A single-bit synthetic aperture radar imaging method, system, terminal and medium

Abstract

The application provides a single-bit synthetic aperture radar imaging method, system, terminal and medium, and relates to the technical field of synthetic aperture radar imaging.The method comprises the following steps: constructing an initial single-bit echo signal model, reconstructing a target single-bit echo signal model based on a hyperbolic tangent function, constructing an optimization problem with continuous gradient and rank constraint based on the reconstructed model, and solving the optimization problem by using a gradient descent and low rank projection alternating iteration algorithm to determine a target echo signal vector and image.The application converts a non-differentiable imaging model into an optimization problem with continuous gradient by constructing a target single-bit echo signal model based on a hyperbolic tangent function, combines rank constraint, suppresses noise, enhances robustness, and improves imaging effect in a non-sparse scene by using the low rank feature of a synthetic aperture radar image, solves the optimization problem by using an alternating iteration algorithm, and obtains an imaging with more complete detail reservation while maintaining high calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of synthetic aperture radar imaging, and particularly relates to a single-bit synthetic aperture radar imaging method, system, terminal and medium. BACKGROUND

[0002] Although the traditional single-bit sampling technology can overcome the problems of generating massive data, increasing data acquisition, improving the hardware complexity of the analog-to-digital converter, increasing the computational burden of data storage, transmission and subsequent processing, complex hardware implementation and high running cost in the traditional single-bit synthetic aperture radar imaging, the extreme quantization of the single-bit sampling technology will inevitably lead to a serious loss of amplitude information of the original echo signal and introduce a large number of nonlinear high harmonics. These high harmonics will pollute the spectrum, and if they cannot be effectively suppressed or separated, they will seriously reduce the quality of the synthetic aperture radar image, which is manifested as an increase in sidelobe, false targets and overall image noise level. Moreover, due to the nonlinear characteristics of the traditional single-bit sampling technology (such as zero threshold quantization), it is extremely difficult to directly recover the original signal amplitude from 1-bit data, which limits its performance in applications that require accurate amplitude information. For the problems existing in the traditional single-bit sampling technology, although there are various technical solutions to try to balance the system simplification advantage brought by the traditional single-bit sampling technology and the imaging quality requirement, the existing methods are still difficult to significantly improve the overall performance of the system while maintaining the simplicity of the system structure and the extremely low amount of data.

[0003] For example, in order to solve the problems existing in the traditional single-bit sampling technology, the signal recovery method based on compressive sensing has attracted widespread attention at present, such as the binary iterative hard threshold algorithm, which regards the recovery of the signal from 1-bit data as an optimization problem. Although this kind of method can reconstruct the signal from 1-bit measurement value by utilizing the sparsity of the signal, and has a certain positive effect on synthetic aperture radar imaging, it generally has the limitations of high computational complexity, requirement of signal sparsity priori, and possible loss of part of the amplitude information under the signal norm constraint.

[0004] The core shortcomings of the synthetic aperture radar imaging algorithm based on the binary iterative hard threshold value are caused by the direct use of the non-differentiable sign function and the strong assumption of signal sparsity. Firstly, the non-linear characteristics of the sign function amplify noise interference, and the sparse constraint cannot accurately distinguish effective signals from noise components in a strong noise background, so the performance of the algorithm is seriously degraded in a low signal-to-noise ratio environment. Secondly, in terms of applicability, the effectiveness of the synthetic aperture radar imaging algorithm based on the binary iterative hard threshold value is highly dependent on the prior condition that the target scene has a sparse representation in a specific transform domain (such as the wavelet or curvelet domain). If the actual scene does not meet this sparse assumption (such as the presence of a large amount of texture or complex structure), the imaging performance will be significantly reduced. Finally, in terms of imaging quality, the strong constraint imposed by the synthetic aperture radar imaging algorithm based on the binary iterative hard threshold value to pursue sparse solutions will excessively suppress weak scattering signals, resulting in a loss of detailed information in the reconstructed image, a limited dynamic range, and the possible introduction of artifacts.

[0005] Therefore, how to provide a single-bit synthetic aperture radar imaging technical solution that overcomes the above-mentioned shortcomings of the synthetic aperture radar imaging algorithm based on the binary iterative hard threshold value and has high robustness and high-quality imaging effect while maintaining low complexity is a problem that needs to be solved by those skilled in the art at present. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a single-bit synthetic aperture radar imaging method, system, terminal and medium that can maintain high computational efficiency while obtaining a reconstructed image with more complete detail preservation, in view of the above-mentioned defects of the prior art.

[0007] The technical solution adopted by the present application to solve the technical problem is as follows:

[0008] In a first aspect, the present application discloses a single-bit synthetic aperture radar imaging method, wherein the method comprises:

[0009] constructing an initial single-bit echo signal model for single-bit synthetic aperture radar imaging, and reconstructing a target single-bit echo signal model based on the hyperbolic tangent function according to the initial single-bit echo signal model;

[0010] constructing an optimization problem with continuous gradient and rank constraints based on the target single-bit echo signal model;

[0011] solving the optimization problem to determine the target echo signal vector using a pre-constructed alternating iterative algorithm of gradient descent and low-rank projection, and performing imaging according to the target echo signal vector.

