Sparse signal reconstruction method and device, computer device, medium and product

Abstract

The application relates to a sparse signal reconstruction method and device, computer equipment, medium and product. The method comprises the following steps: acquiring a compressed signal and a conversion matrix corresponding to the compressed signal; a plurality of candidate matrices are sequentially extracted from the conversion matrix by using a sliding window method, a first target matrix is determined according to the correlation between the plurality of candidate matrices and a first residual error, and a first-stage reconstruction is performed on an original sparse signal to generate a first-stage target reconstruction signal; a second-stage reconstruction is performed on the original sparse signal according to the first-stage target reconstruction signal, remaining atoms in the conversion matrix except the first target matrix, the conversion matrix and a second residual error, to generate a second-stage target reconstruction signal; and a target reconstruction signal is generated according to the first-stage target reconstruction signal and the second-stage target reconstruction signal. The method can improve the reconstruction accuracy of the sparse signal reconstruction.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, and in particular to a sparse signal reconstruction method, apparatus, computer equipment, medium, and product. Background Technology

[0002] With the rapid development of information technology, the number of electronic signals such as images and voice is constantly increasing. The storage and transmission of large amounts of information put enormous pressure on electronic devices, thus necessitating corresponding signal processing. In the continuous development of signal processing methods, a novel approach has emerged: compressed sensing. Compressed sensing simultaneously samples and compresses the original sparse signal to generate a compressed signal, which is then reconstructed from the compressed signal using a reconstruction algorithm. The original sparse signal refers to a signal that takes a value of zero or close to zero most of the time. In practice, many original sparse signals exhibit a blocky structure, meaning that non-zero values ​​appear in blocks.

[0003] In traditional methods, when reconstructing original sparse signals with block structures, the Block Orthogonal Matching Pursuit (BOMP) method can be used. In BOMP, the original sparse signal with block structures needs to be pre-divided into block regions, and then sparse signal reconstruction is performed based on these divided block regions.

[0004] However, when reconstructing block sparse signals using traditional methods, the reconstruction accuracy is low because the divided block intervals and the block structure of the block sparse signal itself may not match. Summary of the Invention

[0005] Therefore, it is necessary to provide a sparse signal reconstruction method, apparatus, computer device, computer-readable storage medium, and computer program product that can reconstruct the accuracy of the above-mentioned technical problems.

[0006] In a first aspect, this application provides a sparse signal reconstruction method, the method comprising:

[0007] Obtain the compressed signal and the corresponding transformation matrix; the compressed signal is the signal generated by compressing the original sparse signal using the transformation matrix; the transformation matrix contains multiple atoms;

[0008] Multiple candidate matrices are extracted sequentially from the transformation matrix using the sliding window method. The first target matrix is ​​determined based on the correlation between the multiple candidate matrices and the first residual. The original sparse signal is then reconstructed in the first stage to generate the first-stage target reconstruction signal.

[0009] Based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual, the original sparse signal is reconstructed in the second stage to generate the second-stage target reconstruction signal.

[0010] Based on the target reconstruction signals of the first stage and the target reconstruction signals of the second stage, a target reconstruction signal is generated.

[0011] In one embodiment, a sliding window method is used to sequentially extract multiple candidate matrices from the transformation matrix. A first target matrix is ​​determined based on the correlation between the multiple candidate matrices and the first residual. A first-stage reconstruction is then performed on the original sparse signal to generate a first-stage target reconstruction signal, including:

[0012] Multiple candidate matrices are extracted sequentially from the transformation matrix according to a preset sliding window size and a preset step size;

[0013] For each candidate matrix among multiple candidate matrices, calculate the correlation between the candidate matrix and the current first residual, and take the candidate matrix with the highest correlation as the first target matrix;

[0014] Based on the first target matrix and the compressed signal, the original sparse signal is reconstructed in the first stage to generate the first stage reconstructed signal; the initial value of the current residual is the compressed signal.

[0015] The current first residual is updated based on the first-stage reconstruction signal to generate a new current first residual. The new current first residual is used as the current first residual. The first-stage reconstruction signal is iteratively calculated until the first preset iteration stop condition is met. The first-stage reconstruction signal that meets the first preset iteration stop condition is used as the first-stage target reconstruction signal.

[0016] In one embodiment, for each candidate matrix among multiple candidate matrices, the correlation between the candidate matrix and the current first residual is calculated, and the candidate matrix corresponding to the highest correlation is taken as the first target matrix, including:

[0017] Multiply the conjugate transpose of each candidate matrix with the current first residual to generate multiple first initial vectors;

[0018] The correlation between the candidate matrix and the current first residual is calculated based on multiple first initial vectors. The first initial vector corresponding to the highest correlation is obtained, and the first atom index number is obtained based on the first initial vector.

[0019] The atom corresponding to the first atom index number is selected from the transformation matrix based on the first atom index number, and this atom is used as the first target matrix.

[0020] In one embodiment, the first preset iteration stopping condition includes that the product of the number of rows of the compressed signal and a preset parameter is greater than or equal to the sparsity of the first target matrix; updating the current first residual according to the first-stage reconstruction signal to generate a new current residual, using the new current first residual as the current first residual, iteratively calculating the first-stage reconstruction signal until the first preset iteration stopping condition is met, and using the first-stage reconstruction signal that meets the first iteration stopping condition as the first-stage target reconstruction signal, including:

[0021] The current first residual is updated based on the reconstructed signal, compressed signal and first target matrix of the first stage, and a new current first residual is generated;

[0022] Take the new current first residual as the current first residual, iteratively calculate the correlation between the candidate matrix and the current first residual, and take the candidate matrix corresponding to the largest correlation as the new first target matrix;

[0023] Based on the new first target matrix and the compressed signal, the original sparse signal is reconstructed in the first stage to generate a new first-stage reconstructed signal.

[0024] Determine whether the first preset iteration stopping condition is met;

[0025] If the first preset iteration stop condition is met, the first-stage reconstruction signal corresponding to the first target matrix will be used as the first-stage target reconstruction signal.

[0026] In one embodiment, a second-stage reconstruction is performed on the original sparse signal based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual, to generate the second-stage target reconstruction signal, including:

[0027] The weight matrix of the transformation matrix is ​​calculated based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms in the first target matrix. The weight matrix is ​​used to characterize the probability that each atom in the transformation matrix is ​​an atom that was missed in the first stage of reconstruction.

[0028] The second target matrix is ​​calculated based on the weight matrix, the transformation matrix, and the current second residual; the current second residual is the latest first residual during the first-stage reconstruction process.

[0029] Based on the first target matrix, the second target matrix, and the compressed signal, the original sparse signal is reconstructed in the second stage to generate the second-stage reconstructed signal.

