Target high-resolution detection method and device based on deep expansion network

Abstract

The invention discloses a target high-resolution detection method based on a deep expansion network. The method comprises the following steps: receiving observation data from an array; inputting observation data into the trained deep expansion network; the deep expansion network comprises a deep neural network obtained by mapping an ADMM iterative optimization step and a hyper-parameter prediction module for providing penalty parameters for unit blocks of the deep neural network obtained by mapping each iterative optimization step; the hyper-parameter prediction module adaptively adjusts penalty parameters of each layer so as to improve the adaptability to sparseness distribution of different signals; and outputting the recovered sparse vector by the deep expansion network, and obtaining the incident angle and the intensity of the information source from the sparse vector. According to the invention, the hyper-parameter prediction module based on the residual structure is introduced, the dependence on the initial value of the penalty parameter is eliminated, the grid-level dynamic prediction and adaptive control of the penalty parameter are realized, and the limitations of slow convergence and poor adaptability to the noise environment of the algorithm are effectively overcome on the premise of accurately estimating the incident angle of the information source.

Description

Technical Field

[0001] This application relates to the fields of signal processing and depth unfolding technology, and in particular to a high-resolution target detection method and apparatus based on depth unfolding networks. Background Technology

[0002] Direction of Arrival (DOA) estimation involves receiving incident signals from space using a sensor array, estimating the spatial spectrum of the received signals, and then estimating the incident angle of the signal source. It is widely used in several key fields such as radar, communication, and sonar. Classical DOA estimation methods, such as conventional beamforming, have resolution limited by the array aperture. Other subspace methods, such as the Multiple Signal Classification (MUSIC) algorithm, can achieve super-resolution estimation, but rely on accurate covariance estimation over multiple snapshots and require prior knowledge of the number of signal sources. Compressed sensing theory transforms the DOA estimation problem into a sparse signal recovery problem, and the Alternating Direction Multiplier Method (ADMM) is an effective method for solving the convex optimization problem within it. Subsequent deep learning-based methods fully utilize the nonlinear fitting capabilities of neural networks to learn the mapping from input to output, but most of these are black-box models lacking physical interpretability.

[0003] In existing technical solutions, deep unfolded networks based on ADMM (such as the single-shot DOA estimation method based on ADMM-Net) are a similar implementation to this invention. They can recover the signal angle of arrival from single-shot data and train hyperparameters by neural networks, thereby improving the convergence speed and estimation accuracy of ADMM.

[0004] Deep unfolded network technology, as an innovative direction for the integration of deep learning and traditional optimization algorithms, maps each step of the traditional iterative algorithm to a layer of the neural network. While retaining the theoretical optimization convergence of traditional numerical optimization algorithms, it also fully integrates the powerful data-driven adaptive learning capabilities of deep learning, making it an effective solution for solving the DOA estimation problem.

[0005] Traditional ADMM transforms complex optimization problems into multiple simple subproblems that are solved alternately, but often requires hundreds of iterations to converge. Furthermore, regularization parameters, penalty parameters, etc., usually need to be set manually based on experience, lacking adaptive adjustment capabilities and making it difficult to achieve the optimal balance between estimation accuracy and convergence speed.

[0006] Existing deep unfolding networks based on deep unfolding technology pre-convert the high-complexity online matrix operations (such as matrix inversion) in traditional iterative optimization into learnable fixed linear layer mappings shared between layers, or use Toplitz structures and Hermitian matrix constraints to train the guiding matrix, which weakens the physical interpretability of the original ADMM algorithm and uses the same hyperparameters for all samples, ignoring the distribution differences between samples. Summary of the Invention

[0007] The purpose of this application is to overcome the aforementioned problems of the prior art and provide a parameter-adaptive residual ADMM deep unfolding network (ResADMM-Net) for high-resolution target detection. It utilizes the iterative convergence characteristics of ADMM and the feature extraction capability of residual networks, and uses a hyperparameter prediction module based on a one-dimensional residual network to assign appropriate hyperparameters to different signals at different spatial angles. While ensuring physical interpretability, it enhances noise suppression capability according to the characteristics of the signal and retains effective signal components, enabling it to adaptively predict and adjust the optimal penalty parameters based on the input array data.

