Single-bit millimeter wave imaging method based on distance migration enhanced deep unfolding network

Abstract

A single-bit millimeter-wave imaging method based on a distance migration-enhanced deep unfolding network includes: generating a training dataset containing simulated single-bit echo data and corresponding ground truth images; constructing a deep neural network with cascaded stages to unfold the iterative imaging algorithm based on the distance migration operator into a network hierarchical structure; each stage of the deep unfolding network includes a hyperbolic tangent physical gradient module and a spatially aware adaptive non-convex regularization module connected in sequence; at each stage of the deep unfolding network, the hyperbolic tangent physical gradient module is used to update the physical consistency of the input image to generate an intermediate image; the intermediate image is input into the spatially aware adaptive non-convex regularization module for denoising; the deep unfolding network is trained using the training dataset, and the measured single-bit millimeter-wave echo data to be processed is input into the trained deep unfolding network to output the target image.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing and intelligent imaging technology, specifically relating to a single-bit millimeter-wave imaging method based on a range migration enhanced depth unfolding network. Background Technology

[0002] Millimeter-wave imaging possesses a certain degree of penetration capability, and the electromagnetic waves used are non-ionizing radiation, posing minimal impact on the human body when relevant radiation exposure limits are met. Therefore, it is widely used in target detection, security imaging, and industrial inspection. However, with increasing bandwidth and resolution, the amount of echo data grows rapidly, simultaneously increasing the pressure on quantization accuracy at the acquisition end, storage and transmission bandwidth, and backend computing resources. This leads to increased power consumption and cost, impacting the engineering applications of low-cost, lightweight, and real-time imaging systems. Single-bit quantization, which retains only echo symbol information, can significantly reduce the complexity of the acquisition link and decrease the amount of data, thereby alleviating storage and transmission pressures. It is a crucial technical path for achieving low-cost millimeter-wave imaging systems. To improve single-bit imaging performance, existing research has proposed strategies such as time-varying thresholds and dithering quantization. Time-varying thresholds, by varying the threshold over time or through observation, can introduce amplitude-related information to a certain extent and improve reconstruction accuracy. Dithering quantization, by superimposing random perturbations before quantization, can alleviate nonlinear distortion and spectral aliasing, and is more conducive to avoiding point-by-point storage of the threshold sequence.

[0003] Building upon this foundation, compressed sensing (CS) provides a theoretical basis for sparse reconstruction under low-bit or underdetermined observations. Combining jitter quantization with single-bit CS can improve imaging quality by leveraging sparse priors and optimized reconstruction. In recent years, deep learning has also been introduced into the field of millimeter-wave imaging reconstruction: one type of method uses general convolutional networks for end-to-end mapping; another type of method draws on the idea of ​​deep unrolling, unfolding the iterative solution process into a trainable network hierarchical structure, demonstrating the potential to train the iterative process in sparse reconstruction, and is currently the closest technical route to this invention.

[0004] However, existing methods still have significant shortcomings when it comes to single-bit quantization millimeter-wave imaging. First, single-bit quantization compresses amplitude information very strongly, and the sign function is not differentiable, making it difficult to directly adapt to traditional processing procedures based on the linear observation assumption. This often results in decreased contrast, loss of detail, and increased artifacts; scattering intensity is easily distorted, and the target strength relationship is difficult to maintain stably. Second, range migration effects are often more pronounced in millimeter-wave imaging. Reconstruction usually requires frequent frequency domain transformations, phase compensation, and frequency domain resampling related to range migration, resulting in high iterative costs. At the same time, hyperparameters such as step size and regularization weights have a significant impact on convergence speed and imaging quality, leading to high parameter tuning costs and making it difficult to balance accuracy and real-time performance. Third, the end-to-end mapping method using general convolutional networks is more difficult to train and generalize under single-bit quantization conditions due to information loss and strong nonlinearity, and the stability is prone to decrease when system parameters or working environment change. Furthermore, there is still a lack of specialized research on depth unfolding for single-bit quantized millimeter-wave imaging, especially in how to effectively characterize symbolic observation characteristics, adapt distance migration compensation to the trainable iterative process, and reduce computational complexity to an engineering-acceptable range under the conditions of no distortion of scattering strength relationship and controllable artifacts. Summary of the Invention

[0005] This invention provides a single-bit millimeter-wave imaging method based on a distance migration-enhanced deep unfolding network, aiming to address the problems existing in current single-bit millimeter-wave imaging technologies, such as amplitude information loss, high quantization noise, difficulty in adjusting parameters of traditional iterative algorithms, and the lack of physical interpretability and poor generalization ability of general-purpose deep learning networks. This invention integrates distance migration imaging-related operations into the iterative training and inference process of the deep unfolding network as operators, thereby obtaining stable and efficient imaging results under extremely low bit sampling conditions.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A single-bit millimeter-wave imaging method based on range migration-enhanced depth unfolding networks includes the following steps:

[0008] S1. Generate a training dataset containing simulated single-bit echo data and corresponding ground truth images;

[0009] S2, constructing includes The deep neural network with cascaded stages unfolds the iterative imaging algorithm based on the distance migration operator into a network hierarchical structure; in the deep unfolded network, each stage contains a hyperbolic tangent physical gradient module and a spatially aware adaptive nonconvex regularization module connected in sequence.