[0030] The current second residual is updated based on the second-stage reconstruction signal to generate a new current second residual. The new current second residual is used as the current second residual. The second-stage reconstruction signal is iteratively calculated until the second preset iteration stop condition is met. The second-stage reconstruction signal that meets the second preset iteration stop condition is used as the second-stage target reconstruction signal. The second preset iteration stop condition includes that the L2 norm of the current second residual is less than or equal to a preset threshold.

[0031] In one embodiment, the weight matrix of the transformation matrix is ​​calculated based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms corresponding to the first target matrix, including:

[0032] Calculate the minimum distance between the first atom index number corresponding to the first target matrix in the transformation matrix and the atom index number corresponding to the transformation matrix.

[0033] The probability that each atom in the transformation matrix is ​​an atom missed during the first-stage reconstruction is determined based on the minimum distance.

[0034] The weight matrix of the transformation matrix is ​​calculated based on the probability.

[0035] In one embodiment, the second target matrix is ​​calculated based on the weight matrix, the transformation matrix, and the current second residual, including:

[0036] Multiply the weight matrix, the conjugate transpose of the transformation matrix, and the current second residual to generate the second initial vector;

[0037] Calculate the modulus of each element in the second initial vector, select the maximum preset number of moduli from the moduli of each element, and obtain the second atom index number corresponding to the preset number of moduli;

[0038] The atom corresponding to the second atom index number is selected from the transformation matrix based on the second atom index number, and used as the second target matrix.

[0039] Secondly, this application also provides a sparse signal reconstruction apparatus, the apparatus comprising:

[0040] The acquisition module is used to acquire the compressed signal and the corresponding transformation matrix; the compressed signal is the signal generated by compressing the original sparse signal using the transformation matrix;

[0041] The first reconstruction module is used to extract multiple candidate matrices sequentially from the transformation matrix using the sliding window method, and to perform a first-stage reconstruction of the original sparse signal based on the correlation between the multiple candidate matrices and the first residual to generate the first-stage target reconstruction signal.

[0042] The second reconstruction module is used to perform a second-stage reconstruction on the original sparse signal based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual, to generate the second-stage target reconstruction signal.

[0043] The generation module is used to generate a target reconstruction signal based on the first-stage target reconstruction signal and the second-stage target reconstruction signal.

[0044] Thirdly, this application also provides a computer device, the computer device including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method of any one of the first aspects above.

[0045] Fourthly, this application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the method of any one of the first aspects described above.

[0046] Fifthly, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the method of any one of the first aspects described above.

[0047] The aforementioned sparse signal reconstruction method, apparatus, computer equipment, medium, and product employ a sliding window method to sequentially extract multiple candidate matrices. Then, based on the correlation between these candidate matrices and the first residual, a first-stage reconstruction of the original sparse signal is performed. The sliding window method selects all candidate matrices, allowing the calculation of correlation based on these matrices to identify the vast majority of candidate matrices needed for reconstructing the original sparse signal. These matrices serve as the first target matrix, resulting in a relatively accurate first-stage target reconstructed signal. Simultaneously, based on the first-stage target reconstructed signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix itself, and the second residual, pre-atoms missed during the first-stage reconstruction can be calculated. Based on this, a second-stage reconstruction of the original sparse signal is performed to generate the second-stage target reconstructed signal. Since the second-stage target reconstruction signal contains the atoms that were missing in the first-stage target reconstruction signal, the final first-stage target reconstruction signal and the second-stage target reconstruction signal are complete reconstruction signals. Therefore, the target reconstruction signal obtained based on the reconstruction signals obtained in the two stages is also relatively complete. In other words, the accuracy of sparse signal reconstruction based on the first-stage target reconstruction signal and the second-stage target reconstruction signal is higher. Attached Figure Description

[0048] Figure 1This is a diagram illustrating the application environment of a sparse signal reconstruction method in one embodiment.

[0049] Figure 2 This is a flowchart illustrating a sparse signal reconstruction method in one embodiment;

[0050] Figure 3 for Figure 2 A flowchart illustrating the method for generating the first-stage target reconstruction signal;

[0051] Figure 4 for Figure 3 A flowchart illustrating the method for generating the first target matrix;

[0052] Figure 5 for Figure 3 A schematic diagram of a method that uses the first-stage reconstructed signal that meets the first preset iteration stopping condition as the first-stage target reconstructed signal;

[0053] Figure 6 for Figure 2 A flowchart illustrating the method for generating the second-stage target reconstruction signal;

[0054] Figure 7 for Figure 6 A flowchart illustrating the method for calculating the weight matrix of the transformation matrix;

[0055] Figure 8 for Figure 6 A flowchart illustrating the method for calculating the second objective matrix;

[0056] Figure 9 This is a comparison chart of the reconstruction effects of a sparse signal reconstruction method and a traditional method in one embodiment;

[0057] Figure 10 This is a comparison chart of the reconstruction effects of the sparse signal reconstruction method and the traditional method in another embodiment;

[0058] Figure 11 This is a comparison chart of the reconstruction effects of the sparse signal reconstruction method and the traditional method in another embodiment;

[0059] Figure 12 This is a structural block diagram of a sparse signal reconstruction device in one embodiment;

[0060] Figure 13 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0062] With the rapid development of information technology, the number of electronic signals such as images and voice is constantly increasing. The storage and transmission of large amounts of information put enormous pressure on electronic devices, thus necessitating corresponding signal processing. In the continuous development of signal processing methods, a novel approach has emerged: compressed sensing. Compressed sensing simultaneously samples and compresses the original sparse signal to generate a compressed signal, which is then reconstructed from the compressed signal using a reconstruction algorithm. The original sparse signal refers to a signal that takes a value of zero or close to zero most of the time. In practice, many original sparse signals exhibit a blocky structure, meaning that non-zero values ​​appear in blocks.

[0063] In traditional methods, the Block Orthogonal Matching Pursuit (BOMP) method can be used to reconstruct signals from original sparse signals with block structures. This BOMP process requires pre-dividing the original sparse signal with block structures into block regions, and then reconstructing the sparse signal based on these divided block regions. However, when reconstructing block-sparse signals using traditional methods, the reconstruction accuracy is low because the divided block regions and the block structure of the sparse signal itself may not match.

[0064] To address the problem of low reconstruction accuracy in traditional methods for sparse signals, this application proposes a novel signal reconstruction method. Figure 1 This is a schematic diagram illustrating the application environment of a sparse signal reconstruction method in one embodiment, such as... Figure 1As shown, the application environment includes a computer device 120, which can acquire a compressed signal and a corresponding transformation matrix. The compressed signal is a signal generated by compressing the original sparse signal using the transformation matrix. The transformation matrix includes multiple atoms. Multiple candidate matrices are sequentially extracted from the transformation matrix using a sliding window method. A first target matrix is ​​determined based on the correlation between the multiple candidate matrices and the first residual. The original sparse signal is then reconstructed in a first stage to generate a first-stage target reconstruction signal. Based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual, the original sparse signal is reconstructed in a second stage to generate a second-stage target reconstruction signal. Finally, a target reconstruction signal is generated based on the first-stage target reconstruction signal and the second-stage target reconstruction signal. The computer device 120 can be a server or a terminal. The server can be a single server or a server cluster composed of multiple servers. This embodiment does not specifically limit this. The terminal can be, but is not limited to, various personal computers, laptops, smartphones, tablets, and portable wearable devices.

