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

Abstract

The invention discloses an SAR (Synthetic Aperture Radar) interference suppression method based on learnable time-frequency feature separation, which comprises the following steps: firstly, establishing an SAR interference suppression problem model based on learnable time-frequency feature separation, introducing learnable reversible nonlinear transformation into a low-rank sparse decomposition model framework, and then constructing and training an SAR interference suppression network; the method comprises the following steps: carrying out time-frequency transformation on to-be-processed interference-containing SAR echoes, cutting the to-be-processed interference-containing SAR echoes, inputting the to-be-processed interference-containing SAR echoes into a trained network, outputting SAR echo time-frequency spectrums and an interference time-frequency graph, re-splicing the SAR echo time-frequency spectrums output by the network into complete time-frequency data according to a cutting mode to obtain interference-suppressed SAR echo time-frequency spectrums, recovering the interference-suppressed SAR echo time-frequency spectrums into time-domain echoes through inverse short-time Fourier transformation, and outputting the interference-suppressed SAR echoes. Finally, SAR imaging processing is carried out on the time domain echo after interference suppression, and an SAR image after interference suppression is obtained. The method provided by the invention solves the problem that the SAR image quality is damaged or imaging cannot be carried out in an interference environment, and provides reliable performance in the aspects of interference suppression and echo fidelity of a time-frequency domain and an image domain.

Description

Technical Field

[0001] The invention belongs to the technical field of SAR interference suppression, and in particular relates to a SAR interference suppression method based on learnable time-frequency feature separation. Background Art

[0002] As an important remote sensing technology, synthetic aperture radar (SAR) has the unique ability to penetrate clouds and fog and provide uninterrupted imaging day and night. It can accurately capture subtle surface features of land and ocean, and plays an important role in earth mapping, oil spill detection, iceberg detection, disaster monitoring, surveillance and reconnaissance, and many other aspects.

[0003] However, with the increase of electromagnetic equipment, broadband SAR systems will inevitably be affected by interference (RFI). Strong electromagnetic signals from other sources in the same frequency band will form large stripes or bright patches on the SAR image, causing serious troubles in image interpretation. In particular, the form of interference is becoming more and more complex. In the echoes recorded by SAR pulses, there may be various signal forms and time-varying signal components, which brings greater challenges to interference suppression. Therefore, in order to effectively suppress interference in SAR images, it is necessary to design signal processing technology with interference suppression.

[0004] In recent years, deep learning technology has demonstrated excellent performance in SAR high-precision imaging, target enhancement, interference detection and other tasks by virtue of its powerful data learning and representation capabilities. 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" proposed an end-to-end interference suppression network IMN based on ResNet, which uses data-driven learning to convert 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 Aperture Radar Using Dual-path Residual Network with Attention Mechanism. IGARSS2023-2023 IEEE International Geoscience and Remote Sensing Symposium. IEEE" proposes a dual-path residual network with 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 in data-driven, and proposes a network PIS-Net guided by time-frequency feature clustering and low-rank sparse loss function based on the low-rank sparse characteristics of SAR echoes and interference in the time-frequency domain.

[0005] The above interference suppression network design has defects such as data quality dependence, poor interpretability, image interference residue, and insufficient low-rank sparse representation ability under complex interference. The interference suppression effect is not good in complex interference environments. Compared with purely data-driven end-to-end networks, model-driven networks have stronger interpretability. In addition, the nonlinear representation ability of deep networks is strong, which can break through the representation limitations of existing low-rank sparse features and is conducive to improving the separation of interference and echo. Therefore, it is of great significance to design a model-data joint driven network that has both interpretability and representation capabilities. Summary of the invention

[0006] To solve the above technical problems, the present invention provides a SAR interference suppression method based on learnable time-frequency feature separation, which solves the problem that it is difficult to separate echo and interference components in a SAR time-frequency spectrum contaminated by interference.