[0010] S3. At each stage of the deep unfolded network, the hyperbolic tangent physical gradient module is used to update the physical consistency of the input image and generate an intermediate image.

[0011] S4. Input the intermediate image into the spatially aware adaptive non-convex regularization module for noise reduction.

[0012] S5. Train the deep unfolding network using the training dataset, input the measured single-bit millimeter wave echo data to be processed into the trained deep unfolding network, and output the target image.

[0013] Preferably, S1 includes injecting complex Gaussian white noise with dynamic signal-to-noise ratio into the original echo as a jitter source, so that the single-bit symbol data maintains a monotonic response to the amplitude in a statistical sense, thereby generating simulated single-bit echo data.

[0014] Preferably, S2 includes: embedding fixed forward RM mapping and backward RM mapping in the depth unfolding network to realize forward and backward transformation between the echo domain and the image domain; and using backward RM mapping to obtain the initial image of the depth unfolding network.

[0015] Preferably, S2 also includes: a forward RM mapping in the discrete wavenumber domain implementation. and reverse RM mapping It is expressed as follows:

[0016]

[0017]

[0018] in, and These represent the two-dimensional Fourier transform and its inverse transform, respectively. This represents element-wise multiplication. This represents the positive compensation factor determined by system parameters. This represents the input image domain data. As a conjugate compensation factor, , Indicates conjugate. This represents the input echo domain data;

[0019] Simulate single-bit echo The initial image is obtained by inputting the inverse RM mapping:

[0020] .

[0021] As a preferred option, each stage of the deep unfolded network consists of a symbol consistency update unit and a spatial awareness destigmatization unit connected in series, with parameters shared or set independently between stages.

[0022] Preferably, S3 includes:

[0023] The previous stage output image of the deep unfolding network is converted back to the echo domain, and the sign function is approximated by the hyperbolic tangent function to generate the predicted single-bit echo; the predicted single-bit echo is compared with the simulated single-bit echo, and the residual is calculated.

[0024] Based on the predicted single-bit echo, saturation suppression weights are constructed using the tanh derivative relationship; the weighted residuals are then backpropagated to the image domain through adjoint mapping to generate the image update gradient; the image update gradient is then used to update the output image of the previous stage using gradient descent to generate the intermediate image.

[0025] Preferably, S4 includes: performing a convolution operation on the amplitude of the intermediate image using a learnable convolutional layer initialized with a Gaussian kernel, extracting the local energy density reflecting the degree of target aggregation, and generating a pixel-level adaptive threshold matrix; applying MCP near-end mapping to the intermediate image pixel by pixel to obtain the stage output.

[0026] Preferably, S4 includes:

[0027] According to the intermediate image Extracting the amplitude diagram:

[0028]

[0029] For amplitude diagram Perform two-dimensional convolution and use a linear rectified function to ensure non-negativity to generate local energy density. :

[0030]

[0031] in, This represents a two-dimensional convolution operation. The convolution kernel is initialized to... Gaussian kernel;

[0032] Based on local energy density Generate pixel-level adaptive thresholding matrix For any pixel position The following formula is given:

[0033]

[0034] in, As a learnable threshold benchmark, To prevent division by zero of small constants;

[0035] For intermediate images Applying MCP proximal mapping pixel by pixel yields the stage output. ;

[0036] For intermediate images Any pixel in the array is used as a complex value input. And take the value at the corresponding position in the adaptive threshold matrix as the threshold. ,make definition (when )and The proximal mapping of MCP is as follows:

[0037]

[0038] in This is the non-convexity control parameter.

[0039] As a preferred option, in S5, the training of the deep unfolded network includes:

[0040] Sample pairs Input depth unwrap network, To simulate single-bit echo data, For the corresponding truth image; A random undersampling mask is applied to the measurement dimension, with the sampling rate varying randomly within the range of 30% to 100%. The mean squared error after amplitude normalization is used as the loss function, where the network output takes amplitude for supervision, as shown in the following equation:

[0041]

[0042] in, Sample index within a batch B represents the sample collection batch. Indicates the first in this batch A single-bit echo sample after applying a random undersampling mask. Indicates and Corresponding truth intensity map labels, It is the Frobenius norm. This indicates that the maximum element of the magnitude matrix is ​​used for normalization. To prevent division by zero of small constants;

[0043] An adaptive moment estimation optimizer is used for minimization, and the parameter set is jointly updated through backpropagation. Including step size at each stage tanh scaling factor Threshold benchmark and convolution kernel .