[0065] In one embodiment, such as Figure 2 As shown, a sparse signal reconstruction method is provided, which can be applied to... Figure 1 Taking a computer device as an example, the explanation includes the following steps:

[0066] S220, obtain the compressed signal and the corresponding transformation matrix.

[0067] Before explaining this step, let's briefly introduce compressed sensing and its mathematical model. Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. It is widely used in signal processing to obtain and reconstruct sparse or compressible signals. Compressed sensing projects the original N-dimensional sparse signal x into a lower-dimensional space through a transformation matrix A, obtaining an M-dimensional compressed signal y. The mathematical model is represented as y = Ax. The core task of compressed sensing is to reconstruct the original sparse signal x from the compressed signal y.

[0068] The following describes this step, where the compressed signal is a real vector of length M, i.e. The compressed signal is the signal generated by compressing the original sparse signal using a transformation matrix. The transformation matrix is ​​A, which is an M-row, N-column real matrix, i.e. The transformation matrix, described above, contains multiple atoms and is an M x N real matrix containing N atoms. The original sparse signal is a real vector of length N, i.e.

[0069] Specifically, when processing the original sparse signal, compression and sampling are combined in one step. A transformation matrix is ​​used to compress the original sparse signal to obtain a compressed signal. The transformation matrix directly affects the accuracy of sparse signal reconstruction. The transformation matrix is ​​an M-row, N-column real number matrix, and its construction method can be a random Gaussian matrix, a local Hadamard matrix, etc.

[0070] S240: Multiple candidate matrices are extracted sequentially from the transformation matrix using the sliding window method. The first target matrix is ​​determined based on the correlation between the multiple candidate matrices and the first residual. The original sparse signal is then reconstructed in the first stage to generate the first-stage target reconstruction signal.

[0071] The sliding window method refers to a method of searching or selecting by sliding a window of a certain size and a preset step size. The sliding window size and preset step size can be set according to the actual situation. The first residual is the difference between the target reconstructed signal in the first stage and the original sparse signal, and the initial value of the first residual is the compressed signal. The transformation matrix is ​​an M-row, N-column real number matrix containing N atoms, while the candidate matrix is ​​a matrix extracted from the transformation matrix, and therefore it is a matrix composed of at least one atom.

[0072] Specifically, firstly, multiple candidate matrices are selected by sliding within the transformation matrix according to a preset window size and a preset step size. Then, the correlation between the multiple candidate matrices and the first residual is calculated. The correlation can be calculated by multiplying the conjugate transpose of the candidate matrix with the first residual. After calculating the correlation between each candidate matrix and the first residual, further processing can be performed based on the correlation results to select the first target matrix for reconstructing the sparse signal. Finally, the first-stage reconstruction is performed based on the selected first target matrix to generate the first-stage target reconstructed signal.

[0073] S260, based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual, perform a second-stage reconstruction on the original sparse signal to generate the second-stage target reconstruction signal;

[0074] Specifically, the second residual is the difference between the second-stage target reconstructed signal and the original sparse signal. The initial value of the second residual can be set to the first residual generated last in the first-stage reconstruction. In the first-stage reconstruction process, it is necessary to calculate the correlation between multiple candidate matrices and the first residual. During the correlation calculation, some candidate matrices may be missed in the sparse signal reconstruction process due to their low correlation with the first residual. Therefore, the second-stage reconstruction needs to be performed based on the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual. The acquisition of the second-stage target reconstructed signal can adopt a process similar to that of the first-stage reconstruction, such as gradually determining the second-stage target reconstructed signal by calculating the product of the remaining atoms and the current residual. Of course, other methods can also be used.

[0075] S280, Generate a target reconstruction signal based on the first-stage target reconstruction signal and the second-stage target reconstruction signal.

[0076] Specifically, since the compressed signal is obtained through a transformation matrix, sparse signal reconstruction can be performed using the transformation matrix and the compressed signal. In the steps above, the first-stage target reconstruction signal and the second-stage target reconstruction signal have been obtained. The first-stage reconstruction signal is obtained from the candidate matrix in the observation matrix and the compressed signal, and the second-stage reconstruction signal is also obtained from the observation matrix and the compressed signal. Therefore, the target reconstruction signal can be generated based on the first-stage and second-stage target reconstruction signals.

[0077] In the aforementioned sparse signal reconstruction method, multiple candidate matrices are extracted sequentially using a sliding window method. Then, the original sparse signal is reconstructed in the first stage based on the correlation between these candidate matrices and the first residual. The sliding window method selects all candidate matrices, allowing the calculation of correlation based on these matrices to identify the vast majority of those needed for reconstructing the original sparse signal as the first target matrix. Therefore, the first-stage target reconstruction signal generated based on this first target matrix is ​​relatively accurate. Simultaneously, based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix itself, and the second residual, the atoms missed during the first-stage reconstruction can be calculated, and a second-stage reconstruction is performed to generate the second-stage target reconstruction signal. Since the second-stage target reconstruction signal contains the atoms missed in the first-stage target reconstruction signal, both the first-stage and second-stage target reconstruction signals are complete reconstruction signals. Therefore, the target reconstruction signal obtained from both stages is also relatively complete, meaning that the accuracy of sparse signal reconstruction based on the first-stage and second-stage target reconstruction signals is higher.

[0078] The above embodiment mentioned generating the first-stage target reconstruction signal. The following describes the specific process of generating the first-stage target reconstruction signal from the original sparse signal, such as... Figure 3 As shown, S240 includes:

[0079] S242, extract multiple candidate matrices sequentially from the transformation matrix according to the preset sliding window size and preset step size.

[0080] Specifically, the sliding window size and preset step size can be set according to the expected reconstruction efficiency and accuracy requirements. Extraction using the sliding window method can extract multiple candidate matrices from the transformation matrix. For example, if the transformation matrix is ​​an M-row, N-column real number vector, when the window size is set to 4 and the preset step size is 1, N-3 candidate matrices can be extracted from the transformation matrix.

[0081] S244: For each candidate matrix among multiple candidate matrices, calculate the correlation between the candidate matrix and the current first residual, and take the candidate matrix with the highest correlation as the first target matrix.

[0082] Specifically, for multiple candidate matrices, the correlation between each candidate matrix and the current residual can be calculated. This correlation calculation determines the most correlated atom block, which corresponds to a blocky structure in the compressed signal. Then, based on the determined atom block, the corresponding candidate matrix can be selected from the transformation matrix and used as the first target matrix.