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

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

[0009] According to the time-frequency distribution characteristics of SAR echoes and interference, the basic model of interference suppression based on low rank and sparse decomposition is set, and the expression is as follows:

[0010]

[0011] Among them, ||·|| * represents the nuclear norm, ||·||1 represents the l1 norm, λ represents the weighting factor, L represents the low-rank component, S represents the sparse component, and X represents 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 echo and interference are enhanced respectively, and the SAR interference suppression problem is modeled as a low-rank sparse decomposition model based on learnable transformation, which is expressed as follows:

[0013]

[0014] Reconstruct the solution of the augmented Lagrangian function, the expression is as follows:

[0015]

[0016] Among them, ρ represents the penalty factor, Λ represents the Lagrange multiplier, and <·> represents the inner product, that is, the sum of the products of the corresponding elements of the matrix.

[0017] Then, the ADMM algorithm is used to solve the equation (3) and decompose it into three sub-problems. In each step, only one variable is updated and the other variables are fixed, and the updates are repeated alternately. For the number of iterations k = 1, 2, 3, ..., the expressions of the three iterative sub-problems 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 expansion 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 solution containing 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] Among them, the network modules corresponding to L, S and Λ are updated as follows:

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

[0024]

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

[0026]

[0027] Among them, ω α represents the learnable coefficient factor, θ α To control α p As the number of layers p changes, setting θ α >1 to constrain α p Reduce layer by layer.

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

[0029]

[0030] in, represents the reversible nonlinear transformation for enhancing the time-frequency representation of SAR echoes, is its inverse transform. represents the soft threshold operator, and controls the parameter β of the soft threshold p The expression is as follows:

[0031]

[0032] Among them, ω β and θ β represents the learnable parameters, θ β To control β p As the number of layers p changes, setting θ β >1 to constrain β p It decreases as p increases.

[0033] 3) Update module ΛM of the Lagrange multiplier Λ in the pth 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] Among them, ω γ and θ γ represents a learnable parameter, and the index p is greater than 1. When θ γ >1, γ p It increases with the number of layers p.

[0038] S22, reversible nonlinear transformation learning network;

[0039] The reversible nonlinear transformation learning network divides the input into two parts, constructs the transformation through cross-coupling between the two parts, and processes complex time spectrum data. First, use the reconstruction operator Combining the real and imaginary parts of X, Reorganize into a tensor with two channels The expression is as follows:

[0040]

[0041] in, represents the complex domain, represents the real number domain, m represents the discrete time sampling point, q represents the discrete frequency sampling point, N m Indicates the number of time sampling points, N q Indicates the number of frequency sampling points.

[0042] Then along the channel dimension Divided into two parts The forward process is performed during the positive transformation, and the two components are learned through the function Cross coupling is achieved. The forward process expression of the i-th coupling layer is as follows:

[0043]

[0044] Here, ψ(·) represents a reversible downsampling operator, which is used to convert the spatial dimension into the channel dimension, maintaining the dimensions of the two parts of the sum equal. and Regardless of the model, 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 coupling layer are not symmetrical. A combination of l coupling layers is 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.

[0046] Among them, l>3.

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

[0048]

[0049] S3, converting the interference-containing SAR echo data to be processed into the time-frequency domain pulse by pulse using short-time Fourier transform, and then cutting the time-frequency domain data into a processable size for the SAR interference suppression network constructed in step S2;

[0050] Short-time Fourier transform (STFT) is used to analyze and process time-frequency data. The local time-frequency characteristics X of signal x[n] are tf The expression of [m,q] is as follows:

[0051]

[0052] Wherein, w[n] represents the time domain analysis window, x[n] represents the echo to be processed of a pulse, n represents the discrete time variable, that is, the position of the analysis window on the time axis, and R represents the step size.

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

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

[0055] Supervised training is performed, and the time-frequency spectra of SAR echoes in different scenarios and the time-frequency spectra of interferences of different types and parameters are used as the true values ​​of the separation results to construct training and validation data sets.

[0056] The interference pollution time spectrum in the data set Echo time spectrum Interference time spectrum Perform amplitude normalization. Select the maximum and minimum value normalization method, and because the frequency axis range is larger than the signal bandwidth, the minimum amplitude value in the time-frequency graph is 0; to ensure that the normalized triplet meets Maximum value adopted The maximum amplitude of , the normalized operation expression is as follows:

[0057]

[0058] The normalized time-frequency data is then cut into complex time-frequency graphs of uniform size and saved as triplets as training input.