[0008] To achieve the above objectives, the present application provides a high-resolution target detection method based on a deep unfolded network, which receives spatial incident signals through a sensor array, performs spatial spectrum estimation on the received signals, and then estimates the incident angle and intensity of the signal source. The method is characterized by the following steps: Step S1: Receive observation data from the array; Step S2: Input the observation data into the trained deep unfolding network; the deep unfolding network includes: a deep neural network obtained by mapping the ADMM iterative optimization steps, and a hyperparameter prediction module that provides penalty parameters for the unit blocks of the deep neural network obtained by each iterative optimization step; the hyperparameter prediction module adaptively adjusts the penalty parameters of each layer to improve the adaptability to different signal sparsity distributions; Step S3: The deep unfolding network outputs the recovered sparse vector, from which the source incident angle and intensity are obtained.

[0009] As a preferred embodiment of the above method, the hyperparameter prediction module includes a first ordinary convolutional layer connected to a ReLU activation function, then connected to stacked residual blocks, and the stacked residual blocks are then connected to a second ordinary convolutional layer and a Softplus activation function in sequence before being output, which is used to extract multi-scale features of the incident signal orientation.

[0010] As another preferred embodiment of the above method, the residual block includes: a first dilated convolutional layer connected to a ReLU activation function and then connected to a second dilated convolutional layer, the output of the second dilated convolutional layer being added to the input of the residual block and then output after passing through a ReLU activation function.

[0011] As another preferred embodiment of the above method, the ADMM iterative optimization of the first... The next iteration update step is represented as follows: (7) (8) (9) in, It is an overcomplete dictionary built based on a discretized grid. It is observation data. It is the identity matrix. , It is a dual variable. It is a penalty parameter; Represents the soft threshold function. This is the threshold parameter.

[0012] As another preferred embodiment of the above method, the hyperparameter prediction module adaptively adjusts the penalty parameter of each layer using the following formula. : (12) in, This indicates that the hyperparameter prediction module performs the operation. and This represents the output of the previous iteration step.

[0013] As a further preferred method of the above method, in formula (7) use mean : (13) Where N represents the continuous spatial angular range Discretize into Grid points.

[0014] As a further preferred method, the deep neural network obtained by mapping the ADMM iterative optimization steps includes: constructing a deep neural network by cascading multiple identical unit blocks, each unit block corresponding to one iterative solution step of the ADMM algorithm; adding a learnable hyperparameter prediction module between adjacent unit blocks to predict grid-level penalty parameters for data updates in the next unit block.

[0015] As a further preferred embodiment of the above method, training the deep unfolded network specifically includes the following steps: Construct a dataset containing multiple samples; Set the normalized mean squared error loss function, specifically defined as: (18) in , It refers to the batch size. and They represent the first The estimated signal and the true signal of a sample; The total number of training rounds and batch size are set, and training is performed in an end-to-end manner. The optimization objective of training the network is to minimize the normalized mean square error loss function.

[0016] To achieve the above objectives, the present invention also provides a high-resolution target detection device based on a deep unfolded network, characterized in that it comprises: A sensor array used to receive incident signals from space; The data acquisition module is used to acquire the output data of the sensor array; A memory for storing the data and computer programs; A processor is used to execute the computer program to implement the steps of the above-described high-resolution target detection method.

[0017] To achieve the above objectives, the present invention also provides a computer-readable storage medium, characterized in that it includes a stored computer program, which can be executed by a processor to implement the steps of the above-described high-resolution target detection method.

