Signal reconstruction method and device, electronic equipment and storage medium

Abstract

The invention relates to the technical field of signal processing, and provides a signal reconstruction method and device, electronic equipment and a storage medium, and the method comprises the steps: carrying out the sampling of a to-be-reconstructed signal based on a self-adaptive observation matrix, and obtaining an observation value of the to-be-reconstructed signal; performing signal reconstruction based on the dictionary and the observation value, and performing binarization processing on the reconstructed signal to obtain a current reconstruction signal; and updating each atom in the adaptive observation matrix and the dictionary and the weight of each atom based on the current reconstruction signal and the observation value, and iteratively carrying out signal sampling and signal reconstruction by applying the updated adaptive observation matrix and dictionary until an original binary sparse signal is obtained. According to the method, by introducing the adaptive observation matrix, the adaptive updating mechanism and binarization processing, the sparsity and the binary structure of the signal can be better adapted, and the reconstruction effect of the binary sparse signal is effectively optimized.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a signal reconstruction method, device, electronic equipment and storage medium. Background Art

[0002] Compressed sensing (CS) technology breaks through the traditional Nyquist sampling theorem by effectively reconstructing sparse signals with a small amount of sampled data. This significantly reduces data acquisition and storage costs, making it a powerful approach to reconstructing high-dimensional sparse signals. With the increasing application of binary sparse signals in fields such as image compression and digital communications, CS technology continues to advance. Unlike traditional sparse signals, binary sparse signals have a strictly binary structure (for example, 0 and 1, or -1 and 1). This property reduces computational complexity and storage requirements in signal processing.

[0003] However, the reconstruction of binary sparse signals faces many challenges. Although there are currently a variety of technical solutions for sparse signal reconstruction, these solutions generally have problems such as insufficient processing capabilities for binary sparse signals, high computational complexity, and unsatisfactory reconstruction accuracy. Summary of the Invention

[0004] The present invention provides a signal reconstruction method, device, electronic device and storage medium to solve the defects of existing signal reconstruction methods, such as insufficient processing capability for binary sparse signals, high computational complexity and unsatisfactory reconstruction accuracy.

[0005] The present invention provides a signal reconstruction method, comprising: Sampling the signal to be reconstructed based on the adaptive measurement matrix to obtain an observation value of the signal to be reconstructed; Reconstructing the signal based on the dictionary and the observation value, and binarizing the reconstructed signal to obtain a current reconstructed signal; Based on the current reconstructed signal and the observation value, the adaptive measurement matrix and each atom and the weight of each atom in the dictionary are updated, and the updated adaptive measurement matrix and dictionary are applied to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0006] According to a signal reconstruction method provided by the present invention, updating the adaptive measurement matrix and each atom and the weight of each atom in the dictionary based on the current reconstructed signal and the observation value includes: Determining a current signal residual based on the current reconstructed signal and the observation value; updating the adaptive measurement matrix based on the current reconstructed signal or the current signal residual to obtain an updated adaptive measurement matrix; Based on the current signal residual and the current reconstructed signal, each atom and the weight of each atom in the dictionary are updated to obtain an updated dictionary.

[0007] According to a signal reconstruction method provided by the present invention, updating the adaptive measurement matrix based on the current reconstructed signal or the current signal residual includes: Updating the adaptive measurement matrix based on at least one of an entropy value, sparsity, time domain characteristics, and frequency domain characteristics of the current reconstructed signal; Alternatively, based on the current signal residual, a reinforcement learning algorithm is applied to update the adaptive measurement matrix.

[0008] According to a signal reconstruction method provided by the present invention, the method updates each atom and the weight of each atom in the dictionary based on the current signal residual and the current reconstructed signal to obtain an updated dictionary, including: Selecting target atoms from the atoms in the initial dictionary based on similarities between the current signal residual and atoms in an initial dictionary, and using the target atoms as atoms in the updated dictionary, wherein the atoms in the initial dictionary are pre-learned based on binary characteristics of the signal; The weight of each atom in the dictionary is updated based on the current signal residual and the current reconstructed signal.

[0009] According to a signal reconstruction method provided by the present invention, the signal reconstruction based on the dictionary and the observation value includes: Based on low-rank matrix approximation technology, the sparsity and structure of the signal are utilized to perform low-rank decomposition on the observation value, and the observation value obtained by the decomposition and the dictionary are used to reconstruct the signal.

[0010] A signal reconstruction method provided by the present invention further includes: During each iteration, based on the current reconstructed signal and the observation value, a current signal residual and residuals of different regions of the current signal are determined; Adjusting a sampling rate of the adaptive measurement matrix based on the current signal residual; Based on the residuals of different regions of the current signal, computing resources for different regions of the signal are adjusted and allocated.

[0011] According to a signal reconstruction method provided by the present invention, sampling a signal to be reconstructed based on an adaptive observation matrix to obtain an observation value of the signal to be reconstructed includes: Performing multi-scale decomposition on the signal to be reconstructed to obtain signals of each scale, and sampling the signals of each scale based on an adaptive measurement matrix to obtain observation values of the signals of each scale; The signal reconstruction based on the dictionary and the observation value, and binarization processing of the reconstructed signal to obtain the current reconstructed signal, includes: Performing signal reconstruction and binarization processing based on the dictionary and the observation values of the signals at each scale to obtain current reconstructed signals at each scale; The method includes updating the adaptive measurement matrix and each atom in the dictionary and the weight of each atom based on the current reconstructed signal and the observation value, and applying the updated adaptive measurement matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained, including: Based on the current reconstructed signals at each scale and the observation values at each scale, the adaptive measurement matrix and each atom and the weight of each atom in the dictionary are updated, and the updated adaptive measurement matrix and dictionary are applied to iteratively perform signal sampling and signal reconstruction at each scale until a reconstruction result at each scale is obtained; The reconstruction results of each scale are fused to obtain the original binary sparse signal.

[0012] The present invention also provides a signal reconstruction device, comprising: A sampling unit, configured to sample the signal to be reconstructed based on an adaptive measurement matrix to obtain an observation value of the signal to be reconstructed; a reconstruction unit, configured to reconstruct a signal based on a dictionary and the observation value, and perform binarization processing on the reconstructed signal to obtain a current reconstructed signal; An iterative unit is used to update the adaptive measurement matrix and each atom in the dictionary and the weight of each atom based on the current reconstructed signal and the observation value, and apply the updated adaptive measurement matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0013] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor implements any of the above-mentioned signal reconstruction methods when executing the computer program.

[0014] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which implements any of the above-mentioned signal reconstruction methods when executed by a processor.

[0015] The present invention also provides a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the signal reconstruction method described above is implemented.

[0016] The signal reconstruction method, device, electronic device and storage medium provided by the present invention are updated by updating the atoms and the weights of the atoms in the adaptive measurement matrix and dictionary based on the current reconstructed signal and observation value. This adaptive mechanism helps to match the signal characteristics more accurately, adapt to the sparsity and binary structure of the signal, thereby improving the accuracy of signal reconstruction. Moreover, in each iterative process, based on the current reconstructed signal and observation value, the atoms and the weights of the atoms in the dictionary are updated, and the updated dictionary is applied to reconstruct the signal. This belongs to the application of the adaptive matching pursuit algorithm, which can dynamically adjust the matching process according to the signal characteristics, further improving the reconstruction effect. In addition, the present invention introduces an adaptive measurement matrix and an adaptive matching pursuit algorithm, and binarizes the reconstructed signal after each iteration so that it still maintains the binary characteristics, effectively optimizing the reconstruction effect of the binary sparse signal, and can better restore the original binary sparse signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the present invention or related technologies, the following is a brief introduction to the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0018] Figure 1 This is one of the flow charts of the signal reconstruction method provided by the present invention; Figure 2 This is one of the flowcharts of a specific embodiment of the signal reconstruction method provided by the present invention; Figure 3 This is the second flowchart of a specific embodiment of the signal reconstruction method provided by the present invention; Figure 4 This is the second flow chart of the signal reconstruction method provided by the present invention; Figure 5 It is a structural schematic diagram of the signal reconstruction device provided by the present invention; Figure 6 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0019] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0020] Compressed sensing (CS) is a signal reconstruction method that breaks through the traditional Nyquist sampling theorem, effectively recovering sparse signals using only a small amount of sampled data. The core concept of CS is that for sparse signals (i.e., signals where most elements in a given basis or dictionary are zero), the characteristics of the original signal can be recovered using only a small amount of linear measurement data, significantly reducing the cost of data acquisition and storage.