[0059] The network output is the separated SAR echo time-frequency spectrum and interference time-frequency spectrum, and considering the reconstruction error of the network output interference and SAR echo time-frequency spectrum, the loss function is defined as The expression is as follows:

[0060]

[0061] Among them, L′ and S′ represent the interference and SAR echo time-frequency decomposition results of the network output, respectively, σ represents the parameter for adjusting the weight, and ||·|| F Represents the F norm of the matrix. The processed data are all complex data, and the F norm calculates the sum of the squares of the differences between the network output data and the complex values ​​of each pixel between the labels.

[0062] S5, performing time-frequency transformation and cutting the interference-containing SAR echo to be processed according to step S3, and then inputting the cut time-frequency data into the SAR interference suppression network trained in step S4 for processing, to obtain the SAR echo time-frequency spectrum and interference time-frequency diagram output by the network;

[0063] S6, re-joining the SAR echo time-frequency spectrum output by the network obtained in step S5 into complete time-frequency data in a cropping manner to obtain the SAR echo time-frequency spectrum after interference suppression, and restoring it into a time domain echo through inverse short-time Fourier transform, i.e., the time domain echo after interference suppression;

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

[0065] Beneficial effects of the present invention: The method of the present invention first establishes a SAR interference suppression problem model based on learnable time-frequency feature separation, introduces learnable reversible nonlinear transformation in the low-rank sparse decomposition model framework, then constructs a SAR interference suppression network and trains it, performs time-frequency transformation on the interference-containing SAR echo to be processed and cuts it into the trained network, outputs the SAR echo time-frequency spectrum and the interference time-frequency diagram, and then re-joins the SAR echo time-frequency spectrum output by the network into complete time-frequency data in a cut manner to obtain the SAR echo time-frequency spectrum after interference suppression, restores it to the time domain echo through inverse short-time Fourier transform, and finally performs SAR imaging processing on the time domain echo after interference suppression to obtain the SAR image after interference suppression. The method of the present invention solves the problem that the SAR image quality is impaired or cannot be imaged in an interference environment, combines data-driven with model-driven, introduces a learnable nonlinear transformation network on the basis of low-rank sparse decomposition theory to enhance the features of interference and SAR echo, realizes effective separation of interference and echo, and expands the iterative solution process into a parameter-learnable network to avoid manual parameter debugging, and provides reliable performance in terms of interference suppression and echo fidelity in the time-frequency domain and image domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 The present invention is a flow chart of a SAR interference suppression method based on learnable time-frequency feature separation.

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

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

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

[0070] Figure 5 Schematic diagram of training data triples used in an embodiment of the present invention.

[0071] Figure 6 4 is a comparison diagram of the interference suppression effects in the time and frequency domains of different methods in the embodiments of the present invention.

[0072] Figure 7 1 is a comparison diagram of image domain interference suppression effects of different methods in an embodiment of the present invention. DETAILED DESCRIPTION

[0073] To facilitate those skilled in the art to understand the technical content of the present invention, the method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0074] like Figure 1 As shown, a flow chart of a SAR interference suppression method based on learnable time-frequency feature separation of the present invention, the specific steps are as follows:

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

[0076] According to the time-frequency distribution characteristics of SAR echoes and interference, the basic model of interference suppression based on low rank and sparse decomposition is set, and the expression is as follows:

[0077]

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

[0079] After analysis, it is found that the low rank and sparsity of the time-frequency spectrum of the SAR echo and the ideal interference signal are coupled. It is difficult to accurately separate the echo and interference components using only the low rank and sparse decomposition model. Therefore, this embodiment introduces two learnable nonlinear transformations based on the low rank sparse decomposition model. and The feature representations of SAR echo and interference are enhanced respectively, and the SAR interference suppression problem is modeled as a low-rank sparse decomposition model based on learnable transformation, which is expressed as follows:

[0080]

[0081] Reconstruct the solution of the augmented Lagrangian function, the expression is as follows:

[0082]

[0083] Among them, ρ represents the penalty factor, Λ represents the Lagrange multiplier, and <·> represents the inner product, that is, the sum of the products of the corresponding elements of the matrix.