[0018] Compared with the prior art, the advantages of the present invention are as follows: Compared with existing technologies, this invention introduces a hyperparameter prediction module based on residual structure, eliminating the dependence on the initial value of the penalty parameter and achieving grid-level dynamic prediction and adaptive control of the penalty parameter. This effectively overcomes the limitations of slow convergence and poor adaptability to noisy environments while accurately estimating the source incidence angle. Experimental results show that, with a computation time only about one-third that of the traditional ADMM algorithm, this network outperforms traditional iterative algorithms and existing mainstream depth unfolding methods in key indicators such as detection rate, accuracy, and reconstruction accuracy, achieving a balance between performance and efficiency. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the ADMM data flow in the prior art; Figure 2 This is a schematic diagram of the ResADMM-Net data flow of the present invention.

[0020] Figure 3 This is the hyperparameter prediction module in a specific embodiment of the present invention. Structural diagram; Figure 4 This is the hyperparameter prediction module in a specific embodiment of the present invention. Schematic diagram of the structure of the intermediate residual block; Figure 5(a) shows the DOA estimation spectrum of the same sample using the ResADMM-Net method at an SNR of 15dB; Figure 5(b) shows the DOA estimation spectrum of the same sample using the ADMM-Net method at an SNR of 15dB. Figure 5(c) shows the DOA estimation spectrum of the same sample using the THADMM-Net method when the SNR is 15dB; Figure 5(d) shows the DOA estimation spectrum of the same sample using the ADMM method when the SNR is 15dB; Figure 5(e) shows the DOA estimation spectrum of the same sample using the ISTA-Net method when the SNR is 15dB. Figure 5(f) shows the DOA estimation spectrum of the same sample using the LISTA method when the SNR is 15dB; Figure 6 This is a graph showing the relationship between the detection rate and SNR of the method using the specific embodiments of the present invention and other methods; Figure 7 This is a graph showing the relationship between the accuracy and SNR of the method using the specific embodiments of this invention and other methods. Figure 8(a) is a graph showing the relationship between amplitude RMSE and SNR using the method of the specific embodiment of the present invention and other methods; Figure 8(b) is a graph showing the relationship between RMSE and SNR from the perspective of using the method of the specific embodiment of the present invention and using other methods. Detailed Implementation

[0021] The technical solutions provided in this application are further illustrated below with reference to the embodiments.

[0022] This invention introduces a hyperparameter prediction module based on residual structure, thereby eliminating the dependence on the initial value of the penalty parameter and realizing grid-level dynamic prediction and adaptive control of the penalty parameter. Under the premise of accurately estimating the incident angle of the signal source, it effectively overcomes the limitations of slow convergence and poor adaptability to noisy environments.

[0023] As a specific implementation, the present invention provides a high-resolution target detection method based on a deep unfolded network, used to receive spatial incident signals through a sensor array, perform spatial spectrum estimation on the received signals, and then estimate the incident angle and intensity of the signal source. The method is characterized by the following steps: Step S1: Receive observation data from the array; Step S2: Input the observation data into the trained deep unfolding network; the deep unfolding network includes: a deep neural network obtained by mapping the ADMM iterative optimization steps, and a hyperparameter prediction module that provides penalty parameters for the unit blocks of the deep neural network obtained by each iterative optimization step; the hyperparameter prediction module adaptively adjusts the penalty parameters of each layer to improve the adaptability to different signal sparsity distributions; Step S3: The deep unfolding network outputs the recovered sparse vector, from which the source incident angle and intensity are obtained.

[0024] To facilitate understanding, the specific implementation methods of this invention will be described in detail below from the aspects of signal model, principle explanation, network structure, and simulation experiment.