[0021] Traditional signal processing techniques often require a large number of sampling points during signal recovery, each of which must provide useful information, limiting their efficiency and applicability. Compressed sensing, by leveraging the sparsity of sampled data, effectively reduces the amount of data required for signal recovery, making it a powerful tool for addressing high-dimensional sparse signal recovery. By effectively leveraging signal sparsity, compressed sensing can significantly reduce redundant data and improve the efficiency of data transmission and storage.

[0022] Assuming a signal is sparse in a certain basis, meaning it has only a few non-zero elements, the goal of compressed sensing is to extract these sparse elements from a small amount of measurement data, thereby restoring the signal's original appearance. However, in many practical applications, signals are not only sparse but may also have a specific binary structure. Binary sparse signals typically refer to signals that can only take on two discrete values within a specific range (for example, 0 and 1, or -1 and 1). Such signals have a wide range of applications in specific fields, such as image binarization, binary image compression, and binary signal coding in digital communications.

[0023] Traditional sparse signals have only a few nonzero elements, which are typically continuous real numbers. However, the key difference between binary sparse signals and traditional sparse signals is that their nonzero elements are no longer continuous real numbers but are constrained to two discrete values. Specifically, the nonzero portion of a binary sparse signal (the portion of the signal that carries actual semantic information) is strictly restricted to two discrete values (such as 0 or 1). For example, in the context of switching signals, indicator signals, or coded signals, the nonzero portion is set to 0 or 1, where "0" represents the off state and 1 represents the on state. This binary constraint of binary sparse signals can significantly reduce computational complexity and storage requirements during signal processing. However, because such signals often have a clear structure or pattern, their reconstruction under sparsity constraints can be more complex than typical sparse signal recovery problems and requires specialized processing methods.

[0024] Currently, there are many technical solutions dedicated to the recovery and reconstruction of sparse signals, but these solutions generally have problems such as insufficient processing capabilities for binary sparse signals, high computational complexity, or unsatisfactory recovery accuracy. For example, traditional sparse signal reconstruction methods based on L1 norm optimization, Bayesian inference, and dictionary learning, although they can effectively recover sparse signals, are unable to model the characteristics of binary signals well. This results in the binary structure of the signal often not being effectively maintained when reconstructing binary sparse signals, resulting in deviations in the recovery results and reduced accuracy. For another example, signal reconstruction methods based on deep learning, although they have shown strong capabilities in signal recovery, require a large amount of training data and computing resources for training, which is often difficult to meet in practical applications, especially when data is limited or computing resources are restricted. Moreover, for binary sparse signals, existing deep learning methods are usually unable to fully capture their binarization constraints, resulting in unsatisfactory signal recovery results.

[0025] To address this issue, the present invention provides a binary sparse signal reconstruction method based on an adaptive matching pursuit algorithm, combined with an energy optimization mechanism, to address the limitations of existing solutions in binary sparse signal recovery, improve signal recovery efficiency, optimize computing resource allocation, and ensure accurate reconstruction of binary characteristics, thereby overcoming the aforementioned shortcomings. The method provided by the present invention can significantly improve the accuracy and efficiency of binary sparse signal recovery in practical applications such as image processing and digital communications, providing new ideas and methods for the development of efficient signal processing technology.

[0026] It is understandable that the Adaptive Matching Pursuit (AMP) algorithm is an efficient algorithm for sparse signal reconstruction. Unlike the traditional Matching Pursuit (MP) algorithm, the AMP algorithm can more effectively reconstruct binary sparse signals by introducing improved strategies such as residual weighted update, binarization constraint and dynamic dictionary selection. Here, residual weighted update refers to the way of affecting residual calculation and update by dynamically adjusting the weights of dictionary atoms in each iteration; binarization constraint refers to binarizing the reconstructed signal after each iteration to ensure that the reconstructed signal always maintains binary characteristics; dynamic dictionary selection refers to dynamically selecting dictionary atoms according to the characteristics of the current signal residual at each iteration to better adapt to the sparsity and structure of the signal. The technical solution provided by the present invention will be introduced in detail below.

[0027] It's important to note that compressed sensing reconstruction of binary sparse signals can be applied in many fields. For example, in image compression, pixel values can be converted into a binary image through a transformation (such as thresholding), and then compressed and encoded using a sparse representation. Furthermore, in digital communications, transmitted signals are often represented as binary signals, so they can be reconstructed as binary sparse signals.

[0028] Figure 1 This is one of the flow charts of the signal reconstruction method provided by the present invention, such as Figure 1 As shown, the method includes: Step 110: sampling the signal to be reconstructed based on the adaptive measurement matrix to obtain an observation value of the signal to be reconstructed.

[0029] It should be noted that the signal to be reconstructed refers to a binary sparse signal that was originally complete but, due to various reasons (such as data transmission, storage limitations, or the sampling process), has become incomplete or needs to be restored from a compressed form. For example, the signal to be reconstructed can be a binary sparse image signal. This is the target signal that needs to be restored to its original form through subsequent sampling and reconstruction steps. Its non-zero portion (i.e., the portion of the signal that contains actual semantic information) is typically 0 or 1.

[0030] An adaptive measurement matrix refers to a matrix used for compressive sampling of the signal to be reconstructed. Unlike the traditional randomly generated compressed sensing measurement matrix, the adaptive measurement matrix in the embodiment of the present invention takes into account the binary structure of the binary sparse signal. While having a certain degree of randomness in design to avoid interfering with the sparse structure of the signal, it is also optimized for the characteristics of the binary sparse signal to ensure that no excessive errors are generated during the reconstruction process. It should be understood that the initial setting of the adaptive measurement matrix can be obtained by random initialization or initialization based on prior knowledge of the signal. After the initial setting is completed, the adaptive measurement matrix can be applied to sample the signal. In the subsequent iterative optimization process, the adaptive measurement matrix will be dynamically adjusted and updated according to the characteristics of the signal and the feedback information in the reconstruction process to better adapt to the binary sparsity characteristics of the signal and improve the accuracy and efficiency of signal reconstruction.

[0031] Specifically, the adaptive measurement matrix can be used to sample the signal to be reconstructed to obtain the observation value of the signal to be reconstructed. Here, the observation value refers to the result obtained after sampling the signal to be reconstructed using the adaptive measurement matrix. It is a low-dimensional vector that contains the main information of the signal to be reconstructed, but its dimension is much lower than that of the original signal. Due to the sparsity of the signal, although the dimension of the observation value is low, in theory, the original binary sparse signal can still be effectively restored from the observation value through an appropriate reconstruction algorithm. In the reconstruction process, the observation value is used as a known condition together with information such as a dictionary to solve the most sparse signal that satisfies the binary characteristics.

[0032] Specifically, signal sampling can be achieved by linearly combining the adaptive measurement matrix with the signal to be reconstructed. Assume that the current adaptive measurement matrix is , the signal to be reconstructed is , then the sampling process can be expressed as ,in is the observation value obtained by the current sampling.

[0033] Step 120 : reconstruct the signal based on the dictionary and the observation value, and perform binarization processing on the reconstructed signal to obtain the current reconstructed signal.

[0034] It should be noted that a dictionary is a set of basis vectors or atoms used for sparse signal representation. In the context of binary sparse signal reconstruction, the elements in the dictionary can effectively represent the sparse structure of the target signal. It provides a complete or overcomplete library of basis functions for sparse signal decomposition, allowing the signal to be represented as a linear combination of a small number of atoms in the dictionary. For example, in image processing, the dictionary can be a set of various image patches (such as edges, textures, and other features), and these atoms can effectively represent local image features.