[0044] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0045] 1. Unlike traditional iterative algorithms (such as iterative shrinkage thresholding algorithms and their variants), which treat distance migration compensation as an independent preprocessing step, require repeated frequency domain transformation and phase compensation in each iteration, leading to computational redundancy and difficulties in hyperparameter tuning, this invention adopts a technical solution that embeds the forward distance migration mapping and adjoint mapping into each stage of the deep unfolded network in the form of fixed operators, and jointly learns the step size and regularization parameters through end-to-end training. This deeply integrates the distance migration compensation and iterative optimization process, eliminates the computational redundancy caused by repeated compensation, and allows reconstruction to be completed without external iteration during the inference stage. The running time is extremely fast, significantly improving efficiency compared to traditional high-performance iterative algorithms and meeting the real-time processing requirements of millimeter-wave imaging. At the same time, the network parameters are automatically optimized through data-driven processes, fundamentally avoiding the high cost of manual parameter tuning.

[0046] 2. Unlike existing single-bit reconstruction methods that directly embed the sign function into gradient updates, leading to non-differentiability, or use general convolutional networks for end-to-end mapping, resulting in a lack of physical interpretability and instability in amplitude recovery and weak target protection, this invention employs a combination of a hyperbolic tangent physical gradient module and a spatially aware adaptive non-convex regularization module. The former dynamically adjusts the approximation of the sign function by tanh using a learnable scaling factor and constructs anti-saturation weights to suppress gradient vanishing, solving the problems of non-differentiability of the single-bit quantization sign function and network oscillation. The latter utilizes local energy features to generate pixel-level adaptive thresholds, lowering the threshold in target-clustered regions to protect weak targets and raising the threshold in background regions to suppress noise. Combined with the unbiased estimation characteristics of MCP near-end mapping, it maintains the true scattering intensity of strong targets. This allows the invention to achieve optimal imaging performance under all sampling rate conditions, effectively solving the problems of amplitude distortion and weak target loss caused by single-bit quantization.

[0047] The inventiveness of this invention is reflected in the following two aspects:

[0048] Firstly, this project introduces a physical operator-based deep learning method into the field of single-bit millimeter-wave sparse imaging for the first time, forming an enhanced range migration deep unfolding network. Existing traditional deep unfolding methods are typically designed for linear observation models, with relatively simple forward operator structures. The innovation of this deep learning network lies in embedding the complete physical link of range migration, including two-dimensional Fourier transform, phase compensation, and frequency domain resampling, into each unfolding stage as a fixed physical module, and enabling it to work in conjunction with the nonlinear gradient update of single-bit symbol observations. Faced with the mutually constraining challenges of strong nonlinearity in single-bit quantization and high computational cost of range migration, unifying the modeling of both within the unfolding framework is not an obvious technical choice. Direct combination would lead to gradient coupling problems between physical operators and symbol approximation modules in the backpropagation path, requiring a specially designed anti-saturation weight mechanism to ensure training stability. This design cannot be directly derived from existing technologies.

[0049] Secondly, the synergistic design of hyperbolic tangent anti-saturation weights and spatially aware pixel-level adaptive thresholds is non-obvious. Using tanh to approximate the sign function alone is not novel in deep learning, and similar work has been done on using adaptive thresholds for sparsification. However, directly constructing the tanh derivative as a saturation suppression weight to suppress the interference of the predicted saturation region in the echo domain on the gradient, while simultaneously using local convolution energy to dynamically generate pixel-level thresholds related to the target aggregation degree in the image domain, and replacing the soft threshold with MCP near-end mapping to eliminate strong target amplitude shrinkage bias, the joint design of these two approaches in the specific scenario of single-bit millimeter-wave imaging addresses the core challenge of the contradictory relationship between sign quantization nonlinearity and target amplitude hierarchy preservation. Its synergistic effect cannot be obtained by simply superimposing the individual components, thus possessing outstanding substantive characteristics. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the method flow of Embodiment 1 of the present invention;

[0051] Figure 2 This is a schematic diagram of the method framework of Embodiment 1 of the present invention;

[0052] Figure 3 This is an optical image of scene imaging according to Embodiment 1 of the present invention;

[0053] Figure 4 This is a scene diagram of Embodiment 1 of the present invention;