[0025] 1. Signal Model Consider a containing A sparse linear array (SLA) with n elements, along Axial distribution, array element positions are ,in And satisfy The positions of the first and last array elements are fixed at... and At this location, the array aperture length is When the far field of space exists A narrowband uncorrelated signal source (frequency: , wavelength is From and The angle between the axis and the perpendicular direction is When the signal is incident on the array in the direction of the incident light, the array receives the observation signal. In the snap It can be represented as (1) in, yes A signal source in The signal is transmitted at all times. It is additive white Gaussian noise. For the array guiding matrix, its first... Column corresponding incident angle The guiding vector (2) in, Representing the signal propagation speed, based on the conventional half-wavelength array layout, the element spacing of the full array is set to... Then the guiding vector of the sparse linear array can be simplified to (3) To transform the DOA estimation problem into a sparse signal recovery problem, the continuous spatial angular range... Discretize into grid points , of which the number of grids Much larger than the number of array elements and source number (Right now A complete dictionary is constructed based on this discretized grid. , its first Listed as (4) The observation model can then be reconstructed into the following sparse representation. (5) in, It is the sparse vector to be recovered. This represents noise. Ideally, yes A subset, yes Sparse. If the actual angle of incidence... With a certain grid point If they coincide, then the steering vector corresponding to that source is... It's equivalent to a dictionary The first in List At this time, sparse vectors It will be in the A non-zero value appears at each position. Therefore The grid angles corresponding to the positions of non-zero elements represent the true incident direction of the signal, and the amplitudes of the non-zero elements correspond to the signal intensity. Therefore, the DOA estimation problem is transformed into estimation from low-dimensional observations... Reconstructing high-dimensional sparse signals Underdetermined problems are usually solved by... To achieve the optimization problem of norm regularization (6) in, and They represent Norm and Norm, It is a regularization parameter that balances sparsity and signal recovery error.

[0026] Formula (6) above is the solution object for the depth unfolding network of the present invention; The input to the deep unfolded network is the observation signal received by the array. The output is a sparse vector. The grid angle corresponding to the position of the non-zero element represents the true incident direction of the signal, and the amplitude of the non-zero element corresponds to the signal strength.

[0027] 2. Principle Explanation This invention is based on ADMM. First, we review the basic principles of ADMM, and then elaborate on the ADMM depth expansion DOA estimation method based on residual structure in this invention.

[0028] ADMM is a classic method for solving convex optimization problems. Its core idea is to decompose a complex optimization problem into multiple independently solvable subproblems, thereby significantly improving the solution efficiency. The algorithm's first... The next iteration update step can be represented as: (7) (8) (9) in, ( These are dual variables, i.e., Lagrange multipliers. It is a penalty parameter; Represents the soft threshold function. This is the threshold parameter. For any element of the input vector... Soft threshold function The definition is as follows (10) Note that the soft threshold function here is a generalized form for the complex field, therefore ,when The result was 0.

[0029] 3. Network Structure In traditional ADMM, the regularization parameter The penalty parameter of Lagrange It is usually a fixed, manually set scalar. Balancing sparsity and signal recovery error, The larger the value, the stronger the sparsity, but this may lead to the loss of effective signal components; conversely, a smaller value results in stronger sparsity. While it can improve data fitting accuracy, the regularization constraint is too weak to effectively suppress noise and results in insufficient sparsity. On the other hand, Controlling the update magnitude of the dual variable affects the convergence speed of ADMM. Too small a value may result in slow convergence. Excessive size may cause oscillations. However, in practical applications, a fixed value is preferable. and The algorithm struggles to adapt to signal variations across different snapshots, limiting its convergence speed and estimation accuracy. It can be observed that... Only used as a threshold parameter The update process of (8) is jointly participated in, so it can be fixed. Adjust on the basis This achieves the effect of adjusting the threshold while controlling the algorithm's update step size.

[0030] Based on this idea, the present invention maps the ADMM iterative optimization steps into a deep neural network in the proposed ResADMM-Net, and designs a hyperparameter prediction module to adaptively adjust the penalty parameters. To improve adaptability to different signal sparsity distributions, the deep neural network obtained by mapping the ADMM iterative optimization steps includes: constructing a deep neural network by cascading multiple identical unit blocks, with each unit block corresponding to one iterative solution step of the ADMM algorithm; adding a learnable hyperparameter prediction module between adjacent unit blocks to predict grid-level penalty parameters for data updates in the next unit block.