[0012] Optionally, the construction of the initial single-bit echo signal model for single-bit synthetic aperture radar imaging comprises:

[0013] A single-bit quantization model for describing single-bit quantization of a sampled echo signal in synthetic aperture radar imaging is constructed; the single-bit quantization represents symbol decisions on real and imaginary parts of the echo signal, respectively;

[0014] An initial single-bit echo signal model of single-bit synthetic aperture radar imaging is constructed based on the single-bit quantization model;

[0015] The single-bit quantization model is:

[0016] ;

[0017] wherein, is a measurement vector, is an observation matrix, is an echo signal vector, is a noise vector, is a sign function, M is a dimension of the measurement vector, and N is a dimension of the echo signal vector;

[0018] The initial single-bit echo signal model is:

[0019] ;

[0020] wherein, is a quantized noise vector.

[0021] And the target single-bit echo signal model based on a hyperbolic tangent function is reconstructed from the initial single-bit echo signal model, comprising:

[0022] The sign function in the initial single-bit echo signal model is smoothed and approximated by a hyperbolic tangent function to reconstruct the target single-bit echo signal model based on the hyperbolic tangent function;

[0023] The target single-bit echo signal model is:

[0024] ;

[0025] wherein, is a single-bit quantized measurement vector, is a hyperbolic tangent function.

[0026] Optionally, the optimization problem is:

[0027] ;

[0028] ;

[0029] ;

[0030] wherein, is an objective function, is a scale factor, is a preset rank upper bound parameter, is an operation of converting an echo signal vector into a matrix, is a rank constraint on an echo signal vector.

[0031] Optionally, the solving the optimization problem by using an alternating iterative algorithm of a pre-constructed gradient descent and low-rank projection to determine the target echo signal vector comprises:

[0032] determining a gradient of the objective function with respect to the echo signal vector in the optimization problem;

[0033] performing a preliminary update on the echo signal vector of a current iteration by using a gradient descent method and based on the gradient to obtain an updated echo signal vector; wherein, in an initial iteration, a preset initial echo signal vector is determined as the echo signal vector of the current iteration;

[0034] reconstructing the updated echo signal vector into an updated image matrix;

[0035] performing a preset projection operation on the updated image matrix to obtain a corresponding low-rank matrix; the preset projection operation is a hard threshold low-rank projection operation based on singular value decomposition;

[0036] performing vectorization processing on the low-rank matrix to obtain an echo signal vector of a new round of iteration;

[0037] judging whether the echo signal vector of the new round of iteration meets a preset convergence condition;

[0038] in a case where the echo signal vector of the new round of iteration meets the preset convergence condition, determining the echo signal vector of the new round of iteration as the target echo signal vector.

[0039] Optionally, the performing the preset projection operation on the updated image matrix to obtain the corresponding low-rank matrix comprises:

[0040] performing singular value decomposition on the image matrix to obtain a decomposition result in the form of a product of three matrices; the three matrices include a singular value matrix and two unitary matrices;

[0041] performing a hard threshold operation on the singular value matrix in the decomposition result to construct a truncated singular value matrix;

[0042] calculating a corresponding low-rank matrix based on the unitary matrices in the decomposition result and the truncated singular value matrix.

[0043] Optionally, after judging whether the echo signal vector of the new round of iteration satisfies the preset convergence condition, the method further comprises:

[0044] If the echo signal vector of the new round of iteration does not satisfy the preset convergence condition, the echo signal vector of the new round of iteration is determined as the current echo signal vector, and the step of updating the echo signal vector of the current iteration based on the gradient by using the gradient descent method and the subsequent steps are re-executed until the echo signal vector of the new round of iteration satisfies the preset convergence condition.

[0045] Optionally, the imaging according to the target echo signal vector comprises:

[0046] The target echo signal vector is reconstructed into a target image matrix, and the target image matrix is normalized to obtain a normalized synthetic aperture radar image.

[0047] In a second aspect, the present application further discloses a single-bit synthetic aperture radar imaging system, wherein the system comprises:

[0048] a model construction module, configured to construct an initial single-bit echo signal model of single-bit synthetic aperture radar imaging, and reconstruct a target single-bit echo signal model based on a hyperbolic tangent function according to the initial single-bit echo signal model;

[0049] an optimization problem construction module, configured to construct an optimization problem with continuous gradient and rank constraints based on the target single-bit echo signal model;

[0050] an optimization problem solving module, configured to solve the optimization problem by using a pre-constructed alternating iteration algorithm of gradient descent and low-rank projection to determine a target echo signal vector, and perform imaging according to the target echo signal vector.

[0051] In a third aspect, the present application discloses a terminal, comprising a memory, a processor, and a single-bit synthetic aperture radar imaging program stored in the memory and executable on the processor, wherein the single-bit synthetic aperture radar imaging program is executed by the processor to implement the steps of the single-bit synthetic aperture radar imaging method.

[0052] In a fourth aspect, the present application discloses a computer readable storage medium, wherein the computer readable storage medium stores a computer program which can be executed to implement the steps of the single-bit synthetic aperture radar imaging method.