[0054] Figure 5 This is a physical image of the target wrench inside the box in Embodiment 1 of the present invention;

[0055] Figure 6 This is a comparison of the imaging results of the wrench inside the box under full sampling conditions in Embodiment 1 of the present invention;

[0056] Figure 7 This is a comparison of the imaging results of the wrench inside the box under a 70% sampling rate condition in Embodiment 1 of the present invention;

[0057] Figure 8 This is a comparison of the imaging results of the wrench inside the box under a 50% sampling rate condition in Embodiment 1 of the present invention;

[0058] Figure 9 This is a comparison of the imaging results of the wrench inside the box under a 30% sampling rate condition in Embodiment 1 of the present invention. Detailed Implementation

[0059] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0060] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0061] This invention adopts a deep integration of model-driven and data-driven technologies to construct a deep unfolded network that includes a physical propagation mechanism. Its core innovations are: to address the non-differentiability of the sign function and the vanishing gradient problem caused by single-bit quantization, a hyperbolic tangent physical gradient module is designed, which achieves adaptive gradient correction through a learnable scaling factor and anti-saturation weights; to address the contradiction between the easy loss of weak targets and noise suppression, a spatially aware adaptive non-convex regularization module is designed, which dynamically generates pixel-level thresholds using local energy features and combines the unbiased estimation properties of the Minimax Concave Penalty (MCP) activation function to maintain the amplitude of strong targets.

[0062] This embodiment provides a millimeter-wave (MMW) sparse imaging method for single-bit quantized echoes. The overall process includes: construction of training data and supervision labels, single-bit quantization with complex Gaussian dithering, deep unfolded network construction, end-to-end training, and rapid reconstruction of measured echoes. This method addresses problems such as the difficulty in amplitude recovery due to single-bit observations retaining only symbol information, the instability of traditional iterative updates due to quantization nonlinearity, and the sensitivity of iterative algorithms to step size and regularization parameters. It embeds the mapping between the echo domain and image domain in the range migration (RM) imaging process into the network using a fixed computation module and unfolds the iterative solution into... The network consists of several stages. Each stage first performs sign-consistent gradient updates based on the hyperbolic tangent function, followed by spatially aware pixel-level adaptive thresholding for denoising. Near-end mapping using the MCP function is employed to achieve non-convex sparsity constraints, thereby suppressing quantization distortion and background clutter while preserving the amplitude hierarchy of weak and strong scattering as much as possible. The network learns the step size, tanh approximation scale, threshold baseline, and convolutional kernel parameters for each stage through end-to-end training, enabling it to adapt to data with different sampling rates under a certain range of random jitter intensity.

[0063] For ease of description, the following notation will be used: and These represent the forward distance migration mapping and its adjoint mapping, respectively. , These represent the two-dimensional Fourier transform and its inverse transform, respectively. , These represent taking the real part and taking the imaginary part, respectively. This indicates taking the modulus or absolute value of a complex number; This indicates element-wise multiplication.

[0064] Example 1:

[0065] like Figure 1 , Figure 2 The single-bit millimeter-wave imaging method shown includes the following steps: (The method is described in the original text.)

[0066] S1. Generate a training dataset containing simulated single-bit echoes and corresponding ground truth images;

[0067] To enable the network to recover amplitude with only symbol information, a Gaussian jitter quantization mechanism is employed: complex Gaussian white noise with dynamic signal-to-noise ratio is injected into the original echo as a jitter source, establishing a monotonic mapping relationship between the statistical characteristics of a single-bit symbol and the amplitude of the original signal. By introducing complex Gaussian jitter as an auxiliary variable, the single-bit symbol data maintains a monotonic response to amplitude in a statistical sense, mitigating the amplitude loss problem.

[0068] The specific process is as follows:

[0069] like Figure 3 As shown, taking the Frequency-Modulated Continuous Wave (FMCW) millimeter-wave imaging system as an example, the starting frequency is set to... The frequency modulation slope is Fast sampling rate The imaging region is discretized into The grid, the imaging plane and the antenna reference distance are denoted as . Each time a training sample is generated, it is randomly generated within the imaging region. Point scatterer ( ), No. The planar coordinates of the scatterers are The equivalent scattering amplitude is ,in For any grid point on the imaging plane , to the Two-way distance of each scatterer Defined as:

[0070]

[0071] Under the FMCW de-modulation model, let At the speed of light, For fast sampling time, The imaginary unit is used to coherently superimpose the echoes from all scatterers to obtain the pure complex echo. :

[0072]

[0073] To introduce complex Gaussian dithering, first use... This represents the number of fast-time sampling points, calculated. The average power is given by the following formula:

[0074]

