotes a reversible nonlinear transform enhancing the time-frequency representation of the SAR echo, is its inverse transform; denotes a soft threshold operator, the parameter β controlling the soft threshold p The expression is as follows: where ω β and θ β represent learnable parameters, θ β is used to control the degree of change of β p with respect to the layer number p, and θ β > 1 is set to constrain β p to decrease with increasing p; 3) a module ΛM for updating the Lagrange multiplier Λ in the p-th layer p The expression is as follows: Λ (p) =Λ (p-1) +γ p (L (p) +S (p) -X) (9) where the learnable penalty factor γ p The expression is as follows: where ω γ and θ γ represent learnable parameters, and the exponent p is greater than 1, then when θ γ > 1, γ p increases with the growth of the number of layers p; S22. Reversible nonlinear transformation learning network; The reversible nonlinear transform learning network divides the input into two parts, constructs the transform through cross-coupling between the two parts, and the processing object is complex time-frequency spectrum data; first, a reconstruction operator is used The real part and the imaginary part of X are combined to be Recombined into a tensor with two channels The expression is as follows: wherein denotes the complex domain, denotes the real domain, m denotes a discrete time sample point, q denotes a discrete frequency sample point, N m denotes the number of time sample points, N q denotes the number of frequency sample points; Then along the channel dimension is divided into two parts The forward process is performed at the forward transform, both components pass through a learned function Cross-coupling is implemented; the forward process expression of the ith coupling layer is as follows: wherein, ψ(·) represents a reversible down-sampling operator, used to convert spatial dimensions into channel dimensions, maintaining the two parts of the summation equal in dimension; the reversibility of the coupling layer is independent of and a convolutional neural network (CNN) module is adopted to extract effective deep features through linear and nonlinear operations in the network. The operation on X1 and X2 in a coupling layer is not symmetrical, and l coupling layer combinations are constructed as a reversible transformation network module, that is, a reversible nonlinear transformation learning network; after the coupling layer, the two output components are merged along the channel dimension as the result of the forward transformation; Wherein, l > 3; The reverse process is performed when inverse transformation is performed, and the expression of the reverse process of the i-th coupling layer is as follows: S3. The SAR echo data containing interference to be processed is converted into time-frequency domain pulse by short-time Fourier transform, and then the time-frequency domain data is cropped to the size that can be processed by the SAR interference suppression network constructed in step S2; Short-time Fourier transform (STFT) is used to realize time-frequency data analysis and processing. The local time-frequency characteristics X tf [m,q] of the signal x[n] are expressed as follows: Wherein, w[n] represents a time domain analysis window, x[n] represents a pulse of echo to be processed, n represents a discrete time variable, that is, the position of the analysis window on the time axis, and R represents a step size; After short-time Fourier transform, the time-frequency domain data is cropped to a unified network processable size; S4. Training the SAR interference suppression network based on learnable time-frequency feature separation; Supervised training is performed, and different scene SAR echo time-frequency spectrum and different types and parameters of interference time-frequency spectrum are used as the true value of the separation result to construct the training and verification data set; Interference pollution in time-frequency spectrum of data set Echo time-frequency spectrum Interference time-frequency spectrum Amplitude normalization processing is performed; the maximum and minimum value normalization method is selected, and since the frequency axis range is greater than the signal bandwidth, the minimum value of the amplitude in the time-frequency diagram is 0; to ensure that the normalized triplets satisfy The maximum value adopts The amplitude maximum value, and the normalization operation expression is as follows: The normalized time-frequency data is then cut into complex time-frequency maps of uniform size, saved as triplets as training input; The network outputs are separated SAR echo time-frequency spectrum and interference time-frequency spectrum, and a loss function is defined considering the reconstruction error of the interference and SAR echo time-frequency spectrum of the network output The expression is as follows: where L' and S' represent the interference and SAR echo time-frequency spectrum decomposition results of the network output respectively, and σ represents a parameter of the adjustment weight, ||·||F F represents the F-norm of a matrix; all the processed data are complex data, and the F-norm calculates the sum of the modulus squares of the differences between the complex values of each pixel of the network output data and the labels; S5. The SAR echo containing interference to be processed is time-frequency transformed and cropped according to step S3, and then the cropped time-frequency data is input into the SAR interference suppression network trained in step S4 for processing, to obtain the SAR echo time-frequency spectrum and interference time-frequency graph output by the network. S6, the SAR echo time-frequency spectrum output by the network obtained in step S5 is spliced into complete time-frequency data in a clipping manner to obtain an interference-suppressed SAR echo time-frequency spectrum, which is recovered into a time-domain echo through inverse short-time Fourier transform, i.e. an interference-suppressed time-domain echo; S7, the interference-suppressed time-domain echo obtained in step S6 is subjected to SAR imaging processing to obtain an interference-suppressed SAR image.

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