[0053] This invention provides a single-bit synthetic aperture radar (SAP) imaging method, system, terminal, and medium. The SAP imaging method includes: constructing an initial single-bit echo signal model for SAP imaging; reconstructing a target single-bit echo signal model based on the hyperbolic tangent function based on the initial single-bit echo signal model; constructing an optimization problem with continuous gradient and rank constraints based on the target single-bit echo signal model; solving the optimization problem using a pre-built alternating iterative algorithm of gradient descent and low-rank projection to determine the target echo signal vector; and performing imaging based on the target echo signal vector. Therefore, this invention, by constructing a target single-bit echo signal model based on the hyperbolic tangent function, can transform the original non-differentiable imaging model into an optimization problem with continuous gradients. Combined with rank constraints, it fully utilizes the inherent low-rank characteristics of the synthetic aperture radar image itself, which can suppress noise, enhance robustness, and improve the reconstruction effect in non-sparse scenes. Finally, the optimization problem is solved by a pre-constructed gradient descent and low-rank projection alternating iterative algorithm, achieving an efficient and stable solution to the optimization problem. Thus, while maintaining high computational efficiency, it can obtain a reconstructed image with more complete detail preservation. Attached Figure Description

[0054] Figure 1 This is a flowchart of a preferred embodiment of the single-bit synthetic aperture radar imaging method in this invention;

[0055] Figure 2 This is a schematic diagram comparing a specific sign function and a hyperbolic tangent function disclosed in this invention;

[0056] Figure 3 This is a flowchart illustrating the single-bit synthetic aperture radar imaging method of the present invention.

[0057] Figure 4 This is a logical block diagram of a preferred embodiment of the single-bit synthetic aperture radar imaging method in this invention;

[0058] Figure 5 This is a schematic diagram illustrating a specific single-bit SAR imaging effect comparison disclosed in this invention;

[0059] Figure 6 This is a schematic diagram comparing the three-dimensional effects of a specific single-bit SAR imaging disclosed in this invention;

[0060] Figure 7 This is a functional principle block diagram of a preferred embodiment of the terminal in this invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0062] It should be noted that SAR (Synthetic Aperture Radar), as an advanced remote sensing technology, plays a crucial role in fields such as Earth observation, disaster monitoring, and resource exploration due to its unique all-weather, all-time capability and ability to penetrate clouds and fog. It works by having a carrier platform (such as an aircraft or satellite) move along a specific trajectory, transmit LFM (Linear Frequency Modulation) signals, and receive target echoes. Then, using complex signal processing algorithms, it synthesizes an equivalent large-aperture antenna, thereby acquiring high-resolution two-dimensional images of the Earth's surface, expanding the range and depth of human perception of the Earth. In the field of SAR imaging, the application of single-bit sampling technology—that is, directly quantizing the continuously changing analog SAR echo signal into a 1-bit digital signal containing only "+1" or "-1" by comparing it with a preset threshold—greatly simplifies the design and implementation of ADCs (Analog-to-Digital Converters), replacing multi-bit ADCs with simple comparators, thereby significantly reducing hardware costs and system complexity. The drastic reduction in data volume (from tens of bits to 1 bit) drastically reduces data transmission bandwidth and storage space requirements, significantly improving real-time processing capabilities and efficiency, which is particularly important for platforms such as UAV-borne SAR or small satellite SAR. Even using only 1 bit of data, acceptable focused SAR images can be obtained through appropriate signal processing, and even advanced applications such as interferometry can be supported. However, the extremely simplified quantization of single-bit sampling technology inevitably leads to a severe loss of amplitude information in the original echo signal and introduces a large number of nonlinear high-order harmonics. These high-order harmonics pollute the spectrum, and if they are not effectively suppressed or separated, they will severely degrade the quality of synthetic aperture radar images, manifesting as increased sidelobes, false targets, and an increased overall image noise level. Moreover, traditional single-bit sampling techniques (such as zero-threshold quantization) are extremely difficult to recover the original signal amplitude directly from 1 bit of data due to their nonlinear characteristics, which limits their performance in applications that require accurate amplitude information.

[0063] Despite various attempts to balance the advantages of system simplification and imaging quality requirements brought about by traditional single-bit sampling technology, these solutions still struggle to achieve a significant improvement in overall system performance while maintaining a simple system structure and extremely low data volume.

[0064] For example, in order to solve the problems of traditional single-bit sampling techniques, signal recovery methods based on compressed sensing have received widespread attention, such as binary iterative hard thresholding algorithms. These methods treat signal recovery from 1-bit data as an optimization problem. Although these methods can reconstruct from 1-bit measurements by utilizing the sparsity of the signal and have a certain positive effect on synthetic aperture radar imaging, they generally have limitations such as high computational complexity, requiring the signal to have sparsity priors, and the potential loss of some amplitude information under signal norm constraints.

[0065] Among them, the core drawback of the synthetic aperture radar (SAR) imaging algorithm based on binary iterative hard thresholding stems from the direct use of non-differentiable sign functions and the strong assumption of signal sparsity. First, the nonlinear characteristics of the sign function amplify noise interference, and the sparsity constraint makes it difficult to accurately distinguish between effective signal and noise components in a noisy environment, causing the algorithm's performance to degrade significantly in low signal-to-noise ratio (SNR) environments. Second, in terms of applicability, the effectiveness of the SAR imaging algorithm based on binary iterative hard thresholding heavily relies on the prior condition that the target scene has a sparse representation in a specific transform domain (such as wavelet or curve domain). Once the actual scene does not meet this sparsity assumption (such as the presence of a large amount of texture or complex structure), its imaging performance will significantly decrease. Finally, in terms of image quality, the strong constraints imposed by the SAR imaging algorithm based on binary iterative hard thresholding in pursuit of sparse solutions will excessively suppress weak scattering signals, resulting in the loss of detail information in the reconstructed image, limited dynamic range, and potential introduction of artifacts.