[0035] Specifically, to effectively apply compressed sensing to recover binary sparse signals, it is first necessary to construct a sparse dictionary tailored to the signal's characteristics. The elements in this dictionary should be able to well represent the sparse structure of the target signal. Each element in the dictionary is called an atom. Atoms are the basic building blocks of the dictionary and have specific structures and characteristics. In a binary sparse signal, each non-zero element corresponds to one or more atoms in the dictionary. These atoms are the basic building blocks of signal decomposition. By selecting appropriate combinations of atoms, the original signal can be approximately represented. For example, in speech signal processing, atoms can be sine or cosine waves of different frequencies, and by combining these atoms, the speech signal can be reconstructed.

[0036] The weight of each atom refers to the coefficient corresponding to the linear combination of each atom in the dictionary. These weights represent the importance or contribution of each atom in representing the signal. In binary sparse signals, since the non-zero part of the signal (that is, the part of the signal with actual semantic information) is usually 0 or 1, the coefficient of each signal in the dictionary can only be 0 or 1, that is, the weight of the atom can usually only be 0 or 1. In other words, the non-zero part of the signal can only be represented by a few atoms in the dictionary with a specific weight combination. For example, if a signal can be represented as s =1× a 1+0× a 2+1× a 3, among which a 1. a 2. a 3 is the atom in the dictionary, and 1, 0, 1 are the corresponding weights.

[0037] Specifically, once the initial dictionary is constructed, it can be applied to the observed values for initial signal reconstruction. For example, an adaptive matching pursuit algorithm can be used to select the atoms from the dictionary that are most correlated with the current signal residual, and then update the signal estimate. Here, during the initial iteration, the current signal residual (i.e., the initial residual) is the observed value, while in subsequent iterations, the current signal residual is determined based on the current reconstructed signal and the observed value. During each iteration, the algorithm selects the atom that is most correlated with the current signal residual based on the similarity between the current signal residual and each atom in the dictionary, as well as the similarity between each atom. The signal estimate is then updated based on this atom and the observed value, and a new signal residual is calculated.

[0038] In addition, in traditional signal reconstruction methods, there are usually no clear binarization constraints, which means that the reconstructed signal may contain some floating values close to zero, thereby losing the characteristics of a binary sparse signal. In order to ensure that the reconstructed signal strictly complies with the binarization constraints, an embodiment of the present invention proposes to binarize the reconstructed signal after each iteration so that all coefficients of the reconstructed signal are strictly limited to 0 or 1, thereby obtaining a current reconstructed signal that is more in line with the binary characteristics. For example, this binarization process can be achieved by a hard thresholding method, that is, for each reconstructed signal element, if its value is greater than a certain threshold, it is set to 1, otherwise it is set to 0. For another example, a soft thresholding method can also be introduced to make the signal transition smoother near 0, but still maintain the binary characteristics.

[0039] It can be understood that the current reconstructed signal refers to the signal estimate obtained after each iteration of the signal reconstruction process. It is the intermediate result obtained by reconstructing the signal using the observations based on the current adaptive observation matrix, dictionary, and reconstruction algorithm. For example, when the signal to be reconstructed is a binary sparse image signal, the current reconstructed signal is the reconstructed image obtained at each iteration. As the iteration process progresses, the current reconstructed signal will continuously approach the original binary sparse signal until the stopping condition is met, at which point the current reconstructed signal becomes the final reconstructed signal.

[0040] Step 130, based on the current reconstructed signal and observation value, the atoms and the weights of the atoms in the adaptive measurement matrix and dictionary are updated, and the updated adaptive measurement matrix and dictionary are applied to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0041] Specifically, in each iteration, the current signal residual can be calculated based on the current reconstructed signal and the observed value. The specific calculation formula is as follows: in, The current signal residual represented by iterations), represents the observation value of the current iteration, represents the current adaptive observation matrix (updated with iteration), Indicates the current reconstruction signal, Represents the current dictionary (updated with iteration), Represents the weight of the current dictionary atom (that is, the current sparse coefficient).

[0042] Based on the current signal residual, an optimization algorithm (such as gradient descent) is used to adjust the elements of the adaptive measurement matrix, allowing subsequent sampling to better capture the key signal features and reduce information loss. Alternatively, some signal characteristics (such as entropy, sparsity, and time-frequency characteristics) can be obtained based on the current reconstructed signal and incorporated into the measurement matrix update process to obtain an updated adaptive measurement matrix.

[0043] Similarly, during each iteration, the dictionary update process can be guided by the current signal residual and the current reconstructed signal, thereby improving the accuracy of signal recovery and reconstruction. Specifically, each atom in the dictionary can be replaced or adjusted based on the current signal residual. For example, atoms in the dictionary with low similarity to the current signal residual can be replaced with atoms that more accurately represent the signal characteristics. This can be achieved by learning new atoms from a large number of samples using a learning algorithm, or by using mathematical methods (such as principal component analysis and singular value decomposition) to generate new atoms based on the characteristics of the current reconstructed signal. For another example, existing atoms in the dictionary can be fine-tuned to change their shape, orientation, and other features to better adapt them to the current signal. For example, in image processing, the texture characteristics of atoms can be adjusted to better match the local characteristics of the image.

[0044] The weights of each atom in the dictionary can be updated based on the current signal residual and the current reconstructed signal. For example, for the parts of the current reconstructed signal that are close to zero (i.e., the parts of the signal that do not have actual semantic information), the weights can be adjusted to be smaller, thereby reducing the impact of these parts on signal reconstruction; on the contrary, for the non-zero parts of the signal (i.e., the important parts), the weights can be increased to make the reconstruction of this part of the signal more accurate. In an embodiment of the present invention, by adjusting the weights of each part of the signal during each iteration, that is, giving a larger weight to the non-zero part of the signal, the accuracy and efficiency of signal reconstruction can be effectively improved, while reducing the interference of the parts close to zero. This weight update mechanism is particularly suitable for signal reconstruction tasks with local structural features (such as binary features) and can more accurately restore key information.

[0045] After completing the update of the adaptive matrix and dictionary, a new iterative process can be entered. Specifically, the updated adaptive observation matrix can be used to sample the signal to be reconstructed to obtain new observation values. The signal is reconstructed based on the updated dictionary and the new observation values, and the reconstructed signal is binarized to obtain a new current reconstructed signal. Based on the new current reconstructed signal and the new observation values, a new current signal residual is determined. It is then determined whether the residual is less than a preset threshold or whether the preset maximum number of iterations has been reached. If the stopping condition is met, the iteration ends, and the final reconstructed signal (i.e., the original binary sparse signal) is obtained. Otherwise, the process returns to the signal sampling step and continues to the next iteration (i.e., repeating steps 110 and 120 above).

[0046] It can be understood that a raw binary sparse signal refers to a complete, unprocessed signal whose non-zero portion (i.e., the portion of the signal containing actual semantic information, or the important portion) can only be 0 or 1. For example, in image processing, a raw binary image signal can be an image composed of pixels with values of 0 (black) and 1 (white); in digital communications, a transmitted binary signal (such as a bit stream composed of 0s and 1s) can also be considered a raw binary sparse signal.

[0047] The method provided by the embodiment of the present invention updates the atoms and weights of the adaptive measurement matrix and dictionary based on the current reconstructed signal and observation value. This adaptive mechanism helps to match the signal characteristics more accurately, adapt to the sparsity and binary structure of the signal, and thus improve the accuracy of signal reconstruction. Moreover, in each iteration, based on the current reconstructed signal and observation value, the atoms and weights of the dictionary are updated, and the updated dictionary is applied to reconstruct the signal. This is an application of the adaptive matching pursuit algorithm, which can dynamically adjust the matching process according to the signal characteristics, further improving the reconstruction effect. In addition, the present invention introduces an adaptive measurement matrix and an adaptive matching pursuit algorithm, and binarizes the reconstructed signal after each iteration so that it still maintains the binary characteristics, effectively optimizing the reconstruction effect of the binary sparse signal, and can better restore the original binary sparse signal.