[0031] Unlike purely data-driven end-to-end DOA estimation methods, each cell block in the deep unfolded network of this invention corresponds to one iteration of the ADMM algorithm. The physical meaning of the parameters is clear, preserving the interpretability of the ADMM algorithm. The input is observation data. The output is the recovered sparse vector. First of all, Perform linear transformation (11) in, This represents the conjugate transpose of the dictionary matrix. This step maps the observed domain data to the sparse domain, serving as the initial features and bias inputs for the linear reconstruction of each layer of the network.

[0032] Figure 1 and Figure 2 These are schematic diagrams of the ADMM data flow and the ResADMM-Net data flow of this invention, respectively. The difference between this invention and the traditional ADMM algorithm is that ResADMM-Net... The first unit introduces a hyperparameter prediction module based on a one-dimensional residual structure. Its structure is as follows Figure 3 Show.

[0033] like Figure 3 As shown, this hyperparameter prediction module uses the magnitude of the intermediate variable in the current iteration. As input, the signal is passed through a first ordinary convolutional layer connected to a ReLU activation function, then connected to stacked residual blocks. The stacked residual blocks are then connected to a second ordinary convolutional layer and a Softplus activation function in sequence before being output, thus extracting multi-scale features of the incident signal's orientation.

[0034] like Figure 4The residual block structure shown includes: a first dilated convolutional layer connected to a ReLU activation function, followed by a second dilated convolutional layer. The output of the second dilated convolutional layer is added to the input of the residual block, and then passed through a ReLU activation function before being output. ResADMM-Net uses the same dilation rate within each residual block, while the dilation rate increases progressively between different residual blocks to detect signal changes within different ranges. Simultaneously, the residual connections allow each layer to perform incremental optimization based on existing features, resulting in output parameters that better match the current signal characteristics.

[0035] (12) Unlike traditional algorithms that use fixed scalars, ResADMM-Net outputs appropriate hyperparameter prediction modules for different input signals to the network. This is done to match the characteristics of the current signal, thereby accelerating the convergence of the ADMM algorithm.

[0036] Subsequent nonnegative parameter vector Continue to participate and The update. From formula (7), we can see... The update involves matrix inversion; if vectors are used directly... This would require calculating a different inverse matrix for each sample, resulting in a huge computational overhead. Therefore, using... mean (13) Construct a shared inverse matrix using this scalar. , making The update only requires one matrix inversion operation, which speeds up the forward inference and backward propagation processes.

[0037] (14) In the update step formula (8), the soft threshold function shrinks small-amplitude components. If the same threshold is applied to all signals or different positions of the same signal, it may lead to excessive signal shrinkage or inappropriate noise preservation. Therefore, the complete vector information output by the prediction module is used. For each angle on the frequency grid Both provide adaptive parameters (i.e., grid-level hyperparameter prediction), combined with Applying soft thresholding to the signal grid by grid acts as a filter, reducing noise while preserving the target signal.

[0038] (15) (16) In this process, for potential signal directions, the network tends to predict larger ones. (i.e., a smaller threshold to protect signal components from excessive contraction, or according to...) (Value adjustment), while for noisy regions, the prediction is smaller. In order to suppress the impact of noise in the area.

[0039] 4. Simulation Experiment A multi-source signal simulation dataset was constructed for the DOA estimation task of SLA. The dataset includes a training set and a validation set, both of which are generated based on array signals to simulate the scenario of far-field narrowband signals incident on a sensor array.

[0040] Parameters are set to , For each data sample, randomly generate There are multiple signal sources, each with a uniformly distributed amplitude and phase, thus constructing a multi-source signal scene with random intensity and phase. Complex Gaussian white noise is then superimposed, and the standard deviation of the noise is calculated based on a predetermined signal-to-noise ratio (SNR). (17) in, This is the average power of the signal. In the training and validation sets, the SNR is fixed at 15dB to ensure training stability; in the test set, the SNR value is... dB.