[0075] in, For the first The corresponding time point is sampled using a fast time method. Then, within the interval... Internal random sampling signal - jitter power ratio And determine the jitter power accordingly. with standard deviation As shown in the following formula:

[0076]

[0077] Generate complex Gaussian dithering terms ,in and Independent and subordinating ,in Representing an interval A continuous and uniform distribution is achieved. To maintain consistency with the set jitter power, a distribution boundary is set. The echo after adding jitter is obtained as follows:

[0078]

[0079] right The real and imaginary parts are symbolically quantized separately to obtain a simulated single-bit echo. As shown in the following formula:

[0080]

[0081] in If and only if ,otherwise At the same time, based on the location of the scatterer With amplitude ,exist Generating ground truth intensity maps on the grid As a supervisory label, it is used for error calculation during the training phase.

[0082] S2, constructing includes A deep neural network with multiple cascaded stages expands the iterative imaging algorithm based on the distance migration operator into a network hierarchical structure; each stage shares or independently has trainable network parameters.

[0083] Build including The deep unfolding network consists of cascaded stages, with fixed forward and backward RM mappings embedded in the network to achieve forward and backward transformations between the echo domain and the image domain. The adjoint mapping is used to obtain the initial value of the network, i.e. the initial image of the deep unfolding network.

[0084] The specific process is as follows:

[0085] Build includes A deep unfolded network with cascaded stages, denoted as [network forward mapping]. ,in This is the set of trainable parameters for the network. The network contains fixed embedded positive RM mappings. and its reverse RM mapping This is used to perform forward / backward transformations between the image domain and the echo domain. Taking the discrete wavenumber domain implementation as an example, let... and These represent the two-dimensional Fourier transform and its inverse transform, respectively. This represents element-wise multiplication. This represents the positive compensation factor determined by system parameters. Representing the input image domain data, we have the following formula:

[0086]

[0087] The adjoint mapping uses a conjugate compensation factor ( (indicating conjugation) This represents the input echo domain data, which is then calculated. As shown in the following formula:

[0088]

[0089] To obtain reasonable initial values, simulate single-bit echoes. The initial image is obtained by inputting the comorbid mapping.

[0090]

[0091] Stack on top of this Each stage consists of a symbol consistency update unit and a spatial awareness destigmatization unit connected in series, and parameters between stages can be shared or set independently.

[0092] The specific network structure parameter configurations for the single-stage iterative module are shown in Table 1:

[0093] Table 1: Parameter Table of Single-Stage Iterative Module Network Structure

[0094]

[0095] S3. At each stage of the deep unfolded network, the hyperbolic tangent physical gradient module is used to update the physical consistency of the input image and generate an intermediate image.

[0096] At each stage of the deep unfolded network, the input image is updated with physical consistency using a hyperbolic tangent physical gradient module. This module is based on the aforementioned distance migration operator; it approximates the sign function of single-bit quantization using the hyperbolic tangent (tanh) function and introduces a learnable scaling factor to dynamically adjust the approximation, while constructing a gradient descent rule with anti-saturation weights to prevent network oscillations.

[0097] Within each stage, a sign-consistency update is performed. The sign function is smoothly approximated using the hyperbolic tangent function, and its derivative is used to construct saturation suppression weights, forming a stable gradient update rule. The specific process is as follows:

[0098] For the stage( The input is the output of the previous stage. First, calculate the echo domain predictor, and then approximate the sign function using tanh. Let... This is the learnable scaling factor for this stage. and Let represent the real and imaginary parts of the predicted single-bit echo after smoothing approximation, respectively, and their calculation is as follows:

[0099]

[0100] The residual is constructed as follows:

[0101]

[0102] in and These represent the stage residuals of the real and imaginary parts, respectively. The element-wise squaring operation of a matrix or vector is represented by the tanh derivative relation, and the saturation suppression weights are constructed as follows:

[0103]

[0104] in and Let represent the anti-saturation weights of the real and imaginary parts, respectively. The weighted residuals are backpropagated to the image domain through the adjoint mapping to obtain the stage gradient (image update gradient) as follows:

[0105]

[0106] make The learnable step size for this stage is updated to obtain the intermediate image as follows:

[0107]

[0108] S4. Input the intermediate image into the spatially aware adaptive non-convex regularization module for noise reduction.

[0109] After gradient update, the intermediate image is input into a spatially aware adaptive non-convex regularization module for denoising. This module uses learnable convolutional layers initialized with Gaussian kernels to convolve the amplitude of the intermediate image, extracting the local energy density that reflects the degree of target aggregation. Based on this, a pixel-level adaptive threshold matrix is ​​generated: a lower threshold is generated in the target clustering region to protect weak targets; and a higher threshold is generated in the background region to strongly suppress noise. Then, the minimum maximum concave penalty near-end operator is used as a nonlinear activation function to output the denoised image. The MCP operator has unbiased estimation characteristics for large-amplitude pixels, perfectly preserving the true scattering intensity of strong targets and compensating for amplitude distortion caused by single-bit quantization.