[0083] S246, Based on the first target matrix and the compressed signal, perform a first-stage reconstruction of the original sparse signal to generate a first-stage reconstructed signal. The initial value of the current residual is the compressed signal.

[0084] The initial value of the current residual is the compressed signal. The method to generate the first-stage reconstruction signal can be to first determine the current initial reconstruction signal from the compressed signal and the current first target matrix, and then, based on the least squares method, project the compressed signal onto the plane formed by the first target matrix and the initial reconstruction signal to obtain the first-stage reconstruction signal.

[0085] S248, update the current first residual according to the first stage reconstruction signal, generate a new current first residual, use the new current first residual as the current first residual, iteratively calculate the first stage reconstruction signal until the first preset iteration stop condition is met, and use the first stage reconstruction signal that meets the first preset iteration stop condition as the first stage target reconstruction signal.

[0086] Specifically, in the above correlation calculation process, only the first target matrix corresponding to the maximum correlation was selected, and the first-stage reconstructed signal was generated based on this first target matrix and the compressed signal. Therefore, the reconstructed signal obtained in one step is insufficient to complete the reconstruction of the sparse signal, so multiple iterations are needed to generate the first-stage target reconstructed signal. The updated first residual can be obtained from the compressed signal, the first-stage reconstructed signal, and the first target matrix. Let the compressed signal be y, and the first-stage reconstructed signal be... Where t represents the iteration number, which can be initially set to 0, and the first target matrix is ​​denoted as At. Then the updated first residual can be expressed as: After updating the first residual, the correlation between the candidate matrix and the current first residual can be calculated for each candidate matrix in the multiple candidate matrices, and the first-stage reconstruction signal can be calculated until the first preset iteration stop condition is met. The first-stage reconstruction signal that meets the first preset iteration stop condition is taken as the first-stage target reconstruction signal.

[0087] In this implementation, the sliding window method is used to extract multiple candidate matrices sequentially from the transformation matrix according to a preset sliding window size and a preset step size. Compared with the traditional method of dividing intervals, the sliding window method can select all possible candidate matrices. Therefore, the first target matrix can be determined more completely based on the selected candidate matrices. Consequently, the accuracy of the reconstructed signal generated based on the more complete first target matrix and the compressed signal will also be higher.

[0088] The above embodiments mention calculating the correlation between each candidate matrix and the current first residual for multiple candidate matrices, and using the candidate matrix with the highest correlation as the first target matrix. The specific method is described below. In one embodiment, such as... Figure 4 As shown, S244 includes:

[0089] S402, multiply the conjugate transpose of each candidate matrix with the current first residual to generate multiple first initial vectors.

[0090] Specifically, the conjugate transpose matrix is ​​formed by taking the conjugate value of each element of the matrix and then transposing the rows and columns. Multiplying multiple candidate matrices selected by the sliding window method by the current first residual yields multiple first initial vectors. The candidate matrix can be represented as A. <j>=[a j ,…,a j+L-1 ].

[0091] S404, calculate the correlation between the candidate matrix and the current first residual based on multiple first initial vectors, obtain the first initial vector corresponding to the largest correlation, and obtain the first atom index number based on the first initial vector.

[0092] Specifically, the correlation between the candidate matrix and the current first residual can be calculated using the following formula:

[0093]

[0094] Where A H <j>Let r be the conjugate transpose of the candidate matrix. t-1 Given the current first residual, multiplying the conjugate transpose of each candidate matrix with the current first residual yields the first initial vector. Then, taking the first initial vector and calculating its L2 norm, we find the index j of the largest correlated atomic block corresponding to the value with the maximum L2 norm. t The first atom index number can be determined based on the block index number and the preset sliding window size.

[0095] S406: Select the atom corresponding to the first atom index number from the transformation matrix according to the first atom index number, and use it as the first target matrix.

[0096] Specifically, each atom in the candidate matrix corresponds to an atom index number. Therefore, after obtaining the first atom index number, the atom corresponding to the first atom index number can be selected from the transformation matrix as the first target matrix A. t This process can be represented as in This can be understood as taking the union of the first atom index number obtained in each calculation with the first atom index number obtained in the previous calculation. After obtaining the first atom index number each time, the corresponding atom needs to be selected from the transformation matrix based on the first atom index number to form the first target matrix, i.e., the first target matrix A. t It is also a set of candidate matrices selected through multiple iterations.

[0097] In this embodiment, the atom block index number is determined by calculating the maximum correlation between the candidate matrix and the current first residual, and then the first atom index number is determined based on the block index number. Then, the first target matrix can be accurately selected from the transformation matrix based on the first atom index number. Furthermore, since the transformation matrix is ​​the matrix used to compress the original sparse signal, the sparse signal can be reconstructed relatively accurately based on the above target matrix.

[0098] The above embodiment mentioned iteratively calculating the first target signal and generating the first-stage target reconstruction signal. The specific process is described below. In one embodiment, as... Figure 5 As shown, the current first residual is updated based on the first-stage reconstruction signal to generate a new current first residual. This new current first residual is then used as the current first residual. The first-stage reconstruction signal is iteratively calculated until a first preset iteration stop condition is met. The first-stage reconstruction signal that meets the first preset iteration stop condition is then used as the first-stage target reconstruction signal, including:

[0099] S502, update the current first residual based on the first-stage reconstructed signal, compressed signal and first target matrix to generate a new current first residual.

[0100] Specifically, the compressed signal is represented by y, and the first-stage reconstructed signal is... Where t represents the iteration number, and the first objective matrix is ​​denoted as At, then the updated first residual can be expressed as: Therefore, the first residual can be updated based on the compressed signal, the first-stage reconstructed signal, and the first target matrix.

[0101] S504: Take the new current first residual as the current first residual, iteratively calculate the correlation between the candidate matrix and the current first residual, and take the candidate matrix corresponding to the largest correlation as the new first target matrix.

[0102] Specifically, when the residual is updated, the result of the subsequent calculation of the first target matrix will also change. Therefore, it is necessary to multiply the updated residual with the transpose of the candidate matrix and calculate the L2 norm multiple times, and take the candidate matrix with the highest correlation as the first target matrix. That is, the new first target matrix is ​​determined by using the new current first residual and formula (1-1).

[0103] S506, based on the new first target matrix and the compressed signal, perform the first-stage reconstruction of the original sparse signal to generate a new first-stage reconstructed signal.

[0104] Specifically, the process of generating a new first-stage reconstructed signal can be represented as follows: The compressed signal y is about to be directed to A t X t The resulting space is projected to obtain the first-stage reconstruction signal.

[0105] S508, determine whether the first preset iteration stop condition is met.

[0106] Specifically, the first preset iteration stopping condition includes the product α of the number of rows M of the compressed signal and the preset parameter being greater than or equal to the sparsity K of the first target matrix, which can be expressed as αM≥K.