[0041] To construct the overcomplete dictionary required for the sparse recovery task , range of angles Discretize into To construct ground truth data for supervised learning, a nearest neighbor mapping strategy is adopted, which maps the generated continuous frequencies to the grid points in the discrete dictionary grid that have the closest Euclidean distance to them, thereby generating sparse label vectors.

[0042] The final dataset contains 120,000 samples, which are randomly divided into a training set (100,000 samples) and a validation set (20,000 samples) in a 5:1 ratio. The test set generates 1,000 samples for different SNRs, for a total of 7,000 test samples, to evaluate the model's generalization performance.

[0043] For network training, the Adam optimizer was used to update the model parameters, and the learning rate was set to [value missing]. The total number of training epochs is set to 30, the batch size is set to 512, and the optimization objective of the network is to minimize the normalized mean squared error loss function, which is specifically defined as: (18) in , It refers to the batch size. and They represent the first The estimated signal and the true signal of a sample.

[0044] To evaluate the performance of the proposed ResADMM-Net method, two representative algorithms were selected as benchmarks for comparison: the traditional iterative algorithm ADMM and data-driven deep unfolded networks, including LISTA, ISTA-Net, ADMM-Net, and THADMM-Net. The number of layers in ResADMM-Net, LISTA, ISTA-Net, ADMM-Net, and THADMM-Net was set to 20, and a comparative analysis was performed with the traditional ADMM algorithm after 200 iterations.

[0045] Figures 5(a) to 5(f) show the estimated spectra obtained using the ResADMM-Net, ADMM-Net, THADMM-Net, ADMM, ISTA-Net, and LISTA methods respectively, when the SNR is 15dB.

[0046] Figures 5(a) to 5(f) show the estimation results for the same test sample with an SNR of 15dB. The red crosses in the figures represent the location and amplitude information of the real signal sources. It can be observed that, except for ResADMM-Net and ADMM which can detect all signal sources, other methods miss some targets. However, there is significant noise around the true spectral peak in the ADMM result graph, indicating that the ADMM algorithm is highly susceptible to noise and prone to high false alarm rates in practical applications. LISTA's estimated spectrum perfectly suppresses noise, but it also misclassifies and filters out sources with lower amplitude and weaker energy as noise, leading to missed detections of small signals. Although ISTA-Net's estimated spectrum does not filter out small signals as noise, its peak value is significantly suppressed. In contrast, ResADMM-Net's estimated spectrum achieves the detection of all real signal sources while effectively suppressing noise interference.

[0047] The following section provides a quantitative analysis of the method's computational efficiency, detection rate, precision, and estimation accuracy. The set of real information sources is denoted as... ,in For the first Spectrum index of a real source, Its corresponding amplitude value, The estimated set of sources is denoted as the actual number of sources. ,in For the first Spectral index of an estimated information source For its corresponding amplitude, To estimate the total number of sources (only signals with amplitudes above a threshold of 0.04 are retained). For real sources... If an estimated source of information exists satisfy ( (for grid index threshold) and the magnitude satisfies ( If the amplitude threshold is used, then the determination is made. and The estimated source matches only one real source.

[0048] On the same hardware platform (Intel Core i5 and NVIDIA GeForce RTX 5060) and software environment (Python 3.12.8, Pytorch 2.7.0+cu128), 200 Monte Carlo simulation experiments were performed. For 7000 samples in the test set, the average time required for each algorithm to complete one full signal recovery was calculated. The results are shown in Table 1.

[0049] Table 1 Comparison of Algorithm Computation Time

[0050] Among them, LISTA and ADMM-Net are the fastest (<1 second), mainly because they pre-convert the high-complexity online matrix operations (such as matrix inversion and Gram matrix multiplication) in traditional iterative optimization into a learnable fixed linear layer mapping shared by each layer. Although this static structure greatly improves the computation speed, it ignores the distribution differences between samples.