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

[0085]

[0086] Low-rank and sparse models have limited characterization capabilities for time-frequency domain interference and SAR echoes, and iterative methods have problems with difficult hyperparameter setting and high computational cost. This embodiment introduces data assistance into the model-driven solution to enhance the feature characterization of time-frequency domain interference and echoes, and learns a more robust and efficient parameter solution 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 expansion 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 containing 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] Among them, the network modules corresponding to L, S and Λ are updated as follows:

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

[0092]

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

[0094]

[0095] Among them, ω α represents the learnable coefficient factor, θ α To control α p As the number of layers p changes, set θ α >1 to constrain α p Reduce layer by layer.

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

[0097]

[0098] in, represents the reversible nonlinear transformation for enhancing the time-frequency representation of SAR echoes, is its inverse transform. represents the soft threshold operator, and controls the parameter β of the soft threshold p The expression is as follows:

[0099]

[0100] Among them, ω β and θ β represents the learnable parameters, θ β To control β p As the number of layers p changes, set θ β >1 to constrain β p It decreases as p increases.

[0101] 3) Update module ΛM of the Lagrange multiplier Λ in the pth 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] Among them, ω γ and θ γ represents a learnable parameter, and the index p is greater than 1. When θ γ >1, γ p It increases with the number of layers p.

[0106] S22, reversible nonlinear transformation learning network;

[0107] The reversible nonlinear transformation network constructs a nonlinear transformation through data fitting to enhance the characteristic representation of interference and SAR echo. and It has good reversibility to achieve lossless conversion of information between the feature domain and the time-frequency domain. 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 figure are transformed by cross-coupling between the two parts. The superscripts 1, 2, ..., I represent the number of coupling layers. The network processes complex time spectrum data.

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

[0109]

[0110] in, represents the complex domain, represents the real number domain, m represents the discrete time sampling point, q represents the discrete frequency sampling point, N m Indicates the number of time sampling points, N q Indicates the number of frequency sampling points.

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

[0112]

[0113] Among them, ψ(·) represents the reversible downsampling operator, which is used to convert the spatial dimension into the channel dimension and maintain the dimensions of the two parts of the sum equal. The operation diagram is as follows Figure 3 shown.

[0114] Thanks to the special structure, the reversibility of the coupling layer is and Not relevant. and It can be implemented by any deep neural network module. This embodiment adopts 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 coupling layer are not symmetric, in order to make all dimensions affect each other, this embodiment constructs a combination of four coupling layers as a reversible transformation network module, that is, a reversible nonlinear transformation learning network. After the four coupling layers, the two output components are merged along the channel dimension as the result of the forward transformation.

[0116] When inverse transform is performed Figure 2 (b) shows the reverse process, where the reverse process expression of the i-th coupling layer is as follows:

[0117]

[0118] The reverse process does not require calculation and Therefore, we can flexibly construct and The structural enhancement feature representation does not affect the transformation and Without performing any additional operations, the forward transform plus the inverse transform can achieve perfect reversibility, that is,

[0119] S3, converting the interference-containing SAR echo data to be processed into the time-frequency domain pulse by pulse using short-time Fourier transform, and then cutting the time-frequency domain data into a processable size for the SAR interference suppression network constructed in step S2;

[0120] During processing, the SAR echo data containing interference to be processed is first converted pulse by pulse into the time-frequency domain using short-time Fourier transform. As a two-dimensional feature domain, the time-frequency domain can provide instantaneous time and frequency information of the signal, which is suitable for revealing the comprehensive information of non-stationary signals. This embodiment uses short-time Fourier transform (STFT) to implement time-frequency data analysis and processing. The local time-frequency feature X of the signal x[n] is tf The expression of [m,q] is as follows:

[0121]

[0122] Wherein, w[n] represents the time domain analysis window, x[n] represents the echo to be processed of a pulse, n represents the discrete time variable, that is, 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, training a SAR interference suppression network based on learnable time-frequency feature separation;