[0107] S510, if the first preset iteration stop condition is met, then the first stage reconstruction signal corresponding to the first target matrix is ​​taken as the first stage target reconstruction signal.

[0108] Specifically, when the first preset condition is met, it indicates that all candidate matrices needed for sparse signal reconstruction have been selected during the first-stage reconstruction process, meaning the first-stage reconstruction is complete. At this point, the first-stage reconstruction signal corresponding to the first target matrix is ​​used as the first-stage target reconstruction signal, and the current first residual is updated again based on the first-stage target reconstruction signal. When the preset iteration stop condition is not met, the first-stage reconstruction signal is iteratively calculated until the first preset iteration stop condition is met.

[0109] In this embodiment, by iteratively calculating the first target matrix and performing a first-stage reconstruction to generate a new first-stage reconstruction signal, and then determining whether the first preset iteration stop condition is met, the candidate matrices that need to be used for sparse signal reconstruction can be selected as the first target matrix. Furthermore, based on the selected first target matrix, the sparse signal can be reconstructed more accurately.

[0110] The above embodiments mentioned performing a second-stage reconstruction of the original sparse signal to generate a second-stage target reconstruction signal. The specific process is described in detail below. In one embodiment, such as... Figure 6 As shown, S260 includes:

[0111] S602, calculate the weight matrix of the transformation matrix based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index number of the first atom corresponding to the first target matrix.

[0112] Specifically, the weight matrix is ​​used to characterize the probability that each atom in the transformation matrix is ​​an atom missed in the first stage of reconstruction. The higher the probability, the more likely it is to be a missed atom. The weight matrix of the transformation matrix can be calculated based on the distance between the remaining atoms in the transformation matrix excluding the first target matrix and the first atom index corresponding to the first target matrix.

[0113] S604. Calculate the second target matrix based on the weight matrix, transformation matrix, and the current second residual.

[0114] Among them, the current second residual is the latest first residual during the first-stage reconstruction process.

[0115] Specifically, in the first stage of reconstruction, most of the first target matrices that need to be used for sparse signal reconstruction have been selected, but there may be some unselected atoms that have been missed. Therefore, it is necessary to calculate the second target matrix based on the weight matrix, the transformation matrix and the current second residual.

[0116] S606, based on the first target matrix, the second target matrix and the compressed signal, perform a second-stage reconstruction of the original sparse signal to generate a second-stage reconstructed signal.

[0117] Specifically, the method for the second stage reconstruction of the original sparse signal is similar to that of the first stage reconstruction. It can be achieved by calculating the product of the transpose of the transformation matrix, the current second residual, and the weight matrix, and then further processing the product to select the missing atoms that need to be used for sparse signal reconstruction based on the processing result.

[0118] S608, update the current second residual according to the second stage reconstruction signal to generate a new current second residual, use the new current second residual as the current second residual, iteratively calculate the second stage reconstruction signal until the second preset iteration stop condition is met, and use the second stage reconstruction signal that meets the second preset iteration stop condition as the second stage target reconstruction signal.

[0119] The second preset iteration stopping condition includes the fact that the L2 norm of the current second residual is less than or equal to a preset threshold.

[0120] Specifically, after obtaining the second-stage reconstruction signal, the residual needs to be updated. Simultaneously, a second preset iteration stopping condition is used to determine whether the second-stage reconstruction is complete. This second preset iteration stopping condition includes the fact that the L2 norm of the current second residual is less than or equal to a preset threshold, which can be expressed as ||r t ||2≤δ. When the updated second residual is less than or equal to δ, it means that all atoms needed for sparse signal reconstruction have been selected through the first and second stages of reconstruction, and the second stage of reconstruction can be stopped at this point. If the updated second residual is greater than δ, then the second stage of reconstructed signal is iteratively calculated.

[0121] In this embodiment, the second-stage reconstruction can select atoms missed in the first-stage reconstruction, thus improving the accuracy of sparse signal reconstruction. Simultaneously, the second preset iteration stopping condition ensures the completion of the second-stage reconstruction, thereby obtaining an accurate second-stage target reconstruction signal. Therefore, setting the second preset iteration stopping condition also guarantees the accuracy of sparse signal reconstruction.

[0122] In one embodiment, such as Figure 7 As shown, the weight matrix of the transformation matrix is ​​calculated based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms corresponding to the first target matrix. This includes:

[0123] S702, calculate the minimum distance between the first atom index number and the atom index number corresponding to the first target matrix in the transformation matrix and the atom index number corresponding to the transformation matrix.

[0124] Specifically, during the first-stage reconstruction process, a portion of the first target matrix has already been selected from the transformation matrix. The closer an atom is to the selected first target matrix, the more likely it is to be an atom missed during the first-stage reconstruction. The formula for calculating this distance is as follows:

[0125]

[0126] Where λ is the index number of each atom in the first target matrix, i.e., the index number of the first atom.

[0127] S704, determine the probability that each atom in the transformation matrix is ​​an atom missed during the first-stage reconstruction process based on the minimum distance.

[0128] Specifically, the probability that an atom index missing in the first stage of reconstruction is different depends on the distance between the first atom index and the atom indices in the transformation matrix. This probability can be calculated using the following formula:

[0129]

[0130] Where a and b are shape parameters, this formula can be used to determine the probability that each atom in the transformation matrix is ​​an atom that was missed in the first stage of reconstruction.

[0131] S706, calculate the weight matrix of the transformation matrix based on the probability.

[0132] Specifically, the weight matrix of the transformation matrix can be represented as P t =diag(p t,0 ,…,p t,N-1 The specific meaning of this is the probability that the remaining atoms that were not selected during the first-stage reconstruction process are atoms that should have been selected but were not selected during the first-stage reconstruction process, after the first-stage target reconstruction signal is generated.

[0133] In this embodiment, a weight matrix is ​​calculated using distance and probability. Based on this weight matrix, the probability that the remaining atoms in the transformation matrix are atoms missed in the first-stage reconstruction process can be determined. Based on this probability, the first-stage reconstruction process can be further improved, thereby increasing the accuracy of sparse signal reconstruction.

[0134] The above embodiments mentioned the calculation of the second objective matrix. The specific calculation methods involved are described below. Figure 8 As shown, the calculation of the second objective matrix, based on the weight matrix, transformation matrix, and the current second residual, includes:

[0135] S802, multiply the weight matrix, the conjugate transpose of the transformation matrix, and the current second residual to generate the second initial vector.

[0136] Specifically, the current second residual is the latest current first residual in the first-stage reconstruction process. Multiplying the weight matrix, the conjugate transpose of the transformation matrix, and the current second residual yields the second initial vector, which can be represented as P. t A H r t-1 .

[0137] S804, calculate the modulus of each element in the second initial vector, select the maximum preset number of moduli from the moduli of each element, and obtain the second atom index number corresponding to the preset number of moduli.