[0048] Based on the above embodiments, Figure 2 FIG. 1 is a flow chart of a specific embodiment of the signal reconstruction method provided by the present invention. Figure 2 As shown, the method includes: Step 210: sampling the signal to be reconstructed based on the adaptive measurement matrix to obtain an observation value of the signal to be reconstructed; Step 220: reconstruct the signal based on the dictionary and the observation value, and perform binarization processing on the reconstructed signal to obtain the current reconstructed signal; Specifically, during each iteration, the current adaptive observation matrix can be used to sample the signal to be reconstructed to obtain the current observation value. The signal is then reconstructed based on the current observation value and the dictionary, and the reconstructed signal is binarized to obtain the current reconstructed signal. It should be noted that the specific implementation of steps 210 and 220 can refer to the specific implementation of steps 110 and 120 in the above embodiment and will not be repeated here.

[0049] Step 230, based on the current reconstructed signal and the observation value, determine the current signal residual; according to the current reconstructed signal or the current signal residual, update the adaptive measurement matrix to obtain an updated adaptive measurement matrix; according to the current signal residual and the current reconstructed signal, update each atom and the weight of each atom in the dictionary to obtain an updated dictionary; apply the updated adaptive measurement matrix and the updated dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0050] Specifically, in binary sparse signal reconstruction, the current signal residual is a key indicator to measure the difference between the current reconstructed signal and the observed data, which is obtained by With the current reconstruction signal Through the observation matrix The error between the projections is calculated to drive the iterative optimization of the algorithm.

[0051] Furthermore, in step 230, the adaptive measurement matrix is updated based on the current reconstructed signal or the current signal residual, including: updating the adaptive measurement matrix based on at least one of the entropy, sparsity, time domain characteristics, and frequency domain characteristics of the current reconstructed signal; Alternatively, based on the current signal residual, a reinforcement learning algorithm is applied to update the adaptive observation matrix.

[0052] It should be noted that the initial setting of the adaptive measurement matrix can use a random matrix as a starting point. For example, initially, a random matrix that conforms to a standard normal distribution can be used as the measurement matrix. The advantage of this method is that it is highly random and can effectively meet the RIP (Restricted Isometry Property) condition, thereby ensuring that the signal can be effectively reconstructed. For another example, in some specific application scenarios, a binary matrix (with elements of ±1 or 0 and 1) can be used as the measurement matrix for initialization. For another example, a random matrix with elements following a uniform distribution can also be selected, especially for applications that require a more constrained matrix structure. The choice of these initialization methods generally depends on the experimental context, signal characteristics, and the actual needs of the system.

[0053] Furthermore, if the structure or sparsity of the signal is known, the initial measurement matrix can be set based on this prior knowledge. For example, in some applications, the sparsity of the signal or certain characteristics (such as frequency domain characteristics or time domain characteristics) are known. In this case, a matrix that matches the signal structure can be used for initialization. If the signal has a certain block structure (such as local stationarity in an image), this structure can be exploited to design the initial measurement matrix. For example, a block-sparse measurement matrix can be designed to simulate the local structure of the signal.

[0054] After the initial setup is complete, the adaptive measurement matrix enters the optimization phase. Specifically, the measurement matrix is dynamically adjusted based on the signal reconstruction error after each reconstruction round (i.e., the current signal residual). The following describes how the adaptive measurement matrix is dynamically updated.

[0055] For example, to improve recovery accuracy, an information-theoretic approach can be used to design an adaptive measurement matrix. Specifically, after each iteration, by calculating the entropy, mutual information, or other information metrics of the currently reconstructed signal, the structure and parameters of the measurement matrix are automatically adjusted to better match the sparsity and binary characteristics of the target signal. This effectively improves data acquisition efficiency in compressed sensing and reduces redundant measurements, while maximally preserving the binary nature of the signal.

[0056] For example, to further enhance the effectiveness of binary sparse signal recovery, a sparsity-guided measurement matrix optimization algorithm can be employed. After each iteration, by analyzing the sparse distribution of the currently reconstructed signal, the measurement matrix can be customized based on the signal's sparsity pattern. Optimization methods with sparsity constraints are then used to dynamically update the elements of the measurement matrix, ensuring that key signal information is preserved as much as possible during the compression process. In other words, by introducing sparsity constraints into the design of the measurement matrix, the measurement matrix not only captures the global characteristics of the signal but also focuses on the signal's "non-zero elements," thereby improving the accuracy and efficiency of signal recovery.

[0057] For example, a multi-level optimization algorithm can be designed to adaptively select appropriate measurement matrix combinations based on the different signal characteristics of the current reconstructed signal (such as signal sparsity, time domain characteristics, and frequency domain characteristics). This algorithm then adjusts the combination to improve the accuracy and stability of signal reconstruction. This approach uses different levels of measurement matrix combinations to observe and sample the signal from multiple angles at different scales. This allows for capturing the signal from multiple dimensions, both globally and locally. This significantly improves the effectiveness and quality of the measurement matrix, particularly for recovering details from binary sparse signals.

[0058] For another example, reinforcement learning can be incorporated into the design of the measurement matrix. By training a proxy model, the parameters of the measurement matrix are continuously adjusted based on feedback from the current reconstructed signal and reconstruction error. Specifically, each element of the measurement matrix is gradually optimized using a reinforcement learning strategy, resulting in an optimal matrix design that maximizes signal recovery accuracy.

[0059] For example, by leveraging the structural characteristics of graph neural networks, it is possible to design a measurement matrix based on these networks. By treating the measurement matrix as a graph structure, the graph neural network can automatically optimize the sampling weights of each node through message passing and learning between nodes, thereby improving the performance of the measurement matrix. This approach effectively captures the dependencies and structural characteristics of the signal, providing more flexible and precise matrix design, and ensuring that key signal information is preserved to the greatest extent possible during the sampling process.

[0060] In addition, a multimodal measurement matrix integration strategy can be used to dynamically adjust the measurement matrix. Signals often have multiple modes (for example, time, frequency, and spatial domains), and a single measurement matrix may not be able to fully capture all of the signal's characteristics. Therefore, a multimodal measurement matrix integration strategy is proposed. This involves simultaneously observing and sampling from multiple modalities or multiple signal processing domains, fusing the measurement matrices of each modality to form a multimodal measurement matrix combination. This integration strategy can effectively improve the robustness of complex signal recovery, especially in changing environments, and can more comprehensively recover the signal's structural information.

[0061] Furthermore, in step 230, each atom in the dictionary and the weight of each atom are updated based on the current signal residual and the current reconstructed signal, including: Based on the similarity between the current signal residual and the atoms in the initial dictionary, as well as the similarity between the atoms in the initial dictionary, target atoms are selected from the atoms in the initial dictionary and used as atoms in the updated dictionary. The atoms in the initial dictionary are pre-learned based on the binary characteristics of the signal. Based on the current signal residual and the current reconstructed signal, the weight of each atom in the dictionary is updated.

[0062] It should be noted that traditional compressed sensing theory is usually based on the selection of sparse dictionaries and transformation bases in signal sparsity modeling, emphasizing the sparsity characteristics of the signal. However, in the reconstruction process of binary sparse signals, common sparsity modeling often ignores the discreteness and strong binary constraints of the signal. To this end, the embodiment of the present invention introduces a dictionary structure based on binary feature learning to accurately describe the structural characteristics of binary sparse signals. Specifically, by optimizing the construction of the signal dictionary under the compressed sensing framework, it is ensured that the dictionary atoms strictly conform to the binary characteristics. This new dictionary design can not only effectively express the sparse structure of the signal, but also reduce the computational complexity caused by the binary constraints in the reconstruction process. In the embodiment of the present invention, by introducing binary dictionary learning, dictionary atoms can be adaptively selected according to the binary characteristics of the signal, instead of relying on the traditional sparse dictionary construction method. In this way, not only the efficiency is improved in the reconstruction process, but also the accuracy of the binary constraints is ensured.