[0110] After the symbol consistency update, sparse descatification is performed. A pixel-level adaptive threshold map is generated based on the local energy, and the near-end mapping of the MCP function is used as a non-convex threshold operator to reduce the shrinkage bias of strong scattering amplitudes and preserve weak scattering details. The specific process is as follows:

[0111] intermediate image Input spatially aware descrambling unit. To avoid directly altering the phase structure during complex convolution, the amplitude map is extracted first. .right Two-dimensional convolution is performed to obtain local energy density, and the convolution kernel is denoted as... And by using a rectified linear unit (ReLU) function to ensure non-negativity, the local energy density is obtained as follows:

[0112]

[0113] in This represents a two-dimensional convolution operation. Can be initialized to A Gaussian kernel (step size 1, padding 1) is used to maintain output size consistency with input. This is based on local energy density. Generate pixel-level adaptive threshold matrix For any pixel position We have the following formula:

[0114]

[0115] in As a learnable threshold benchmark, To prevent division by zero of small constants. Then... Applying MCP proximal mapping pixel by pixel yields the stage output. For intermediate images Any pixel in the array is used as a complex value input. And take the value at the corresponding position in the adaptive threshold matrix. as a threshold (i.e., order) ),definition (when )and The MCP proximal mapping is then expressed as follows:

[0116]

[0117] in For non-convexity control parameters, this embodiment takes... The mapping employs an identical output in the large amplitude region, which reduces the shrinkage bias of strong scattering amplitude; in the small amplitude region, it performs sparsification according to a threshold, which helps suppress discrete strays and isolated artifacts.

[0118] S5. Train the deep unfolding network using the training dataset, input the measured single-bit millimeter wave echo data to be processed into the trained deep unfolding network, and output the target image.

[0119] End-to-end joint training was employed, with training data input into the deep unrolled network in a randomly undersampled manner. Backpropagation was used to jointly optimize the physical gradient layer stride, tanh scaling factor, adaptive threshold baseline, and convolutional kernel weights at each stage of the network. After training, the actual measured single-bit millimeter-wave echo data to be processed was input into the network. Background thermal noise in the actual test environment was used as a natural jitter source, and the network was then... The rapid forward inference process in each stage directly outputs a high-precision target image (reconstructed image) containing accurate radar cross section (RCS) intensity.

[0120] End-to-end joint training was employed to learn the step size, tanh approximate scale, threshold benchmark, and convolutional kernel parameters at each stage. After training, the measured single-bit echo was directly input into the network, and then... Each stage of forward computation outputs a reconstructed image.

[0121] The specific process is as follows. During the training phase, the sample pairs... Input network. To cover different sparse sampling conditions, [the following is done / implemented]: A random undersampling mask is applied to the measurement dimension, with the sampling rate varying randomly within the range of 30% to 100%. The batch size is denoted as... The mean squared error after amplitude normalization is used as the loss function, where the amplitude of the network output is taken for supervision as follows:

[0122]

[0123] in, Sample index within a batch , Indicates the first in this batch A single-bit echo sample after applying a random undersampling mask. Indicates and Corresponding truth intensity map labels, It is the Frobenius norm. This indicates that the maximum element of the magnitude matrix is ​​used for normalization. To prevent small constants from being divided by zero, an Adaptive Moment Estimation (Adam) optimizer is used to minimize the above equation, and the parameter set is jointly updated through backpropagation. Including step size at each stage tanh scaling factor Threshold benchmark and convolution kernel In this embodiment, the number of training samples is 1000, and the scene size is [missing information]. Batch size is set to 4, initial learning rate is set to... The loss decreases adaptively, and the training epochs are set to 50. This can be achieved using... , , This serves as initialization. The optimal parameters are saved after training. The inference phase will involve measuring single-bit echoes. enter ,through Each stage of forward computation directly outputs the reconstructed image without the need for additional external iterations; the random jitter components commonly found in the measured link are statistically similar to the complex Gaussian jitter introduced during the training stage, and the symbolic statistical regularities learned by the network can be directly used for amplitude level recovery.