[0051] In contrast, while ResADMM-Net introduces additional inference computation (4.75s), this overhead is used to support the hyperparameter prediction module's adaptive prediction of grid-level parameters for each sample. This design gives the network stronger physical interpretability and enables it to adapt to the feature differences of different samples with only about 1 / 3 the time required by the traditional ADMM algorithm, achieving higher detection rates and accuracy while ensuring interpretability and computational efficiency.

[0052] The detection rate is used to measure the algorithm's ability to correctly identify real sources, and is defined as the number of successfully matched real sources. Total number of real sources The ratio: (19) like Figure 6As shown, for the estimation of a single snapshot, the method proposed in this invention has a higher detection rate than other comparative algorithms when the SNR is above 10dB, while the detection rates of ISTA-Net and LISTA are only below 0.85.

[0053] Precision measures the degree to which an algorithm does not misidentify false sources, and is defined as the number of correctly matched sources. Compared with the estimated total number of information sources The ratio: (20) like Figure 7 As shown, the accuracy of the traditional ADMM algorithm is relatively low because it is greatly affected by noise and will calculate the noise during the iteration process. However, the method proposed in this paper has a good effect on noise smoothing. Thanks to the grid-level hyperparameter prediction, it can effectively suppress background interference unrelated to the signal source based on the signal characteristics, and verify the effectiveness of the model in extracting sparse features in noisy environments.

[0054] To quantify the accuracy of the algorithm's amplitude and angle estimations, we used... and Measuring the incident amplitude and angle of the true source (normalized to) The deviation between the frequency domain value and the estimated value. In this context, a penalty of zero estimated amplitude (squared deviation) is imposed on unmatched real sources. ),exist In this process, an index threshold is applied to unmatched real information sources. The normalized squared deviation.

[0055] (twenty one) . (twenty two) Finally, calculate according to the RMSE calculation method. (twenty three) . (twenty four) Figure 8(a) shows the relationship between amplitude RMSE and SNR using the method of the specific embodiment of the present invention and other methods; Figure 8(b) shows the relationship between angle RMSE and SNR using the method of the specific embodiment of the present invention and other methods. As can be seen from Figures 8(a) and 8(b), under different SNR conditions, the ResADMM-Net proposed in this invention outperforms the traditional ADMM algorithm and depth unfolding comparison methods such as LISTA, ISTA-Net, and ADMM-Net in both amplitude and angle estimation accuracy, verifying the effectiveness of the parameter adaptive mechanism based on the residual structure.

[0056] Accordingly, a specific embodiment of the present invention also provides a high-resolution target detection device based on a deep unfolded network, characterized in that it includes: A sensor array used to receive incident signals from space; The data acquisition module is used to acquire the output data of the sensor array; A memory for storing the data and computer programs; A processor is used to execute the computer program to implement the steps of the above-described high-resolution target detection method.

[0057] The present invention also provides a computer-readable storage medium, characterized in that it includes a stored computer program, which can be executed by a processor to implement the steps of the above-described high-resolution target detection method.

[0058] From the detailed description of the above specific embodiments, the key points of the present invention can be clearly understood as follows: 1. Figure 2 Data flow modeling in the ADMM deep unfolded network structure is shown.

[0059] 2. Figure 3 The hyperparameter prediction module structure design is shown.

[0060] 3. Grid-level hyperparameter prediction method based on formula (12).

[0061] 4. In formula (13), the mean of the penalty parameter vector is used to construct a globally shared inverse matrix.