[0138] Specifically, by calculating the modulus of each element in the second initial vector, the largest preset number of moduli are selected from the moduli of each element. For example, s atoms can be selected, and the second atom index numbers corresponding to the s atoms can be extracted. The largest modulus selected from the moduli of each element can be represented as abs(P t A H r t-1 ).

[0139] S806: Select the atom corresponding to the second atom index number from the transformation matrix according to the second atom index number, and use it as the second target matrix.

[0140] Specifically, after determining the second atom index, the atom corresponding to the second atom index can be found in the transformation matrix. This atom is then extracted from the transformation matrix to form the target matrix. By updating the residual multiple times, the target matrix can be selected multiple times, and finally, a second target matrix is ​​generated based on the selected target matrix.

[0141] In this embodiment, by calculating the modulus of each element in the second initial vector, the index numbers of multiple missing atoms in the first stage reconstruction can be determined at once, and then the second target matrix can be obtained based on the index numbers. Since this process can select multiple missing atoms at once, it can improve the reconstruction accuracy and efficiency of the sparse signal reconstruction process.

[0142] The sparse signal reconstruction method described above is illustrated below with a specific embodiment. The sparse signal reconstruction method includes:

[0143] The first step is to obtain the compressed signal and the corresponding transformation matrix.

[0144] The compressed signal is the signal generated by compressing the original sparse signal using a transformation matrix; the transformation matrix contains multiple atoms.

[0145] The second step is to extract multiple candidate matrices from the transformation matrix sequentially according to the preset sliding window size and preset step size.

[0146] The third step is to multiply the conjugate transpose of each candidate matrix with the current first residual to generate multiple first initial vectors.

[0147] The fourth step is to calculate the correlation between the candidate matrix and the current first residual based on multiple first initial vectors, obtain the first initial vector corresponding to the highest correlation, and obtain the first atom index number based on the first initial vector.

[0148] The fifth step is to select the atom corresponding to the first atom index number from the transformation matrix based on the first atom index number, and use it as the first target matrix.

[0149] The sixth step is to perform a first-stage reconstruction of the original sparse signal based on the first target matrix and the compressed signal to generate the first-stage reconstructed signal.

[0150] Step 7: Update the current first residual based on the reconstructed signal, compressed signal and first target matrix of the first stage to generate a new current first residual.

[0151] Step 8: Using the new current first residual as the current first residual, iteratively calculate the correlation between the candidate matrix and the current first residual, and use the candidate matrix corresponding to the highest correlation as the new first target matrix.

[0152] The ninth step involves performing a first-stage reconstruction of the original sparse signal based on the new first target matrix and the compressed signal to generate a new first-stage reconstructed signal.

[0153] Step 10: Determine whether the first preset iteration stopping condition is met.

[0154] In the eleventh step, if the first preset iteration stop condition is met, the first-stage reconstruction signal corresponding to the first target matrix is ​​taken as the first-stage target reconstruction signal.

[0155] Step 12: Calculate the minimum distance between the first atom index number and the atom index number corresponding to the first atom index number in the transformation matrix and the atom index number corresponding to the transformation matrix.

[0156] Step 13: Determine the probability that each atom in the transformation matrix is ​​an atom that was missed during the first stage of reconstruction based on the minimum distance.

[0157] Step fourteen: Calculate the weight matrix of the transformation matrix based on the probability.

[0158] The weight matrix represents the probability that each atom in the transformation matrix is ​​an atom that was missed during the first-stage reconstruction process.

[0159] Step 15: Multiply the weight matrix, the conjugate transpose of the transformation matrix, and the current second residual to generate the second initial vector.

[0160] Step sixteen: Calculate the modulus of each element in the second initial vector, select the maximum preset number of moduli from the moduli of each element, and obtain the second atom index number corresponding to the preset number of moduli.

[0161] Step 17: Select the atom corresponding to the second atom index from the transformation matrix according to the second atom index, and use it as the second target matrix.

[0162] Step 18: Based on the first target matrix, the second target matrix, and the compressed signal, perform a second-stage reconstruction of the original sparse signal to generate a second-stage reconstructed signal.

[0163] Step 19: Update the current second residual according to the second-stage reconstruction signal to generate a new current second residual. Use the new current second residual as the current second residual and iteratively calculate the second-stage reconstruction signal until the second preset iteration stop condition is met. Use the second-stage reconstruction signal that meets the second preset iteration stop condition as the second-stage target reconstruction signal. The second preset iteration stop condition includes that the L2 norm of the current second residual is less than or equal to a preset threshold.

[0164] Step 20: Generate a target reconstruction signal based on the target reconstruction signals from the first stage and the second stage.

[0165] In this embodiment, the sliding window method selects all candidate matrices. Therefore, calculating the relevance based on the selected candidate matrices allows for the selection of the vast majority of candidate matrices needed for reconstructing the original sparse signal, which are then used as the first target matrix. Consequently, the first-stage target reconstruction signal obtained by reconstructing the original sparse signal based on the first target matrix is ​​more accurate. Simultaneously, based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix itself, and the second residual, the atoms missed during the first-stage reconstruction can be calculated, and a second-stage reconstruction is performed on the original sparse signal to generate the second-stage target reconstruction signal. Since the second-stage target reconstruction signal contains the atoms missed in the first-stage target reconstruction, the target reconstruction signal obtained from both stages is also relatively complete. This means that the accuracy of sparse signal reconstruction based on the first and second-stage target reconstruction signals is higher. Furthermore, the first and second preset iteration stopping conditions limit the processes of the first and second stages of reconstruction, ensuring the completion of both stages and thus guaranteeing the accuracy of the sparse signal reconstruction.

[0166] To make the above description clearer, the sparse signal reconstruction method is described in pseudocode below. The pseudocode involved in the sparse signal reconstruction method is as follows:

[0167] Input: Transformation matrix A, compressed signal y

[0168] Output: Target reconstruction signal

[0169] Initialization: Atomic Index Number Residual r0 = y, iteration number t = 0

[0170] While the second iteration terminates under the condition of false do

[0171] t = t + 1

[0172] If the termination condition of the first iteration is false, then...

[0173] Determine the index number of the largest relevant atomic block:

[0174] Update the first objective matrix:

[0175] Update the first-stage target reconstruction signal:

[0176] Update the first residual:

[0177] else

[0178] Calculate the weight matrix: P t =diag(p t,0 ,…,p t,N-1 ),

[0179] in i∈{0,…,N-1}

[0180] Choose P t A H r t-1 The largest modulus of the s atoms j in the middle element t；0 ,…,j t；s-1

[0181] Update the second objective matrix:

[0182] Update the second-stage target reconstruction signal:

[0183] Update the second residual:

[0184] endif

[0185] endwhile

[0186]

[0187] Output target reconstruction signal: return

[0188] Of course, the above demonstration is only to illustrate the sparse signal reconstruction process more clearly and does not serve as a limitation.