[0124] To verify the imaging performance of the proposed method at different sampling rates, it was compared with the Range Migration Algorithm (RMA), the Iterative Shrinkage-Thresholding Algorithm (ISTA), and several improved iterative methods based on tanh approximation and MCP regularization. Under the same data and implementation conditions, the Normalized Root Mean Square Error (NRMSE), Target-to-Background Ratio (TBR), and Structural Similarity Index Measure (SSIM) were calculated, and the running time was recorded. The quantitative results at different sampling rates are shown in Table 2. Figure 4 , Figure 5 These are scene images and actual target object images, respectively. Figures 6-9 The imaging results under several sampling rate conditions are compared, showing that the proposed method performs stably in terms of weak scattering detail preservation and background clutter suppression. Figure 6 In the lower right image showing the effect of this method, the gap area below the wrench is fuller, and there is a clear advantage in running time. Figures 6-9 The bottom left and middle left images of the four graphs are similar in effect, but in terms of runtime, the tanh function has a clear advantage, providing faster convergence and alleviating the gradient vanishing problem compared to the slr function.

[0125] To verify the effectiveness of this invention, this embodiment constructs a specific experimental environment for network training. The specific training configuration and hyperparameter settings are as follows:

[0126] Dataset size: A training dataset containing 1000 sample pairs was constructed, with each sample containing a 128*128 scene image and 256-point fast time echo data.

[0127] Random undersampling strategy: In order to enable the network to process sparse data, the input echo is randomly undersampled during training. The sampling rate is randomly distributed between 30% and 100%, which forces the network to learn robust features of the image by reconstructing it using incomplete data.

[0128] Network initialization: To accelerate convergence, the network's learnable parameters are initialized with specific physical values.

[0129] gradient step size Initialized to 0.5, threshold baseline. Initialized to 0.01, Tanh scaling factor The value is 1.

[0130] Training hyperparameters: Optimizer is Adam optimizer; initial learning rate is set to... It also incorporates an adaptive decay strategy, automatically halving the loss when it stops decreasing; the training rounds are set to 50; and the batch size is set to 4.

[0131] After training is complete, save the optimal parameter set. The single-bit echo data actually collected by the radar Input the data into the network. At this point, no further iterative optimization is needed. The network utilizes the learned nonlinear mapping relationship and, after K stages of forward inference, directly outputs a high-precision target reconstruction image.

[0132] Quantitative Evaluation and Performance Comparison Analysis: To verify the comprehensive performance of the proposed method (RM-TMist-net), it was compared in detail with traditional distance migration (RMA), iterative shrinkage thresholding (ISTA), and existing advanced iterative algorithms—including the ISTA algorithm incorporating hyperbolic tangent approximation (TANH-ISTA), the ISTA algorithm combining logistic regression approximation and minimum-maximum concavity penalty (SLR-ISTA-MCP), and the ISTA algorithm simultaneously combining hyperbolic tangent approximation and minimum-maximum concavity penalty (TANH-ISTA-MCP). The experimental results are shown in Table 2 below:

[0133] Table 2: Numerical evaluation of each algorithm under different sampling rates

[0134]

[0135] Based on the analysis of the above experimental data, the imaging quality is significantly improved. At all sampling rates (100% to 30%), the method of this invention achieves the best imaging performance. The average TBR reaches 51.41 dB, and the NRMSE is reduced to 0.1656, demonstrating the effectiveness of the hyperbolic tangent physical gradient and spatially aware regularization strategy in recovering amplitude information. The inference speed shows an order-of-magnitude leap. Thanks to the non-iterative inference characteristics of the deep unfolding architecture, this invention runs extremely fast, significantly improving efficiency compared to traditional high-performance iterative algorithms, meeting the requirements of real-time imaging. Robustness at low sampling rates is also demonstrated. At an extremely low sampling rate of 30%, traditional linear algorithms (RMA) essentially fail, while this invention still maintains a high target-to-background ratio, exhibiting extremely strong sparse reconstruction capabilities.

[0136] To more intuitively demonstrate the advantages of the method of the present invention in target detail restoration and background noise suppression, Figures 6 to 9 The imaging results of the proposed method and the comparison algorithm for the wrench target inside the box are presented under full sampling, 70% sampling, 50% sampling and 30% sampling conditions, respectively.

[0137] The above are merely preferred embodiments of the present invention and are not intended to limit the invention in any way. Any simple modifications, alterations, and equivalent changes made to the above embodiments based on the inventive essence shall still fall within the protection scope of the present invention.