[0063] Specifically, after constructing the initial dictionary, the atoms in the initial dictionary can be used to reconstruct the signal. During each iterative reconstruction process, the atom selection in the dictionary can be dynamically adjusted according to the current signal residual to make it better adapt to the characteristics of binary sparse signals, thereby improving the accuracy and speed of signal reconstruction.

[0064] Understandably, the traditional matching pursuit algorithm selects the most relevant atoms at each iteration by calculating the inner product of the residual and the dictionary atoms. However, this approach has two major problems: first, as iterations proceed, the selection of dictionary atoms may be influenced by previously selected atoms, leading to overfitting; second, traditional methods fail to fully consider the local structure of the signal, which can lead to large errors in the signal recovery process.

[0065] To address this, the adaptive matching pursuit algorithm introduces an adaptive mechanism that dynamically adjusts the selection of dictionary atoms based on the current signal residual and local characteristics during each iteration. By decomposing or weighting the residual, the adaptive mechanism allows the algorithm to better adapt to the sparsity and structure of the signal. This is particularly true for binary sparse signals, effectively avoiding misselection and overfitting, thereby improving reconstruction accuracy and efficiency.

[0066] Specifically, in the AMP algorithm, the selection of dictionary atoms has a significant impact on reconstruction accuracy. To further improve the algorithm's adaptability, dictionary atoms can be dynamically selected at each iteration based on the characteristics of the current signal residual. Traditional matching pursuit algorithms select the most relevant atoms by calculating the inner product between the residual and the dictionary atoms, but this method does not take into account the relationships between dictionary atoms. To optimize dictionary selection, an "adaptive selection" mechanism can be introduced. At each iteration, the algorithm selects the atoms that best suit the current signal characteristics based on the similarity between the current signal residual and the dictionary atoms. In addition, the algorithm can also perform appropriate updates based on the selected dictionary atoms to avoid selecting too many similar dictionary atoms, thereby improving the efficiency and accuracy of signal recovery.

[0067] Furthermore, in traditional matching pursuit algorithms, the residual is typically calculated as the difference between the original signal and the current reconstructed signal. However, binary sparse signals often have prominent local characteristics, and traditional residual update methods may not be able to effectively reflect these characteristics. To better recover binary sparse signals, a weighted update mechanism for the residual can be introduced in each iteration. This mechanism allows the residual update method to be adjusted according to the local characteristics of the signal. For example, for parts of a binary sparse signal that are close to zero, the weights can be adjusted to be smaller, thereby reducing the impact of these parts on signal reconstruction; conversely, for non-zero parts of the signal (i.e., important parts), the weights can be increased, making the recovery of these parts more accurate.

[0068] In this embodiment of the present invention, the adaptive matching pursuit algorithm, by introducing improved strategies such as weighted residual updates, binarization constraints, and dynamic dictionary selection, can more effectively recover binary sparse signals. Compared with traditional algorithms, these improvements enable the algorithm to better cope with the sparsity of binary signals and avoid misselection and overfitting. The algorithm is particularly robust when processing binary sparse signals with high noise and complex structures.

[0069] Based on any of the above embodiments, Figure 3 This is a second flow chart of a specific embodiment of the signal reconstruction method provided by the present invention. Figure 3 As shown, the method includes: Step 310: sampling the signal to be reconstructed based on the adaptive measurement matrix to obtain an observation value of the signal to be reconstructed.

[0070] It should be noted that the specific implementation of step 310 can refer to the specific implementation of step 110 in the above embodiment, and will not be repeated here.

[0071] Step 320, based on the low-rank matrix approximation technology, utilizes the sparsity and structure of the signal to perform low-rank decomposition on the observation value, applies the decomposed observation value and the dictionary to reconstruct the signal, and binarizes the reconstructed signal to obtain the current reconstructed signal.

[0072] Specifically, the computational overhead of reconstructing large-scale sparse signals is often high, especially when the signal dimension is very high. Traditional matrix operations can impose a significant computational burden. To accelerate the computational process, low-rank matrix approximation methods can be introduced to significantly reduce the computational complexity. Low-rank matrix approximation techniques exploit the sparsity and structure of the signal to reduce redundant computations by performing a low-rank decomposition (for example, singular value decomposition or principal component analysis) on the signal matrix (i.e., the observations obtained by sampling the signal through the observation matrix). This approach preserves the key signal information (i.e., the decomposed observations) while reducing computational resource consumption, thereby accelerating the signal recovery process. Low-rank matrix approximation is particularly effective in reconstructing binary sparse signals, as binary signals often have significant local structural features that can be more accurately represented using low-rank approximation.

[0073] Step 330, based on the current reconstructed signal and the observation value, determine the current signal residual; according to the current reconstructed signal or the current signal residual, update the adaptive measurement matrix to obtain an updated adaptive measurement matrix; according to the current signal residual and the current reconstructed signal, update each atom and the weight of each atom in the dictionary to obtain an updated dictionary; apply the updated adaptive measurement matrix and the updated dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0074] It should be noted that the specific implementation of step 330 may refer to the specific implementation of step 130 or step 230 in the above embodiment, and will not be repeated here.

[0075] Based on any of the above embodiments, Figure 4 This is the second flow chart of the signal reconstruction method provided by the present invention, such as Figure 4 As shown, the method includes: Step 410: performing multi-scale decomposition on the signal to be reconstructed to obtain signals at each scale, and sampling the signals at each scale based on the adaptive measurement matrix to obtain observation values of the signals at each scale; Step 420 , performing signal reconstruction and binarization processing based on the dictionary and the observed values of the signals at each scale to obtain the current reconstructed signals at each scale; Step 430: Based on the current reconstructed signal at each scale and the observation value at each scale, the atoms and the weights of the atoms in the adaptive measurement matrix and dictionary are updated, and the updated adaptive measurement matrix and dictionary are applied to iteratively perform signal sampling and signal reconstruction at each scale until the reconstruction result at each scale is obtained. Step 440: Fuse the reconstruction results of each scale to obtain the original binary sparse signal.

[0076] It's important to note that traditional compressed sensing methods focus primarily on global signal recovery. However, binary sparse signals often exhibit local structural characteristics. To better recover these signals, a multi-scale signal recovery strategy can be introduced. This involves decomposing the signal recovery process into local reconstructions at multiple scales (such as spatial, frequency, spatiotemporal, and semantic). At each scale, the algorithm processes the signal based on local signal characteristics and, incorporating global information, gradually adjusts the signal recovery process, thereby improving both accuracy and efficiency.

[0077] Specifically, the signal to be reconstructed can be decomposed into multiple scales by a preset method (such as wavelet transform, pyramid decomposition, etc.). For example, the image signal is decomposed by three layers of wavelet to obtain the low-frequency component. L 3 (coarse scale, mainly containing the overall outline of the image) and high-frequency components H 1. H 2. H 3 (fine scale, including edges, textures and other details). Then, the signal of each scale is sampled separately using the measurement matrix to obtain the observation value of each scale. Then, at the lowest scale (such as L 3) Reconstruction is performed using residual weighted updates, binarization constraints, and dynamic dictionary selection to output a coarse-scale reconstruction result in order to quickly locate the main features of the signal and provide an initial estimate. Subsequently, upsampling is performed layer by layer, and the reconstruction result of the current scale is upsampled to the next scale. The residual between the current scale and the observed value is calculated and passed to the next scale. The atoms of the dictionary are dynamically adjusted according to the signal characteristics of the current scale. Repeat the residual weighted update, binarization constraint, and dictionary selection at the next scale to update the reconstructed signal to gradually refine the signal details and reduce the reconstruction error. Finally, after reconstruction is completed at all scales, the reconstruction results of each scale are fused to obtain the corresponding reconstruction result. For example, for the reconstruction result of wavelet decomposition, the final signal can be obtained by inverse wavelet transform; for the reconstruction result of pyramid decomposition, the final signal can be obtained by weighted averaging or nonlinear fusion.

[0078] In embodiments of the present invention, the algorithm uses multi-scale restoration to accurately identify local features in the signal and, combined with global signal information, iteratively optimizes the signal to better capture the local structural features of the signal, improving the accuracy and efficiency of restoration. For binary, sparse signals, the restoration of local structure is crucial. Using a multi-scale approach effectively avoids the loss of local details during global restoration and enables more efficient optimization targeting the signal's sparsity.