[0066] To this end, this application provides a single-bit synthetic aperture radar imaging scheme that can obtain reconstructed images with more complete detail preservation while maintaining high computational efficiency.

[0067] Please see Figure 1 , Figure 1 This is a flowchart of the single-bit synthetic aperture radar imaging method in this invention. For example... Figure 1 As shown, the single-bit synthetic aperture radar imaging method described in this embodiment of the invention includes:

[0068] Step S11: Construct an initial single-bit echo signal model for single-bit synthetic aperture radar imaging, and reconstruct a target single-bit echo signal model based on the hyperbolic tangent function according to the initial single-bit echo signal model.

[0069] Understandably, in order to transform the non-smooth and difficult-to-converge traditional single-bit imaging optimization problem into a smooth and differentiable optimization problem, a target single-bit echo signal model based on the hyperbolic tangent function can be reconstructed.

[0070] It should be noted that in traditional compressed sensing theory, by undersampling the signal and simplifying the sampling process, high-dimensional sparse signals can be recovered from low-dimensional data. The traditional compressed sensing observation model is expressed as: However, traditional compressed sensing frameworks suffer from several problems in practical applications: high-resolution ADCs significantly increase system complexity and hardware costs. While reducing the number of quantization bits can drastically reduce hardware overhead and data processing burden, it also leads to a corresponding decrease in signal reconstruction quality. This issue is particularly pronounced in resource-constrained applications. Therefore, this embodiment employs single-bit compressed sensing technology to overcome this problem. Single-bit compressed sensing technology quantizes the measured values ​​of the echo signal into single-bit data containing only symbol information, thus greatly simplifying the quantization process while preserving key signal features.

[0071] Specifically, a single-bit quantization model is constructed to describe the single-bit quantization of the sampled echo signal in synthetic aperture radar (SAR) imaging. Single-bit quantization involves determining the sign of the real and imaginary parts of the echo signal separately. Based on the single-bit quantization model, an initial single-bit echo signal model for single-bit SAR imaging is constructed. It is understandable that the essence of SAR imaging lies in obtaining the complex scattering coefficients of the target (such as an aircraft or other target to be detected and imaged), and its echo signal also exists in complex form, carrying both amplitude and phase information of the ground object. To achieve single-bit quantization, the real part (in-phase component) and the imaginary part (quadrature component) of the echo signal need to be independently determined for sign.

[0072] The single-bit quantization model is as follows:

[0073] ;

[0074] in, Let M be the measurement vector. The observation matrix consists of M rows and N columns. Let N be the echo signal vector. Let M be the noise vector. Let M be the sign function, M be the dimension of the measurement vector, and N be the dimension of the echo signal vector. Let M be a complex space consisting of complex vectors of length M. Let M be a complex space consisting of M rows and N columns of complex matrices. Let N be a complex space consisting of complex vectors of length N.

[0075] The initial single-bit echo signal model is:

[0076] ;

[0077] in, It is an M-dimensional quantized noise vector, and it is a high-precision quantized noise vector, such as an 8-bit or 10-bit quantized noise vector.

[0078] It should also be noted that under high-precision quantization conditions, the quantization operation can be approximated as a linear process. Therefore, the noise distribution characteristics can be completely preserved in the quantized signal. This allows for the selection of an appropriate norm to construct a fitting function based on the specific noise distribution characteristics. Thus, for single-bit detection and sensing tasks, the key to fully utilizing noise information to construct or select a reasonable fitting function lies in preserving the noise distribution information in the single-bit quantized signal. However, single-bit quantization, as a nonlinear operation, significantly alters the original distribution characteristics of additive noise. Therefore, in this embodiment, the additive noise in the received echo signal is remodeled and subjected to high-precision quantization processing separately. , It is a nonlinear transformation.

[0079] In this embodiment, a target single-bit echo signal model based on the hyperbolic tangent function is reconstructed from the initial single-bit echo signal model. Specifically, this may include: smoothly approximating the sign function in the initial single-bit echo signal model using the hyperbolic tangent function to reconstruct the target single-bit echo signal model based on the hyperbolic tangent function. It can be understood that the initial single-bit echo signal model... Since the objective function is discontinuous and does not satisfy the lower semi-continuous property, solving the single-bit SAR imaging optimization problem based on the echo signal model presents difficulties in analyzing the convergence of the optimization algorithm. Furthermore, current non-convex optimization algorithms typically require the objective function to be a lower semi-continuous function to ensure its monotonically non-increasing property during optimization. Therefore, this embodiment utilizes a continuous and smooth... Function approximation The function is then used to obtain the target single-bit echo signal model based on the hyperbolic tangent function, namely:

[0080] ;

[0081] in, This is the measurement vector after single-bit quantization. It is the hyperbolic tangent function.

[0082] For example, see Figure 2 As shown, The function is a smooth and continuous function, and its performance increases with the scaling factor c. Function approximation function. The continuity and smoothness of the function lay the foundation for the convergence of the optimization algorithm proposed in this embodiment.