[0189] The above embodiments introduced a sparse signal reconstruction method. The following will show the results of sparse signal reconstruction using traditional methods and the sparse signal reconstruction method in this application. Figure 9 This paper describes the relationship between signal block sparsity and reconstruction accuracy when reconstructing a sparse signal under the same observations, where N = 1024, M = 128, and the block length is 6. SBOMP is the sparse signal reconstruction method described in this application. Figure 9 In this context, α is a fixed parameter in the first preset iteration stopping condition, and s is the number of atoms selected during the second-stage reconstruction process. From... Figure 9 It can be seen that under the same observations, even with low signal block sparsity, the sparse signal reconstruction method in this application still has a high reconstruction accuracy, and among various traditional methods, the sparse signal reconstruction method in this application has the highest reconstruction accuracy.

[0190] Figure 10 When the blocky sparse signals are identical, the relationship between the observations and reconstruction accuracy of the sparse signal reconstruction method in this application and traditional sparse signal reconstruction is compared, where N = 1024, the sparse signal contains 8 block structures, and the length of each block structure is 6. From Figure 10 It can be seen that, when the block signal is the same, the reconstruction accuracy of the sparse signal reconstruction method in this application is higher than that of the traditional method when different observations are used.

[0191] Figure 11 The figure shows the relationship between the observations and the reconstruction accuracy when using the sparse signal reconstruction method of this application and traditional methods to reconstruct the same block-shaped sparse signal, where N = 1024, but with Figure 10 The difference is Figure 11 The sparse signal in the data contains three block structures with block lengths of 10, 20, and 30, respectively. Figure 11 It can be seen that the sparse signal reconstruction method used in this application has a higher reconstruction accuracy than traditional methods. In summary, this demonstrates that the sparse signal reconstruction method in this application has a higher reconstruction accuracy than traditional sparse signal reconstruction methods.

[0192] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0193] Based on the same inventive concept, this application also provides a sparse signal reconstruction apparatus for implementing the sparse signal reconstruction method described above. The solution provided by this apparatus is similar to the implementation described in the above method; therefore, the specific limitations in one or more sparse signal reconstruction apparatus embodiments provided below can be found in the limitations of the sparse signal reconstruction method described above, and will not be repeated here.

[0194] In one embodiment, such as Figure 12 As shown, a sparse signal reconstruction device 1200 is provided, including: an acquisition module 1220, a first reconstruction module 1240, a second reconstruction module 1260, and a generation module 1280, wherein:

[0195] The acquisition module 1220 is used to acquire the compressed signal and the corresponding transformation matrix; the compressed signal is the signal generated by compressing the original sparse signal using the transformation matrix; the transformation matrix includes multiple atoms;

[0196] The first reconstruction module 1240 is used to extract multiple candidate matrices sequentially from the transformation matrix using the sliding window method, determine the first target matrix based on the correlation between the multiple candidate matrices and the first residual, and perform a first-stage reconstruction on the original sparse signal to generate the first-stage target reconstruction signal.

[0197] The second reconstruction module 1260 performs second-stage reconstruction on the original sparse signal based on the first-stage target reconstruction signal, the remaining atoms in the transformation matrix excluding the first target matrix, the transformation matrix, and the second residual, to generate the second-stage target reconstruction signal.

[0198] The generation module 1280 is used to generate a target reconstruction signal based on the first-stage target reconstruction signal and the second-stage target reconstruction signal.

[0199] In another embodiment of the sparse signal reconstruction apparatus, the first reconstruction module 1240 includes:

[0200] The extraction unit is used to extract multiple candidate matrices sequentially from the transformation matrix according to a preset sliding window size and a preset step size;

[0201] The correlation calculation unit is used to calculate the correlation between each candidate matrix and the current first residual for each candidate matrix in multiple candidate matrices, and to take the candidate matrix with the highest correlation as the first target matrix.

[0202] The first reconstruction unit is used to perform a first-stage reconstruction of the original sparse signal based on the first target matrix and the compressed signal to generate a first-stage reconstructed signal; the initial value of the current residual is the compressed signal.

[0203] The first iterative calculation unit is used to update the current first residual according to the first stage reconstruction signal, generate a new current first residual, use the new current first residual as the current first residual, iteratively calculate the first stage reconstruction signal until the first preset iteration stop condition is met, and use the first stage reconstruction signal that meets the first preset iteration stop condition as the first stage target reconstruction signal.

[0204] In another embodiment of the sparse signal reconstruction apparatus, the correlation calculation unit includes:

[0205] The first vector generation subunit is used to multiply the conjugate transpose of each candidate matrix with the current first residual to generate multiple first initial vectors;

[0206] The first index number acquisition sub-unit is used to calculate the correlation between the candidate matrix and the current first residual based on multiple first initial vectors, obtain the first initial vector corresponding to the largest correlation, and obtain the first atom index number based on the first initial vector;

[0207] Select a sub-unit, which is used to select the corresponding target matrix from the transformation matrix according to the index number of each element, and use it as the first target matrix.

[0208] In another embodiment of the sparse signal reconstruction apparatus, the first iteration unit includes:

[0209] The residual generation subunit is used to update the current first residual based on the first-stage reconstructed signal, compressed signal and first target matrix, and generate a new current first residual.

[0210] The first matrix calculation subunit is used to take the new current first residual as the current first residual, iteratively calculate the correlation between the candidate matrix and the current first residual, and take the candidate matrix corresponding to the largest correlation as the new first target matrix.

[0211] The reconstruction subunit is used to perform a first-stage reconstruction of the original sparse signal based on the new first target matrix and the compressed signal to generate a new first-stage reconstructed signal.

[0212] The judgment sub-unit is used to determine whether the first preset iteration stop condition is met;

[0213] The target reconstruction signal determination subunit is used to take the first-stage reconstruction signal corresponding to the first target matrix as the first-stage target reconstruction signal if the first preset iteration stop condition is met.

[0214] In another embodiment of the sparse signal reconstruction apparatus, the second reconstruction module 1260 includes:

[0215] The weight matrix calculation unit is used to calculate the weight matrix of the transformation matrix based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms corresponding to the first target matrix. The weight matrix is ​​used to characterize the probability that each atom in the transformation matrix is ​​an atom that was missed in the first stage of reconstruction.

[0216] The target matrix calculation unit is used to calculate the second target matrix based on the weight matrix, the transformation matrix, and the current second residual; the current second residual is the latest first residual during the first-stage reconstruction process.

[0217] The second reconstruction unit performs a second-stage reconstruction of the original sparse signal based on the first target matrix, the second target matrix, and the compressed signal to generate a second-stage reconstructed signal.