[0079] Based on any of the above embodiments, it is considered that in the signal reconstruction process based on compressed sensing, especially in the reconstruction of binary sparse signals, the efficiency and quality of signal recovery directly affect the performance of the entire system. In the reconstruction task of large-scale sparse signals, computational complexity and storage requirements are two major bottlenecks, especially for the processing of high-dimensional signals. Traditional compressed sensing methods usually rely on more complex iterative algorithms, which often require multiple calculations and a large amount of memory consumption, resulting in a longer reconstruction process, especially in the case of limited resources, and low efficiency.

[0080] To this end, the embodiment of the present invention introduces an energy optimization mechanism, which not only improves the overall performance of the algorithm, but also optimizes resource utilization efficiency by reducing unnecessary computational overhead during the calculation process, thereby accelerating the signal reconstruction process. The energy optimization steps include: During each iteration, the current signal residual and the residuals of different regions of the current signal are determined based on the current reconstructed signal and the observation value; the sampling rate of the adaptive observation matrix is adjusted based on the current signal residual; and the computing resources of different regions of the signal are adjusted and allocated based on the residuals of different regions of the current signal.

[0081] It's important to note that the core concept of the energy optimization mechanism is to reduce redundant computations during signal recovery by intelligently adjusting the energy allocation during the computation. Specifically, the signal recovery process can be viewed as searching for a solution in a high-dimensional space that satisfies sparsity and binarization constraints. To optimize this process, energy can be precisely controlled based on the signal's characteristics, ensuring that at each computational step, more resources are allocated to the most critical components for signal recovery.

[0082] In the reconstruction of binary sparse signals, since the non-zero portion (i.e., the important portion) of the signal consists only of 0s and 1s, the restoration process can prioritize those portions that significantly impact signal recovery quality based on the signal's location and energy distribution. For example, for signal regions with high or prominent sparsity, more computing resources can be concentrated in these areas, reducing computation on less important regions. In this way, the algorithm can significantly reduce unnecessary computation and improve computational efficiency while ensuring recovery accuracy. It should be understood that in traditional sparse signal recovery, high-sparsity regions typically refer to portions of the signal where the majority of values are zero or near zero, and changes in these regions have little impact on signal recovery. However, in embodiments of the present invention, "high-sparsity or prominent signal regions" often refer to the non-zero portion of the signal, i.e., the important signal portion. These regions may be sparse (i.e., non-zero at only a few locations), but they are crucial to overall signal recovery. Therefore, more computing resources should be concentrated on these important non-zero regions to achieve more accurate recovery. In other words, the "high-sparsity regions" in embodiments of the present invention refer to important regions. Although they represent a small proportion of the overall signal, their values have a significant impact on the recovery results. Therefore, more computing resources should be concentrated on these areas to improve the accuracy and quality of the recovery. Conversely, for areas close to zero or irrelevant, computing resources can be appropriately reduced to avoid wasting unnecessary computing overhead.

[0083] Specifically, the first strategy for energy optimization is adaptive sampling, which means that during the signal reconstruction process, the sampling rate and computing resources are dynamically adjusted according to the changes in the current signal residual. Traditional sampling methods usually perform an equal number of samples in each round, but in some areas, the signal changes may be small and the sampling redundancy is high. Through the adaptive sampling strategy, the sampling of these redundant parts can be reduced, and more computing resources can be concentrated in areas where the signal changes are large. For example, in the early stages of signal recovery, the signal can be sampled more densely because the initial residual is large and more calculations are required to correct the error. In the later stages, as the reconstruction process gradually approaches the real signal, the residual gradually decreases and the redundant part of the sampling increases. At this time, the number of samples can be reduced and more calculations can be concentrated on the key parts, thereby optimizing computing efficiency.

[0084] The second energy optimization strategy involves weighted updating of energy allocation during signal recovery. By performing a weighted update based on the current signal residual, more computational resources are allocated to regions with larger residuals, while computation is reduced for regions with smaller variations. Specifically, the goal of weighted updating is to dynamically adjust the signal recovery process across different regions, adjusting the allocation of computational resources based on the magnitude of each region's residual. The key point of this weighted update mechanism is that by calculating the residual for each region, it identifies areas of the signal where inaccurate restoration has occurred. For regions with larger residuals (i.e., inaccurate restoration), the algorithm increases computational resources for more refined optimization; whereas for regions with smaller residuals and better restoration, computational resources are reduced to improve overall computational efficiency. It should be understood that this strategy primarily weights different regions based on signal importance and residual magnitude, ensuring more accurate restoration of critical signal portions while reducing computation for less important or near-zero portions. Its advantage lies in its ability to precisely adjust the energy distribution during signal recovery, making the computational process more efficient and avoiding meaningless computation on low-impact regions in each iteration. Especially in the reconstruction of binary sparse signals, the changes in signals are often sudden, so this weighted update strategy can effectively avoid the "overfitting" phenomenon in the algorithm and ensure the accuracy and efficiency of recovery.

[0085] The third strategy for energy optimization is the low-rank matrix approximation technology, which has been introduced in the above embodiments and will not be repeated here.

[0086] Furthermore, with the advent of the big data era, compressed sensing algorithms often face the challenges of enormous computational complexity and limited storage resources when processing high-dimensional, sparse signals. To improve the algorithm's real-time performance and processing capabilities, an algorithmic framework based on parallelization and hardware acceleration can be designed. This allows the compressed sensing algorithm to be efficiently executed on multi-core processors, graphics processing units (GPUs), or specialized hardware (such as FPGAs), thereby accelerating the signal recovery process. Specifically, parallelization modules and hardware-platform-optimized operations can be incorporated into the algorithm design phase to ensure that the algorithm can run efficiently in a variety of hardware environments and meet real-time processing requirements.

[0087] Building on the aforementioned capacity optimization mechanisms and hardware acceleration strategies, the performance and efficiency of signal recovery and reconstruction can be further improved by combining them. In practical applications, these strategies not only increase the speed of signal reconstruction but also significantly reduce computing resource consumption when processing large amounts of data. For example, in the field of image processing, traditional compressed sensing methods are often inapplicable due to their excessive computational overhead when processing large amounts of image or video data. However, improved energy optimization and acceleration strategies can shorten processing time and reduce storage requirements while maintaining image quality. In the reconstruction of binary sparse signals, optimizing energy allocation and computing resource utilization can significantly improve recovery accuracy and effectively reduce the amount of computation. Through strategies such as adaptive sampling, residual weighted updates, and low-rank matrix approximation, the algorithm can complete signal reconstruction tasks in a shorter time without sacrificing recovery quality. These strategies have important practical value, especially in large-scale signal reconstruction and image processing.

[0088] Based on any of the above embodiments, an embodiment of the present invention also introduces a gradient update mechanism guided by sparsity. In traditional matching pursuit algorithms, gradient updates are usually based on minimization of residuals. However, in the process of binary sparse signal recovery, relying solely on minimization of residuals may not fully utilize the sparse structure of the signal, especially when there are multiple small noises or pseudo-sparse elements in the signal, which may lead to the accumulation of errors. To this end, an embodiment of the present invention proposes a sparsity-guided gradient update mechanism, that is, in each gradient update, in addition to paying attention to the minimization of residuals, guidance on signal sparsity is also introduced to avoid unnecessary overfitting.

[0089] Specifically, by incorporating the sparsity characteristics of the signal, a regularization method is introduced into the gradient update to limit the number of non-zero elements in the signal reconstruction process, ensuring accurate recovery of the sparsity and binary characteristics. Guided by sparsity, the algorithm not only focuses on correcting the residual error during each update but also considers the sparsity constraints of the signal, making the signal recovery process more accurate and avoiding the introduction of redundant elements in the reconstruction process.