[0083] Step S12: Construct an optimization problem with continuous gradient and rank constraints based on the target single-bit echo signal model.

[0084] Here, the rank constraint is a low-rank constraint, where low rank means that the rank of the matrix is ​​much smaller than the size of the matrix. The low-rank constraint represents a technique that utilizes the prior knowledge that there is a lot of redundancy and structural similarity within the data to recover the essential and concise data structure from noisy or incomplete data through mathematical methods such as matrix completion and robust principal component analysis.

[0085] In this embodiment, the sign function is smoothly approximated by a continuous and smooth hyperbolic tangent function, and a differentiable optimization problem is constructed by combining rank constraints, such as low-rank constraints, i.e., a smooth and differentiable optimization problem. It can be understood that through this smooth approximation, the originally non-differentiable imaging model is transformed into a differentiable optimization problem with continuous gradients, thus enabling efficient solution using gradient descent algorithms. Furthermore, hard thresholding projection operations are combined to enhance the sparsity or structure of the solution, improving imaging quality. In many scenarios, SAR images exhibit significant low-rank characteristics in appropriate transform domains (such as the image itself or its specific transforms). When the echo signal vector... Reconstructed into a matrix Subsequently, the rank of its matrix is ​​usually low. To utilize this prior knowledge to suppress noise and improve reconstruction quality, a rank constraint can be imposed on the reconstructed image, namely:

[0086] ;

[0087] This constraint-enforcing algorithm searches within a highly structured low-rank matrix space, thereby leveraging the inherent correlations of the image to obtain a more physically stable solution.

[0088] The optimization problem mentioned above is as follows:

[0089] ;

[0090] ;

[0091] ;

[0092] in, Let be the objective function. As a scale factor, and This scaling factor is used to control function pairs The degree of approximation of the function, The upper bound parameter of the preset rank, This refers to operations that convert echo signal vectors into matrices, such as converting... The matrix, This is a rank constraint on the echo signal vector.

[0093] It should be noted that, since the signal and noise in a single-bit synthetic aperture radar imaging signal model are usually in complex form, therefore... The function is generalized to the complex field, thus preserving its element-wise properties and ensuring that it remains smooth and differentiable in the complex field. That is:

[0094] ;

[0095] in, Radar echo signals that exist in complex form and These correspond to the real part and the imaginary part, respectively.

[0096] Step S13: Solve the optimization problem using a pre-built alternating iterative algorithm of gradient descent and low-rank projection to determine the target echo signal vector, and perform imaging based on the target echo signal vector.

[0097] In this embodiment, by alternately executing the gradient descent step and the low-rank projection step, the requirements of data fitting and structural prior are simultaneously satisfied, enabling efficient and stable solution of the optimization problem. Specifically, the gradient of the objective function with respect to the echo signal vector in the optimization problem is determined; the gradient descent method is used, and the echo signal vector of the current iteration is initially updated based on the gradient to obtain the updated echo signal vector; wherein, in the initial iteration, a preset initial echo signal vector is determined as the echo signal vector of the current iteration; the updated echo signal vector is reconstructed into an updated image matrix; a preset projection operation is performed on the updated image matrix to obtain the corresponding low-rank matrix; the preset projection operation is a hard-threshold low-rank projection operation based on singular value decomposition; the low-rank matrix is ​​vectorized to obtain the echo signal vector of the new round of iteration. The process involves several steps: first, determining whether the echo signal vector of the new iteration satisfies a preset convergence condition; if the echo signal vector of the new iteration satisfies the preset convergence condition, then the echo signal vector of the new iteration is determined as the target echo signal vector; if the echo signal vector of the new iteration does not satisfy the preset convergence condition, then the echo signal vector of the new iteration is determined as the current echo signal vector, and the gradient descent method is re-executed to initially update the echo signal vector of the current iteration based on the gradient, obtaining the updated echo signal vector, and subsequent steps, until the echo signal vector of the new iteration satisfies the preset convergence condition. During each iteration, the current iteration number is recorded or the residual of the echo signal vector under each iteration is calculated. The convergence condition can be set as the current iteration number being greater than the maximum iteration number, or the residual being less than a preset residual threshold.

[0098] Furthermore, in this embodiment, a preset projection operation is performed on the updated image matrix to obtain the corresponding low-rank matrix. Specifically, this may include: performing singular value decomposition on the image matrix to obtain a decomposition result that is represented as the product of three matrices; the three matrices include one singular value matrix and two unitary matrices; performing a hard thresholding operation on the singular value matrix in the decomposition result to construct a truncated singular value matrix; and calculating the corresponding low-rank matrix based on the unitary matrix in the decomposition result and the truncated singular value matrix.

[0099] In this embodiment, imaging based on the target echo signal vector may specifically include: reconstructing the target echo signal vector into a target image matrix, and normalizing the target image matrix to obtain a standardized synthetic aperture radar image.

[0100] For example, objective function Regarding variables The gradient calculation expression is:

[0101] ;

[0102] in, The symbol for the Hadamarda complex. This is the symbol for the conjugate transpose.

[0103] After obtaining the gradient, the gradient descent method is used to initially update the echo signal vector of the k-th iteration to reduce the data fitting error, that is:

[0104] ;

[0105] in, Let be the step size, and These are parameters that control the convergence speed and stability of the algorithm. Let be the echo signal vector of the k-th iteration. This is the updated echo signal vector corresponding to the k-th iteration.