[0062] As can be seen from the above detailed description of the present invention, the significant technical effects of the present invention include at least: Compared with existing technologies, this invention introduces a hyperparameter prediction module based on residual structure, eliminating the dependence on the initial value of the penalty parameter and achieving grid-level dynamic prediction and adaptive control of the penalty parameter. This effectively overcomes the limitations of slow convergence and poor adaptability to noisy environments while accurately estimating the source incidence angle. Experimental results show that, with a computation time only about one-third that of the traditional ADMM algorithm, this network outperforms traditional iterative algorithms and existing mainstream depth unfolding methods in key indicators such as detection rate, accuracy, and reconstruction accuracy, achieving a balance between performance and efficiency.

[0063] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A high-resolution target detection method based on a deep unfolded network, used to receive spatial incident signals through a sensor array, perform spatial spectrum estimation on the received signals, and then estimate the incident angle and intensity of the signal source, characterized in that, Includes the following steps: Step S1: Receive observation data from the array; Step S2: Input the observation data into the trained deep unfolding network; the deep unfolding network includes: a deep neural network obtained by mapping the ADMM iterative optimization steps, and a hyperparameter prediction module that provides penalty parameters for the unit blocks of the deep neural network obtained by each iterative optimization step; the hyperparameter prediction module adaptively adjusts the penalty parameters of each layer to improve the adaptability to different signal sparsity distributions; Step S3: The deep unfolding network outputs the recovered sparse vector, from which the source incident angle and intensity are obtained.

2. The high-resolution target detection method as described in claim 1, characterized in that, The hyperparameter prediction module includes a first ordinary convolutional layer connected to a ReLU activation function, then connected to stacked residual blocks, and the stacked residual blocks are then connected to a second ordinary convolutional layer and a Softplus activation function in sequence before outputting, which is used to extract multi-scale features of the incident signal orientation.

3. The high-resolution target detection method as described in claim 1, characterized in that, The residual block includes: a first dilated convolutional layer connected to a ReLU activation function and then connected to a second dilated convolutional layer; the output of the second dilated convolutional layer is added to the input of the residual block and then output after passing through a ReLU activation function.

4. The high-resolution target detection method as described in claim 1, characterized in that, The ADMM iterative optimization of the first The next iteration update step is represented as follows: , (7) , (8) , (9) in, It is an overcomplete dictionary built based on a discretized grid. It is observation data. It is the identity matrix. , It is a dual variable. It is a penalty parameter; Represents the soft threshold function. This is the threshold parameter.

5. The high-resolution target detection method as described in claim 4, characterized in that, The hyperparameter prediction module adaptively adjusts the penalty parameter of each layer using the following formula. : . (12) in, This indicates that the hyperparameter prediction module performs the operation. and This represents the output of the previous iteration step.

6. The high-resolution target detection method as described in claim 5, characterized in that, In formula (7) use mean : . (13) Where N represents the continuous spatial angular range Discretize into Grid points.

7. The high-resolution target detection method as described in claim 1, characterized in that, The deep neural network obtained by mapping the ADMM iterative optimization steps includes: constructing a deep neural network by cascading multiple identical unit blocks, with each unit block corresponding to one iterative solution step of the ADMM algorithm; adding a learnable hyperparameter prediction module between adjacent unit blocks to predict grid-level penalty parameters for data updates in the next unit block.

8. The high-resolution target detection method as described in claim 1, characterized in that, Training the deep unfolded network specifically includes the following steps: Construct a dataset containing multiple samples; Set the normalized mean squared error loss function, specifically defined as: , (18) in , It refers to the batch size. and They represent the first The estimated signal and the true signal of a sample; The total number of training rounds and batch size are set, and training is performed in an end-to-end manner. The optimization objective of training the network is to minimize the normalized mean square error loss function.

9. A high-resolution target detection device based on a deep unfolded network, characterized in that, include: A sensor array used to receive incident signals from space; The data acquisition module is used to acquire the output data of the sensor array; A memory for storing the data and computer programs; A processor for executing the computer program to implement the steps of the target high-resolution detection method as described in claim 1.

10. A computer-readable storage medium, characterized in that, It includes a stored computer program that can be executed by a processor to implement the steps of the target high-resolution detection method of claim 1.

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