[0125] Supervised training is performed, and the time-frequency spectra of SAR echoes in different scenarios and the time-frequency spectra of interferences of different types and parameters of the simulation data of this embodiment are used as the true values ​​of the separation results to construct training and verification data sets. In order to make the echo data of different scenarios and signal-to-interference ratios comparable, it is necessary to compare the time-frequency spectra of interference pollution in the data set. Echo time spectrum Interference time spectrum Perform amplitude normalization. Select the maximum and minimum normalization method. Since the frequency axis range is larger than the signal bandwidth, the minimum amplitude value in the time-frequency graph is 0. In order to ensure that the normalized triplet meets Maximum value adopted The maximum amplitude of , the normalized operation expression is as follows:

[0126]

[0127] Then the normalized time-frequency data is cut into complex time-frequency graphs of uniform size (256*256) and saved as triplets as training input. Figure 5 The training data triples used in this example are

[0128] The network output is the separated SAR echo time-frequency spectrum and interference time-frequency spectrum, and considering the reconstruction error of the network output interference and SAR echo time-frequency spectrum, the loss function is defined as The expression is as follows:

[0129]

[0130] Among them, L′ and S′ represent the interference and SAR echo time-frequency decomposition results of the network output, respectively, σ represents the parameter for adjusting the weight, and ||·|| F Represents the F norm of the matrix. The processed data are all complex data, and the F norm calculates the sum of the squares of the moduli of the differences between the network output data and the complex values ​​of each pixel between the labels. In the iterative process, due to the existence of the L+S=X constraint, the reconstruction error losses of the interference and echo components can restrict and promote each other.

[0131] S5, performing time-frequency transformation and cutting the interference-containing SAR echo to be processed according to step S3, and then inputting the cut time-frequency data into the SAR interference suppression network trained in step S4 for processing, to obtain the SAR echo time-frequency spectrum and interference time-frequency diagram output by the network;

[0132] S6, re-joining the SAR echo time-frequency spectrum output by the network obtained in step S5 into complete time-frequency data in a cropping manner to obtain the SAR echo time-frequency spectrum after interference suppression, and restoring it into a time domain echo through inverse short-time Fourier transform, i.e., the time domain echo after interference suppression;

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

[0134] In order to verify the performance of the method of the present invention, this embodiment experiments on the suppression effect of narrowband and broadband interference with different parameters and combinations, and uses three indicators, NMSE, SSIM and PSNR, to calculate the difference between the interference-suppressed image and the interference-free true image, so as to evaluate the interference suppression performance of the method.

[0135] Figure 6 The time-frequency domain interference suppression performance comparison of the method of the present invention and other methods is shown, including frequency domain filtering, time-frequency domain filtering, RPCA and two aforementioned network-based 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] Through experimental comparison, the method of the present invention has better interference suppression effect and echo fidelity in the time-frequency domain, and has better adaptability to multi-type combined interference situations that are not in the training data. In addition, the method of the present invention can directly obtain the suppressed complex time-frequency spectrum and can simultaneously restore the desired echo amplitude and phase.

[0139] In order to verify the interference suppression and image fidelity performance of the proposed method in SAR images, time-varying narrowband and broadband combined interferences were set, and the image domain interference suppression performances of several methods were compared. Figure 7 As shown. Among them, Figure 7 (a) is the simulated interfered SAR image. Figure 7 (b)-(f) are the imaging results after interference suppression of the five comparison methods: frequency domain filtering, time-frequency domain filtering, RPCA, IMN and PIS-Net. Figure 7 (g) is the imaging result after interference suppression in this embodiment, Figure 7 (h) is a simulated SAR image without interference. Table 2 gives the Figure 7 Comparison of SAR image domain interference suppression performance in three groups of experiments with different imaging scenarios and interference settings.