[0106] To introduce low-rank constraints, a low-rank projection operator is defined. This operator is implemented by truncating singular value decomposition, projecting the matrix onto a matrix space of a given rank r, and is the optimal approximation in this space under the Frobenius norm. Specifically, the hard-thresholding low-rank projection operation based on singular value decomposition can be implemented through the following steps:

[0107] First, the updated echo signal vector obtained from the gradient descent step... Reconstructing the image into matrix form yields the updated image matrix, which facilitates the application of low-rank reduction, i.e.:

[0108] ;

[0109] Next, the reconstructed matrix Perform singular value decomposition, decomposing it into the product of three matrices, namely:

[0110] ;

[0111] in, and It is a unitary matrix. It is a singular value matrix containing non-negative singular values, i.e., a diagonal matrix. For matrix A singular value, For matrix Another singular value.

[0112] Next, a hard thresholding process is applied to the singular value matrix, retaining only the top r largest singular values, to construct the truncated singular value matrix, i.e.:

[0113] ;

[0114] Finally, the low-rank matrix is ​​calculated using the truncated singular value matrix and unitary matrix. The low-rank matrix is ​​as follows:

[0115] ;

[0116] The low-rank matrix obtained by projection is revectorized to obtain the echo signal vector for the new round of iterations, i.e.:

[0117] ;

[0118] This low-rank projection step alternates with the gradient descent update, together forming a complete alternating iterative algorithm. This algorithm can fully utilize the inherent low-rank characteristics of SAR images while minimizing data fitting errors, thereby effectively improving image quality while ensuring reconstruction accuracy. Furthermore, by explicitly applying low-rank constraints, robustness to observation noise and missing data can be enhanced, resulting in more stable and accurate image reconstruction results.

[0119] Obtain the target echo signal vector that satisfies the convergence condition. Then, the optimized target echo signal vector is... Reconstructed into the target image matrix The image is then normalized to obtain a standardized reconstructed image, i.e., a standardized synthetic aperture radar image. The target image matrix is ​​a two-dimensional image matrix.

[0120] As can be seen, in this embodiment of the invention, by constructing a target single-bit echo signal model based on the hyperbolic tangent function, the original non-differentiable imaging model can be transformed into an optimization problem with continuous gradients. Combined with rank constraints, the inherent low-rank characteristics of the synthetic aperture radar image are fully utilized, which can suppress noise, enhance robustness, and improve the reconstruction effect in non-sparse scenes. Finally, the optimization problem is solved by a pre-constructed gradient descent and low-rank projection alternating iterative algorithm, which achieves efficient and stable solution of the optimization problem. Thus, while maintaining high computational efficiency, a reconstructed image with more complete detail preservation can be obtained.

[0121] For example, see Figure 3 As shown, a system based on The target single-bit echo signal model of the function is solved using an alternating iterative algorithm of gradient descent and low-rank projection. The algorithm sequentially calculates the gradient and performs gradient descent updates, and then performs hard-threshold low-rank projection on the updated image matrix based on singular value decomposition until the echo signal vector meets the convergence condition, generating the final SAR image. SAR images naturally have low-rank characteristics due to the structural similarity of their imaging scenes and data correlation.

[0122] Compared with traditional BIHT-based single-bit SAR imaging methods, the technical solution of this invention demonstrates significant advantages in modeling, optimization algorithms, and imaging performance. Traditional BIHT-based single-bit SAR imaging methods directly process discrete observation models constructed from sign functions. Their non-smooth, non-convex optimization objectives make it difficult to guarantee the convergence of the optimization algorithm, and their reliance on the sparsity assumption of the signal in the transform domain limits performance in non-sparse real-world scenarios. This application uses a smooth, continuous hyperbolic tangent function to approximate the sign function, transforming the original discrete optimization problem into a continuously differentiable optimization problem. This retains the advantages of single-bit sampling in terms of hardware simplification and noise suppression, while also laying a theoretical foundation for using efficient gradient-based algorithms. During the optimization process, explicit low-rank constraints are introduced. By performing singular value hard thresholding projection on the iterative intermediate results (i.e., the updated echo signal vector), the structural correlation inherent in the SAR image itself is effectively utilized, enhancing the algorithm's robustness to noise and missing data. This overcomes the detail loss and dynamic range reduction problems caused by strong sparsity constraints in traditional BIHT-based single-bit SAR imaging methods. In other words, the technical solution of this application can obtain reconstructed images with higher radiometric accuracy and more complete detail preservation while maintaining high computational efficiency. Table 1 shows a comparison of the technical solution of this invention with the single-bit SAR imaging performance based on the BIHT method:

[0123] Table 1

[0124]

[0125] In the quality assessment of single-bit SAR imaging, this invention uses SSIM (Structural Similarity Index Measure) and MSE (Mean Squared Error), also known as Normalized Frobenius Norm Error, as evaluation metrics. Furthermore, a comparison of algorithm runtime is used to highlight the computational efficiency of the proposed solution. As shown in Table 1 above, the single-bit SAR imaging based on this invention achieves higher reconstruction accuracy than the BIHT-based single-bit SAR imaging in terms of both SSIM and MSE metrics. Regarding computational efficiency, the single-bit SAR imaging based on this invention significantly reduces runtime, achieving a good balance between imaging quality and processing speed. Applications of single-bit SAR imaging based on this invention include low-cost automotive radar and unmanned platform sensing.