Claims

1. A single-bit millimeter-wave imaging method based on range migration-enhanced depth unfolding networks, characterized in that, Includes the following steps: S1. Generate a training dataset containing simulated single-bit echo data and corresponding ground truth images; S2, constructing includes The deep neural network with cascaded stages unfolds the iterative imaging algorithm based on the distance migration operator into a network hierarchical structure; in the deep unfolded network, each stage contains a hyperbolic tangent physical gradient module and a spatially aware adaptive nonconvex regularization module connected in sequence. S3. At each stage of the deep unfolded network, the input image is updated with physical consistency using the hyperbolic tangent physical gradient module to generate intermediate images; including: The previous stage output image of the deep unfolding network is converted back to the echo domain, and the sign function is approximated by the hyperbolic tangent function to generate the predicted single-bit echo; the predicted single-bit echo is compared with the simulated single-bit echo, and the residual is calculated. Based on the predicted single-bit echo, a saturation suppression weight is constructed using the tanh derivative relationship; the weighted residual is then backpropagated to the image domain through the adjoint mapping to generate the image update gradient; the image update gradient is then used to update the output image of the previous stage by gradient descent to generate an intermediate image. S4. Input the intermediate image into the spatially aware adaptive non-convex regularization module for denoising processing; including: using a learnable convolutional layer initialized with a Gaussian kernel to perform convolution operation on the amplitude of the intermediate image, extracting the local energy density reflecting the degree of target aggregation, and generating a pixel-level adaptive threshold matrix; applying MCP near-end mapping to the intermediate image pixel by pixel to obtain the stage output. S5. Train the deep unfolding network using the training dataset, input the measured single-bit millimeter wave echo data to be processed into the trained deep unfolding network, and output the target image.

2. The single-bit millimeter-wave imaging method based on a range migration-enhanced depth unfolding network according to claim 1, characterized in that, S1 includes injecting complex Gaussian white noise with dynamic signal-to-noise ratio into the original echo as a jitter source, so that the single-bit symbol data maintains a monotonic response to the amplitude in a statistical sense, thereby generating simulated single-bit echo data.

3. The single-bit millimeter-wave imaging method based on a range migration-enhanced depth unfolding network according to claim 1, characterized in that, S2 includes: Fixed forward and backward RM maps are embedded in the deep unfolded network to realize forward and backward transformations between the echo domain and the image domain. The initial image of the deep unfolded network is obtained by using inverse RM mapping.

4. The single-bit millimeter-wave imaging method based on a range migration-enhanced depth unfolding network according to claim 3, characterized in that, S2 also includes: in the discrete wavenumber domain implementation, the forward RM mapping. and reverse RM mapping It is expressed as follows: ； ； in, and These represent the two-dimensional Fourier transform and its inverse transform, respectively. This represents element-wise multiplication. This represents the positive compensation factor determined by system parameters. This represents the input image domain data. As a conjugate compensation factor, , Indicates conjugate. This represents the input echo domain data; Simulate single-bit echo The initial image is obtained by inputting the inverse RM mapping: 。 5. The single-bit millimeter-wave imaging method based on a range migration-enhanced depth unfolding network according to claim 1, characterized in that, Each stage of the deep unfolded network consists of a symbol consistency update unit and a spatial awareness destigmatization unit connected in series, with parameters shared or set independently between stages.

6. The single-bit millimeter-wave imaging method based on range migration enhanced depth unfolding network according to claim 1, characterized in that, S4 include: Based on the intermediate image Extracting the amplitude diagram: ； For amplitude diagram Perform two-dimensional convolution and use a linear rectified function to ensure non-negativity to generate local energy density. : ； in, This represents a two-dimensional convolution operation. The convolution kernel is initialized to... Gaussian kernel; Based on local energy density Generate pixel-level adaptive thresholding matrix For any pixel position The following formula is given: ； in, As a learnable threshold benchmark, To prevent division by zero of small constants; For intermediate images Applying MCP proximal mapping pixel by pixel yields the stage output. ; For intermediate images Any pixel in the array is used as a complex value input. And take the value at the corresponding position in the adaptive threshold matrix as the threshold. ,make definition ,when ,and The MCP proximal mapping is as follows: ； in, This is the non-convexity control parameter.

7. The single-bit millimeter-wave imaging method based on a range migration-enhanced depth unfolding network according to claim 1, characterized in that, In S5, training the deep unfolded network includes: Sample pairs Input depth unwrap network, To simulate single-bit echo data, For the corresponding truth image; A random undersampling mask is applied to the measurement dimension, with the sampling rate varying randomly within the range of 30% to 100%; the mean squared error after amplitude normalization is used as the loss function, where the amplitude of the network output is used for supervision. ； Where b is the sample index within the batch. B represents the sample collection batch. Indicates the first in this batch A single-bit echo sample after applying a random undersampling mask. Indicates and Corresponding truth intensity map labels, It is the Frobenius norm. This indicates that the maximum element of the magnitude matrix is ​​used for normalization. To prevent division by zero of small constants; An adaptive moment estimation optimizer is used for minimization, and the parameter set is jointly updated through backpropagation. Including step size at each stage tanh scaling factor Threshold benchmark and convolution kernel .

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