[0140] Table 2

[0141]

[0142] Due to the different bandwidths and time widths of interference contained in different pulses, the comparison method will lose useful echoes to varying degrees after removing the interference. This results in inconsistent echo energy remaining in different pulses during imaging, causing regional light and dark changes in the image. On the whole, when facing complex time-varying interference, the method of the present invention provides the most stable performance, and can effectively remove interference of different time widths, bandwidths and intensities. While removing interference, the energy of the real scene echo is retained as much as possible, and the image will not have obvious amplitude distortion due to fluctuations in the interference distribution range. The above experiments prove (Table 2) that compared with the comparison method and other network-based methods, the SSIM and PSNR of the method of the present invention are improved by more than 0.014 and 6.22dB, respectively, and have advantages in interference suppression and image fidelity, and have good suppression performance in complex interference environments such as time-varying and multi-signal combination, providing a feasible solution for SAR suppression in complex environments.

[0143] In summary, the method of the present invention enhances the time-frequency representation of SAR echoes and interference by constructing a learnable transformation, thereby improving the separability of the two; by expanding the existing iterative solution process into a network computing architecture, and setting the hyperparameters that require manual debugging in the existing method 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 capability of the deep network.

[0144] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A SAR interference suppression method based on learnable time-frequency feature separation, the specific steps are as follows: S1. Establish a SAR interference suppression problem model based on learnable time-frequency feature separation, introduce learnable reversible nonlinear transformation into the low-rank sparse decomposition model framework, and enhance the feature characterization capability of interference and echo; According to the time-frequency distribution characteristics of SAR echoes and interference, the basic model of interference suppression based on low rank and sparse decomposition is set, and the expression is as follows: in, ||·|| * represents the nuclear norm, ||·||1 represents the l1 norm, λ represents the weighting factor, L represents the low-rank component, S represents the sparse component, and X represents the data to be processed; Then, based on the low-rank sparse decomposition model, two learnable nonlinear transformations are introduced and The feature representations of SAR echo and interference are enhanced respectively, and the SAR interference suppression problem is modeled as a low-rank sparse decomposition model based on learnable transformation, which is expressed as follows: Reconstruct the solution of the augmented Lagrangian function, the expression is as follows: Among them, ρ represents the penalty factor, Λ represents the Lagrange multiplier, and <·> represents the inner product, that is, the sum of the products of the corresponding elements of the matrix; Then the ADMM algorithm is used to solve the equation (3) and decompose it into three sub-problems. In each step, only one variable is updated and the other variables are fixed, and the updates are repeated alternately. For the number of iterations k = 1, 2, 3, ..., the expressions of the three iterative sub-problems are as follows: S2. Based on step S1, construct a SAR interference suppression network based on learnable time-frequency feature separation, including: a deep expansion network of the overall iterative algorithm and a reversible nonlinear transformation learning network; S21, deep expansion network of the overall iterative algorithm; The iterative process of solving equation (4) is expanded into a deep learning solution 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. Among them, the network modules corresponding to L, S and Λ are updated as follows: 1) Update module LM of the low-rank component L in the pth layer p The expression is as follows: in, represents a reversible nonlinear transformation that enhances the interference representation, is its inverse transform, p = 1, 2, ..., P represents the number of layers of the expanded network, corresponding to the number of iterations k in equation (4); The proximal operator representing the nuclear norm is defined as W=UΣV H That is, the singular value decomposition of the matrix W, U represents the left singular vector, V represents the right singular vector, H represents the conjugate transpose of the matrix, Σ=diag(σ1,σ2,...,σ r ) represents a diagonal matrix composed of singular values, r represents the rank of the matrix W; Used to filter out singular values ​​exceeding the threshold; α p Represents the parameter controlling the singular value threshold, which is designed as a learnable network parameter, and as the number of iterations increases, α p As α decreases layer by layer, p The specific expression is as follows: Among them, ω α represents the learnable coefficient factor, θ α To control α p As the number of layers p changes, set θ α >1 to constrain α p Reduce layer by layer; 2) Update module SM for the sparse component S in the pth layer p The expression is as follows: in, represents the reversible nonlinear transformation for enhancing the time-frequency representation of SAR echoes, is its inverse transform; represents the soft threshold operator, and controls the parameter β of the soft threshold p The expression is as follows: Among