[0126] In one embodiment, such as Figure 4 As shown, based on the above-described single-bit synthetic aperture radar imaging method, the present invention also provides a single-bit synthetic aperture radar imaging system, comprising:

[0127] The imaging model construction module 11 is used to construct an initial single-bit echo signal model for single-bit synthetic aperture radar imaging, and to reconstruct a target single-bit echo signal model based on the hyperbolic tangent function based on the initial single-bit echo signal model.

[0128] The optimization problem construction module 12 is used to construct an optimization problem with continuous gradient and rank constraints based on the target single-bit echo signal model.

[0129] The optimization problem solving module 13 is used to solve the optimization problem using a pre-built alternating iterative algorithm of gradient descent and low-rank projection to determine the target echo signal vector, and to perform imaging based on the target echo signal vector.

[0130] Furthermore, it is worth noting that the working process of the single-bit synthetic aperture radar imaging system provided in this embodiment is the same as that of the single-bit synthetic aperture radar imaging method described above, and will not be repeated here. For details, please refer to the working process of the single-bit synthetic aperture radar imaging method described above.

[0131] For example, in actual point target imaging simulation experiments, the specific settings for relevant parameters can be: carrier frequency. Pulse repetition frequency signal bandwidth Platform movement speed Pulse width sampling frequency Antenna aperture size Doppler bandwidth Center slant distance of the imaging scene Azimuth resolution Total number of sampling points in azimuth direction Distance resolution Distance to total number of sampling points The above parameters collectively define the key performance indicators and data acquisition structure of a single-bit synthetic aperture radar imaging system during point target imaging. See also... Figure 5 As shown, the comparison of SAR imaging effects on 25 point targets using high-bit SAR imaging method, traditional single-bit SAR imaging method, BIHT-based single-bit SAR imaging method, and single-bit SAR imaging method based on the present invention is illustrated, and the corresponding 3D effect diagrams are shown in the figure. Figure 6 As shown, high-bit SAR imaging serves as a reference benchmark, presenting a clear distribution of point targets. However, traditional single-bit SAR imaging suffers from significant defocusing and noise interference. While BIHT-based single-bit SAR imaging has improved the quality, some targets remain blurred. In contrast, single-bit SAR imaging based on the method of this invention performs best in terms of target focus and background suppression, and is closest to the effect of high-bit imaging.

[0132] Figure 7 A schematic diagram of the structure of a terminal provided in an embodiment of this application. The terminal may include:

[0133] The memory 501, the processor 502, and the computer program stored on the memory 501 and capable of running on the processor 502.

[0134] When processor 502 executes the program, it implements the single-bit synthetic aperture radar imaging method provided in the above embodiments.

[0135] Furthermore, the terminal also includes:

[0136] Communication interface 503 is used for communication between memory 501 and processor 502.

[0137] The memory 501 is used to store computer programs that can run on the processor 502.

[0138] Memory 501 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0139] If the memory 501, processor 502, and communication interface 503 are implemented independently, they can be interconnected via a bus to communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, only one line is used in the diagram, but this does not imply that there is only one bus or one type of bus.

[0140] Optionally, in a specific implementation, if the memory 501, processor 502, and communication interface 503 are integrated on a single chip, then the memory 501, processor 502, and communication interface 503 can communicate with each other through an internal interface.

[0141] Processor 502 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0142] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the single-bit synthetic aperture radar imaging method described above.

[0143] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein.

[0144] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0145] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can read and execute instructions from and from an instruction execution system, apparatus or device).

[0146] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0147] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A single-bit synthetic aperture radar imaging method, characterized in that, The method includes: An initial single-bit echo signal model for single-bit synthetic aperture radar imaging is constructed, and a target single-bit echo signal model based on the hyperbolic tangent function is reconstructed based on the initial single-bit echo signal model. The initial single-bit echo signal model is as follows: ； For the observation matrix, The echo signal vector, For symbolic functions, This is the quantized noise vector; The target single-bit echo signal model is as follows: ； in, This is the measurement vector after single-bit quantization. It is the hyperbolic tangent function; An optimization problem with continuous gradient and rank constraints is constructed based on the target single-bit echo signal model; the rank constraint is a low-rank constraint, and low rank means that the rank of the matrix is ​​much smaller than the size of the matrix; The optimization problem is: ； ； ； in, Let be the objective function. As a scale factor, The upper bound parameter of the preset rank, This is an operation to convert the echo signal vector into a matrix. To constrain the rank of the echo signal vector; The optimization problem is solved by using a pre-built iterative algorithm of alternating gradient descent and low-rank projection to determine the target echo signal vector, and imaging is performed based on the target echo signal vector. The method of using a pre-built iterative algorithm of alternating gradient descent and low-rank projection to solve the optimization problem to determine the target echo signal vector includes: Determine the gradient of the objective function in the optimization problem with respect to the echo signal vector; The gradient descent method is used, and the echo signal vector of the current iteration is initially updated based on the gradient to obtain the updated echo signal vector; wherein, in the initial iteration, the preset initial echo signal vector is determined as the echo signal vector of the current iteration. The updated echo signal vector is reconstructed into an updated image matrix; A preset projection operation is performed on the updated image matrix to obtain the corresponding low-rank matrix; the preset projection operation is a hard-threshold low-rank projection operation based on singular value decomposition. The low-rank matrix is ​​vectorized to obtain the echo signal vector for the next iteration. Determine whether the echo signal vector of the new round of iteration meets the preset convergence condition; If the echo signal vector in the new iteration satisfies the preset convergence condition, then the echo signal vector in the new iteration is determined as the target echo signal vector.