[0090] Based on any of the above embodiments, considering that in the research and application of compressed sensing and signal reconstruction algorithms, the accuracy of the algorithm is one of the important indicators to measure its performance. Accuracy assessment can not only help researchers and engineers understand the actual effect of the algorithm, but also provide guidance for subsequent algorithm optimization. In the reconstruction of binary sparse signals, since the signal has obvious sparsity characteristics, accurately restoring the zero and non-zero positions and numerical values of the signal is crucial to the quality of the recovery result. Therefore, the accuracy assessment of the algorithm should not only consider the size of the reconstruction error, but also the sparsity of the reconstruction result, the binarization characteristics and the stability of the algorithm. In the embodiment of the present invention, a comprehensive accuracy assessment method is proposed in combination with the characteristics of binary sparse signals, and compared with the existing mainstream algorithms to reveal the advantages and disadvantages of the proposed algorithm.

[0091] Specifically, the reconstruction accuracy evaluation of binary sparse signals can be considered from multiple dimensions, mainly including the following indicators: Reconstruction error is a fundamental metric for evaluating signal reconstruction accuracy, typically measured using the mean squared error (MSE) or the relative error between the signal and the reconstructed signal. For binary sparse signals, reconstruction error can be quantified by calculating the difference between the original and reconstructed signals. A lower reconstruction error indicates that the recovered signal is closer to the original, while a lower error indicates poorer recovery. Because binary sparse signals have a distinct distribution of 0s and 1s, the calculation of reconstruction error requires particular attention to ensuring that the non-zero portion of the signal is accurately recovered. Therefore, error analysis should not only focus on the overall error level but also analyze each component of the signal individually to ensure that the recovery of important parts is not affected.

[0092] For binary sparse signals, another important evaluation metric is the accuracy of non-zero position recovery. Specifically, it measures whether positions that should be 1 in the signal are accurately restored to 1. A common evaluation method is to calculate the "position accuracy" or "position recovery rate," which measures the degree to which the positions of the non-zero elements in the reconstructed signal match those in the original signal. This metric is particularly critical for the reconstruction of binary sparse signals, as even if the reconstruction error is small, if the recovered signal positions are incorrect, it will not meet the requirements of practical applications. Therefore, the ability to accurately recover the positions of non-zero elements demonstrates the effectiveness of the algorithm in sparse signal recovery.

[0093] Sparsity preservation is also an important evaluation metric, especially in the reconstruction of binary sparse signals. Sparsity generally represents the proportion of nonzero elements in a signal. A good reconstruction algorithm should be able to restore the core structure of the signal while minimizing the number of nonzero elements. Sparsity preservation can be evaluated by calculating the sparsity similarity between the original signal and the reconstructed signal (for example, the proportion of nonzero elements), thereby understanding the degree to which the algorithm preserves the signal's sparsity. If the sparsity of the signal recovered by the algorithm deviates from the original signal, it may indicate a high level of redundancy and error in the signal recovery process.

[0094] In the algorithm accuracy evaluation of the embodiments of the present invention, the adaptive matching pursuit algorithm provided by the present invention is compared with several currently mainstream compressed sensing signal recovery algorithms (such as the matching pursuit algorithm, the sparse recovery method based on the least squares method, and the signal recovery method based on Bayesian inference). The comparison mainly includes the reconstruction error (quantified by indicators such as the mean square error (MSE)), the non-zero position recovery rate, the computational efficiency (including the time complexity and number of iterations of the algorithm), and the sparsity preservation.

[0095] In the experiments, multiple standard datasets were used for validation, including 1D and 2D binary sparse signals. In each data set, the signal sparsity was set to 0.1, meaning that 10% of the elements in the signal were non-zero. The experimental results show that the improved adaptive matching pursuit algorithm outperforms the comparison algorithms in the following aspects: In each set of experiments, the improved algorithm (i.e., the adaptive matching pursuit algorithm proposed in this invention) exhibited significantly lower reconstruction error, especially in high-noise conditions, and exhibited greater robustness than other algorithms. For example, when 30% noise was added, the mean squared error of the improved algorithm was more than 20% lower than that of the matching pursuit algorithm. For binary sparse signals, the position recovery rate is an important metric for measuring algorithm accuracy. Across all test datasets, the improved algorithm achieved significantly higher non-zero position recovery rates than the comparison algorithms, especially when signal sparsity was high, with position recovery accuracy exceeding 95%. The improved algorithm also demonstrated superior performance in preserving signal sparsity. Compared with the traditional algorithm, the improved algorithm maintains the sparsity close to the original signal during the recovery process without overfitting, and can effectively avoid redundant elements in the signal.

[0096] Although the improved algorithm introduces additional adaptive mechanisms and optimization strategies, it still maintains a relatively high performance in terms of computational efficiency. Compared with sparse recovery methods based on the least squares method, the improved algorithm has significantly shorter computation time and is suitable for real-time recovery of large-scale signals. Through comparative analysis, it can be concluded that the improved adaptive matching pursuit algorithm can effectively improve the reconstruction accuracy in the reconstruction of binary sparse signals, especially in terms of non-zero position recovery and sparsity preservation. At the same time, the improved algorithm also performs well in computational efficiency, adapting to the dual needs of speed and accuracy in practical applications. Therefore, the algorithm has great application potential and is particularly suitable for signal recovery tasks with high real-time requirements.

[0097] The signal reconstruction device provided by the present invention is described below. The signal reconstruction device described below and the signal reconstruction method described above can be referenced to each other.

[0098] Based on any of the above embodiments, Figure 5 Schematic diagram of the structure of the signal reconstruction device provided by the present invention. Figure 5 As shown, the device includes: The sampling unit 510 is used to sample the signal to be reconstructed based on the adaptive measurement matrix to obtain an observation value of the signal to be reconstructed; The reconstruction unit 520 is used to reconstruct the signal based on the dictionary and the observation value, and perform binarization processing on the reconstructed signal to obtain a current reconstructed signal; The iterative unit 530 is used to update the atoms and the weights of the atoms in the adaptive measurement matrix and dictionary based on the current reconstructed signal and observation value, and apply the updated adaptive measurement matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0099] The device provided by the embodiment of the present invention updates the atoms and weights of each atom in the adaptive measurement matrix and dictionary based on the current reconstructed signal and observation value. This adaptive mechanism helps to match signal features more accurately, adapt to the sparsity and binary structure of the signal, and thus improve the accuracy of signal reconstruction. Moreover, in each iteration, based on the current reconstructed signal and observation value, each atom and the weight of each atom in the dictionary are updated, and the updated dictionary is applied to reconstruct the signal. This is an application of the adaptive matching pursuit algorithm, which can dynamically adjust the matching process according to the signal characteristics, further improving the reconstruction effect. In addition, the present invention introduces an adaptive measurement matrix and an adaptive matching pursuit algorithm, and binarizes the reconstructed signal after each iteration so that it still maintains the binary characteristics, effectively optimizing the reconstruction effect of the binary sparse signal, and can better restore the original binary sparse signal.

[0100] Based on any of the above embodiments, the iteration unit 530 includes: a residual determination subunit, configured to determine a current signal residual based on a current reconstructed signal and an observation value; A matrix updating subunit, configured to update the adaptive measurement matrix based on the current reconstructed signal or the current signal residual to obtain an updated adaptive measurement matrix; The dictionary updating subunit is used to update each atom and the weight of each atom in the dictionary based on the current signal residual and the current reconstructed signal to obtain an updated dictionary.

[0101] Based on any of the above embodiments, the matrix updating subunit is specifically configured to: updating the adaptive measurement matrix based on at least one of the entropy, sparsity, time domain characteristics, and frequency domain characteristics of the current reconstructed signal; Alternatively, based on the current signal residual, a reinforcement learning algorithm is applied to update the adaptive observation matrix.

[0102] Based on any of the above embodiments, the dictionary updating subunit is specifically configured to: Selecting target atoms from the atoms in the initial dictionary based on similarities between the current signal residual and atoms in an initial dictionary, and using the target atoms as atoms in the updated dictionary, wherein the atoms in the initial dictionary are pre-learned based on binary characteristics of the signal; The weight of each atom in the dictionary is updated based on the current signal residual and the current reconstructed signal.