them, ω β and θ β represents the learnable parameters, θ β To control β p As the number of layers p changes, set θ β >1 to constrain β p Decreases as p increases; 3) Update module ΛM of the Lagrange multiplier Λ in the pth layer p The expression is as follows: L (p) =L (p-1) +g p (L (p) +S (p) -X) (9) Among them, the learnable penalty factor γ p The expression is as follows: Among them, ω γ and θ γ represents a learnable parameter, and the index p is greater than 1. When θ γ >1, γ p It increases with the number of layers p; S22, reversible nonlinear transformation learning network; The reversible nonlinear transformation learning network divides the input into two parts, constructs the transformation through cross-coupling between the two parts, and processes complex time spectrum data; first, the reconstruction operator is used Combining the real and imaginary parts of X, Reorganize into a tensor with two channels The expression is as follows: in, represents the complex domain, represents the real number domain, m represents the discrete time sampling point, q represents the discrete frequency sampling point, N m Indicates the number of time sampling points, N q Indicates the number of frequency sampling points; Then along the channel dimension Divided into two parts The forward process is performed during the positive transformation, and the two components are learned through the function Realize cross coupling; the forward process expression of the i-th coupling layer is as follows: Where ψ(·) represents a reversible downsampling operator, which is used to convert the spatial dimension into the channel dimension and maintain the two dimensions of the summation equal; the reversibility of the coupling layer is and It is irrelevant and uses the convolutional neural network (CNN) module to extract effective deep features through linear and nonlinear operations in the network; The operations on X1 and X2 in a coupling layer are not symmetric. A combination of l coupling layers is constructed as a reversible transformation network module, i.e., 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. Among them, l>3; The reverse process is performed during the inverse transformation, where the reverse process expression of the i-th coupling layer is as follows: S3, converting the interference-containing SAR echo data to be processed into the time-frequency domain pulse by pulse using short-time Fourier transform, and then cutting the time-frequency domain data into a processable size for the SAR interference suppression network constructed in step S2; Short-time Fourier transform (STFT) is used to analyze and process time-frequency data. The local time-frequency characteristics X of signal x[n] are tf The expression of [m,q] is as follows: Wherein, w[n] represents the time domain analysis window, x[n] represents the echo to be processed of a pulse, n represents the discrete time variable, that is, the position of the analysis window on the time axis, and R represents the step size; After short-time Fourier transform, the time-frequency domain data is cut into a uniform network-processable size; S4, training a SAR interference suppression network based on learnable time-frequency feature separation; Conduct supervised training, and use the time-frequency spectra of SAR echoes in different scenarios and the time-frequency spectra of interferences of different types and parameters as the true values ​​of the separation results to construct training and validation data sets; The interference pollution time spectrum in the data set Echo time spectrum Interference time spectrum Perform amplitude normalization processing; select the maximum and minimum value normalization method, and because the frequency axis range is larger than the signal bandwidth, the minimum amplitude value in the time-frequency diagram is 0; to ensure that the normalized triplet meets Maximum value adopted The maximum amplitude of , the normalized operation expression is as follows: The normalized time-frequency data is then cut into complex time-frequency graphs of uniform size and saved as triplets As training input; The network output is the separated SAR echo time-frequency spectrum and interference time-frequency spectrum, and considering the reconstruction error of the network output interference and SAR echo time-frequency spectrum, the loss function is defined as The expression is as follows: Among them, L′ and S′ represent the interference and SAR echo time-frequency decomposition results of the network output, respectively, σ represents the parameter for adjusting the weight, and ||·|| F Represents the F norm of the matrix; the processed data are all complex data, and the F norm calculates the sum of the squares of the differences between the network output data and the complex values ​​of each pixel of the label; S5, performing time-frequency transformation and cutting the interference-containing SAR echo to be processed according to step S3, and then inputting the cut time-frequency data into the SAR interference suppression network trained in step S4 for processing, to obtain the SAR echo time-frequency spectrum and interference time-frequency diagram output by the network; S6, re-joining the SAR echo time-frequency spectrum output by the network obtained in step S5 into complete time-frequency data in a cropping manner to obtain the SAR echo time-frequency spectrum after interference suppression, and restoring it into a time domain echo through inverse short-time Fourier transform, i.e., the time domain echo after interference suppression; S7, performing SAR imaging processing on the time domain echo after interference suppression in step S6 to obtain a SAR image after interference suppression.

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