2. The single-bit synthetic aperture radar imaging method according to claim 1, characterized in that, The construction of the initial single-bit echo signal model for single-bit synthetic aperture radar imaging includes: A single-bit quantization model is constructed to describe the single-bit quantization of the sampled echo signal in synthetic aperture radar imaging; the single-bit quantization represents the sign decision of the real part and the imaginary part of the echo signal respectively. An initial single-bit echo signal model for single-bit synthetic aperture radar imaging is constructed based on the single-bit quantization model. The single-bit quantization model is as follows: ； in, For measurement vectors, For the observation matrix, The echo signal vector, For noise vectors, Here, M is the sign function, M is the dimension of the measurement vector, and N is the dimension of the echo signal vector; Furthermore, the reconstructing of the target single-bit echo signal model based on the hyperbolic tangent function according to the initial single-bit echo signal model includes: The sign function in the initial single-bit echo signal model is smoothly approximated using the hyperbolic tangent function to reconstruct the target single-bit echo signal model based on the hyperbolic tangent function.

3. The single-bit synthetic aperture radar imaging method according to claim 1, characterized in that, The step of performing a preset projection operation on the updated image matrix to obtain a corresponding low-rank matrix includes: Singular value decomposition is performed on the image matrix to obtain a decomposition result that is represented as the product of three matrices; the three matrices include one singular value matrix and two unitary matrices. A hard thresholding operation is performed on the singular value matrix in the decomposition result to construct a truncated singular value matrix; The corresponding low-rank matrix is ​​calculated based on the unitary matrix and the truncated singular value matrix in the decomposition result.

4. The single-bit synthetic aperture radar imaging method according to claim 1, characterized in that, After determining whether the echo signal vector of the new iteration satisfies the preset convergence condition, the method further includes: If the echo signal vector in the new iteration does not meet the preset convergence condition, then the echo signal vector in the new iteration is determined as the current echo signal vector, and the step of using the gradient descent method to perform a preliminary update on the echo signal vector of the current iteration based on the gradient is executed again to obtain the updated echo signal vector and subsequent steps, until the echo signal vector in the new iteration meets the preset convergence condition.

5. The single-bit synthetic aperture radar imaging method according to any one of claims 1 to 4, characterized in that, The imaging based on the target echo signal vector includes: The target echo signal vector is reconstructed into a target image matrix, and the target image matrix is ​​normalized to obtain a standardized synthetic aperture radar image.

6. A single-bit synthetic aperture radar imaging system, characterized in that, The system includes: The model building module is used to construct an initial single-bit echo signal model for single-bit synthetic aperture radar imaging, and to reconstruct a target single-bit echo signal model based on the hyperbolic tangent function based on the initial single-bit echo signal model; wherein, the initial single-bit echo signal model is: ； For the observation matrix, The echo signal vector, For symbolic functions, This is the quantized noise vector; The target single-bit echo signal model is as follows: ； in, This is the measurement vector after single-bit quantization. It is the hyperbolic tangent function; The optimization problem construction module is used to construct an optimization problem with continuous gradient and rank constraints based on the target single-bit echo signal model; the rank constraint is a low-rank constraint, and low-rank means that the rank of the matrix is ​​much smaller than the size of the matrix; The optimization problem is: ； ； ； in, Let be the objective function. As a scale factor, The upper bound parameter of the preset rank, This is an operation to convert the echo signal vector into a matrix. To constrain the rank of the echo signal vector; The optimization problem-solving module is used to solve the optimization problem using a pre-built alternating iterative algorithm of gradient descent and low-rank projection to determine the target echo signal vector, and to perform imaging based on the target echo signal vector; The optimization problem solving module is specifically used for: determining the gradient of the objective function in the optimization problem with respect to the echo signal vector; using the gradient descent method and based on the gradient, performing a preliminary update on the echo signal vector of the current iteration to obtain an updated echo signal vector; wherein, in the initial iteration, a preset initial echo signal vector is determined as the echo signal vector of the current iteration; reconstructing the updated echo signal vector into an updated image matrix; performing a preset projection operation on the updated image matrix to obtain a corresponding low-rank matrix; the preset projection operation is a hard-threshold low-rank projection operation based on singular value decomposition; vectorizing the low-rank matrix to obtain the echo signal vector of the new iteration; determining whether the echo signal vector of the new iteration satisfies a preset convergence condition; if the echo signal vector of the new iteration satisfies the preset convergence condition, then the echo signal vector of the new iteration is determined as the target echo signal vector.

7. A terminal, characterized in that, include: The system includes a memory, a processor, and a single-bit synthetic aperture radar (SAR) imaging program stored in the memory and executable on the processor, wherein the single-bit SAR imaging program, when executed by the processor, implements the steps of the single-bit SAR imaging method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that can be executed to implement the steps of the single-bit synthetic aperture radar imaging method as described in any one of claims 1 to 5.

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