[0103] Based on any of the above embodiments, the reconstruction unit 520 is specifically configured to: Based on low-rank matrix approximation technology, the sparsity and structure of the signal are utilized to perform low-rank decomposition on the observations, and the decomposed observations and dictionary are used to reconstruct the signal.

[0104] Based on any of the above embodiments, the device further includes an energy optimization unit, which is configured to: In each iteration, the current signal residual and the residuals of different regions of the current signal are determined based on the current reconstructed signal and the observed value; Based on the current signal residual, the sampling rate of the adaptive measurement matrix is adjusted; Based on the residuals of different regions of the current signal, the computing resources of different regions of the signal are adjusted and allocated.

[0105] Based on any of the above embodiments, the sampling unit 510 is specifically configured to: perform multi-scale decomposition on the signal to be reconstructed to obtain signals at each scale, and sample the signals at each scale based on the adaptive measurement matrix to obtain observation values of the signals at each scale; The reconstruction unit 520 is specifically configured to: perform signal reconstruction and binarization processing based on the dictionary and the observation values of the signals at each scale to obtain the current reconstructed signals at each scale; The iteration unit 530 is specifically used to: update the atoms and the weights of the atoms in the adaptive observation matrix and dictionary based on the current reconstructed signals at each scale and the observation values at each scale, and apply the updated adaptive observation matrix and dictionary to iteratively perform signal sampling and signal reconstruction at each scale until the reconstruction results at each scale are obtained; and fuse the reconstruction results at each scale to obtain the original binary sparse signal.

[0106] Figure 6 An example of a physical structure diagram of an electronic device is shown below. Figure 6 As shown, the electronic device may include: a processor 610, a communication interface 620, a memory 630 and a communication bus 640, wherein the processor 610, the communication interface 620, and the memory 630 communicate with each other via the communication bus 640. The processor 610 may call the logic instructions in the memory 630 to execute a signal reconstruction method, which includes: sampling a signal to be reconstructed based on an adaptive measurement matrix to obtain an observation value of the signal to be reconstructed; reconstructing the signal based on a dictionary and the observation value, and binarizing the reconstructed signal to obtain a current reconstructed signal; updating each atom and the weight of each atom in the adaptive measurement matrix and the dictionary based on the current reconstructed signal and the observation value, and applying the updated adaptive measurement matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0107] In addition, the logic instructions in the aforementioned memory 630 can be implemented in the form of a software functional unit and, when sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the relevant art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0108] On the other hand, the present invention also provides a computer program product, which includes a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the signal reconstruction method provided by the above methods, which includes: sampling the signal to be reconstructed based on an adaptive observation matrix to obtain the observation value of the signal to be reconstructed; reconstructing the signal based on a dictionary and the observation value, and binarizing the reconstructed signal to obtain a current reconstructed signal; updating each atom and the weight of each atom in the adaptive observation matrix and the dictionary based on the current reconstructed signal and the observation value, and applying the updated adaptive observation matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0109] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the signal reconstruction method provided by the above-mentioned methods, the method comprising: sampling the signal to be reconstructed based on an adaptive observation matrix to obtain the observation value of the signal to be reconstructed; reconstructing the signal based on a dictionary and the observation value, and binarizing the reconstructed signal to obtain a current reconstructed signal; updating each atom and the weight of each atom in the adaptive observation matrix and the dictionary based on the current reconstructed signal and the observation value, and applying the updated adaptive observation matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

[0110] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0111] Through the description of the above embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the relevant technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A signal reconstruction method, characterized in that: include: Based on the adaptive measurement matrix, sampling the signal to be reconstructed to obtain an observation value of the signal to be reconstructed; Reconstructing the signal based on the dictionary and the observation value, and binarizing the reconstructed signal to obtain a current reconstructed signal; Based on the current reconstructed signal and the observation value, the adaptive measurement matrix and each atom and the weight of each atom in the dictionary are updated, and the updated adaptive measurement matrix and dictionary are applied to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

2. The signal reconstruction method according to claim 1, wherein: The updating of the adaptive measurement matrix and each atom and the weight of each atom in the dictionary based on the current reconstructed signal and the observation value includes: Determining a current signal residual based on the current reconstructed signal and the observation value; updating the adaptive measurement matrix based on the current reconstructed signal or the current signal residual to obtain an updated adaptive measurement matrix; Based on the current signal residual and the current reconstructed signal, each atom and the weight of each atom in the dictionary are updated to obtain an updated dictionary.

3. The signal reconstruction method according to claim 2, characterized in that: The updating of the adaptive measurement matrix based on the current reconstructed signal or the current signal residual includes: Updating the adaptive measurement matrix based on at least one of an entropy value, sparsity, time domain characteristics, and frequency domain characteristics of the current reconstructed signal; Alternatively, based on the current signal residual, a reinforcement learning algorithm is applied to update the adaptive measurement matrix.

4. The signal reconstruction method according to claim 2, wherein: The updating of each atom and the weight of each atom in the dictionary based on the current signal residual and the current reconstructed signal to obtain an updated dictionary includes: Selecting target atoms from the atoms in the initial dictionary based on similarities between the current signal residual and atoms in an initial dictionary, and using the target atoms as atoms in the updated dictionary, wherein the atoms in the initial dictionary are pre-learned based on binary characteristics of the signal; The weight of each atom in the dictionary is updated based on the current signal residual and the current reconstructed signal.

5. The signal reconstruction method according to claim 1, wherein: The signal reconstruction based on the dictionary and the observation value includes: Based on low-rank matrix approximation technology, the sparsity and structure of the signal are utilized to perform low-rank decomposition on the observation value, and the observation value obtained by the decomposition and the dictionary are used to reconstruct the signal.

6. The signal reconstruction method according to any one of claims 1 to 5, characterized in that: Also includes: During each iteration, based on the current reconstructed signal and the observation value, a current signal residual and residuals of different regions of the current signal are determined; Adjusting a sampling rate of the adaptive measurement matrix based on the current signal residual; Based on the residuals of different regions of the current signal, computing resources for different regions of the signal are adjusted and allocated.

7. The signal reconstruction method according to any one of claims 1 to 5, characterized in that: The sampling of the signal to be reconstructed based on the adaptive observation matrix to obtain the observation value of the signal to be reconstructed includes: Performing multi-scale decomposition on the signal to be reconstructed to obtain signals of each scale, and sampling the signals of each scale based on an adaptive measurement matrix to obtain observation values of the signals of each scale; The signal reconstruction based on the dictionary and the observation value, and binarization processing of the reconstructed signal to obtain the current reconstructed signal, includes: Performing signal reconstruction and binarization processing based on the dictionary and the observation values of the signals at each scale to obtain current reconstructed signals at each scale; The method includes updating the adaptive measurement matrix and each atom in the dictionary and the weight of each atom based on the current reconstructed signal and the observation value, and applying the updated adaptive measurement matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained, including: Based on the current reconstructed signals at each scale and the observation values at each scale, the adaptive measurement matrix and each atom and the weight of each atom in the dictionary are updated, and the updated adaptive measurement matrix and dictionary are applied to iteratively perform signal sampling and signal reconstruction at each scale until a reconstruction result at each scale is obtained; The reconstruction results of each scale are fused to obtain the original binary sparse signal.

8. A signal reconstruction device, characterized in that: include: A sampling unit, configured to sample the signal to be reconstructed based on an adaptive measurement matrix to obtain an observation value of the signal to be reconstructed; a reconstruction unit, configured to reconstruct a signal based on the dictionary and the observation value, and perform binarization processing on the reconstructed signal to obtain a current reconstructed signal; An iterative unit is used to update the adaptive measurement matrix and each atom in the dictionary and the weight of each atom based on the current reconstructed signal and the observation value, and apply the updated adaptive measurement matrix and dictionary to iteratively perform signal sampling and signal reconstruction until the original binary sparse signal is obtained.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the signal reconstruction method according to any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the signal reconstruction method according to any one of claims 1 to 7 is implemented.

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