[0218] The second iterative calculation unit is used to update the current second residual according to the second stage reconstruction signal, generate a new current second residual, use the new current second residual as the current second residual, iteratively calculate the second stage reconstruction signal until the second preset iteration stop condition is met, and use the second stage reconstruction signal that meets the second preset iteration stop condition as the second stage target reconstruction signal; the second preset iteration stop condition includes the second norm of the current second residual being less than or equal to a preset threshold.

[0219] In another embodiment of the sparse signal reconstruction apparatus, the weight matrix calculation unit includes:

[0220] The distance calculation subunit is used to calculate the minimum distance between the first atom index and the atom index of the transformation matrix based on the first atom index corresponding to the first target matrix in the transformation matrix and the atom index corresponding to the transformation matrix.

[0221] The probability calculation subunit is used to determine the probability that each atom in the transformation matrix is ​​an atom that was missed in the first stage of reconstruction based on the minimum distance.

[0222] The weight matrix calculation subunit is used to calculate the weight matrix of the transformation matrix based on probability.

[0223] In another embodiment of the sparse signal reconstruction apparatus, the second target matrix calculation unit includes:

[0224] The second vector calculation subunit is used to multiply the weight matrix, the conjugate transpose of the transformation matrix, and the current second residual to generate the second initial vector;

[0225] The second index number acquisition sub-unit is used to calculate the modulus of each element in the second initial vector, select a preset number of moduli from the moduli of each element, and obtain the second element index number corresponding to the preset number of moduli.

[0226] The second matrix calculation subunit is used to calculate the second target matrix from the atoms corresponding to the second atom index number.

[0227] Each module in the aforementioned sparse signal reconstruction device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0228] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 13 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores data required for the sparse signal reconstruction method, as well as the reconstructed sparse signal. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it implements a sparse signal reconstruction method.

[0229] Those skilled in the art will understand that Figure 13 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0230] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the sparse signal reconstruction method provided in the above method embodiment.

[0231] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the sparse signal reconstruction method provided in the above method embodiment.

[0232] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the sparse signal reconstruction method provided in the above method embodiments.

[0233] It should be noted that all data (including but not limited to data used for analysis, stored data, and displayed data) is information and data that has been authorized by the user or fully authorized by all parties.

[0234] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0235] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0236] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.< / j> < / j>

Claims

1. A sparse signal reconstruction method, characterized in that, The method includes: Obtain a compressed signal and a transformation matrix corresponding to the compressed signal; the compressed signal is a signal generated by compressing the original sparse signal using the transformation matrix; the transformation matrix includes multiple atoms. Multiple candidate matrices are sequentially extracted from the transformation matrix using the sliding window method. The first target matrix is ​​determined based on the correlation between the multiple candidate matrices and the first residual. The original sparse signal is then reconstructed in the first stage to generate the first-stage target reconstruction signal. The weight matrix of the transformation matrix is ​​calculated based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms corresponding to the first target matrix; the weight matrix is ​​used to characterize the probability that each atom in the transformation matrix is ​​an atom missed in the first stage of reconstruction. The second target matrix is ​​calculated based on the weight matrix, the transformation matrix, and the current second residual; the current second residual is the latest first residual during the first stage of reconstruction. Based on the first target matrix, the second target matrix, and the compressed signal, the original sparse signal is reconstructed in the second stage to generate a second-stage reconstructed signal. The current second residual is updated according to the second stage reconstruction signal to generate a new current second residual. The new current second residual is used as the current second residual. The second stage reconstruction signal is iteratively calculated until the second preset iteration stop condition is met. The second stage reconstruction signal that meets the second preset iteration stop condition is used as the second stage target reconstruction signal. The second preset iteration stop condition includes the L2 norm of the current second residual being less than or equal to a preset threshold. A target reconstruction signal is generated based on the first-stage target reconstruction signal and the second-stage target reconstruction signal.

2. The method according to claim 1, characterized in that, The process involves sequentially extracting multiple candidate matrices from the transformation matrix using a sliding window method, determining a first target matrix based on the correlation between the multiple candidate matrices and the first residual, and performing a first-stage reconstruction on the original sparse signal to generate a first-stage target reconstruction signal, including: Multiple candidate matrices are extracted sequentially from the transformation matrix according to a preset sliding window size and a preset step size; For each of the plurality of candidate matrices, the correlation between the candidate matrix and the current first residual is calculated, and the candidate matrix corresponding to the highest correlation is taken as the first target matrix; Based on the first target matrix and the compressed signal, the original sparse signal is reconstructed in the first stage to generate a first-stage reconstructed signal; the initial value of the current first residual is the compressed signal. The current first residual is updated according to the first stage reconstruction signal to generate a new current first residual. The new current first residual is used as the current first residual. The first stage reconstruction signal is iteratively calculated until a first preset iteration stop condition is met. The first stage reconstruction signal that meets the first preset iteration stop condition is used as the first stage target reconstruction signal.

3. The method according to claim 2, characterized in that, The step of calculating the correlation between each candidate matrix and the current first residual for each of the plurality of candidate matrices, and taking the candidate matrix with the highest correlation as the first target matrix, includes: Multiply the conjugate transpose of each candidate matrix with the current first residual to generate multiple first initial vectors; The correlation between the candidate matrix and the current first residual is calculated based on multiple first initial vectors, the first initial vector corresponding to the largest correlation is obtained, and the first atom index number is obtained based on the first initial vector; Based on the first atom index number, the atom corresponding to the first atom index number is selected from the transformation matrix to form the first target matrix.

4. The method according to claim 2, characterized in that, The first preset iteration stopping condition includes that the product of the number of rows of the compressed signal and a preset parameter is greater than or equal to the sparsity of the first target matrix; the step of updating the current first residual according to the first stage reconstruction signal, generating a new current residual, using the new current first residual as the current first residual, iteratively calculating the first stage reconstruction signal until the first preset iteration stopping condition is met, and using the first stage reconstruction signal that meets the first iteration stopping condition as the first stage target reconstruction signal includes: The current first residual is updated based on the first stage reconstruction signal, the compressed signal, and the first target matrix to generate a new current first residual; Using the new current first residual as the current first residual, iteratively calculate the correlation between the candidate matrix and the current first residual, and use the candidate matrix corresponding to the largest correlation as the new first target matrix; Based on the new first target matrix and the compressed signal, the original sparse signal is reconstructed in the first stage to generate a new first-stage reconstructed signal. Determine whether the first preset iteration stopping condition is met; If the first preset iteration stop condition is met, the first-stage reconstruction signal corresponding to the first target matrix will be used as the first-stage target reconstruction signal.

5. The method according to any one of claims 1-4, characterized in that, The step of calculating the weight matrix of the transformation matrix based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms corresponding to the first target matrix includes: Based on the first atom index number corresponding to the first target matrix in the transformation matrix and the atom index number corresponding to the transformation matrix, calculate the minimum distance between the first atom index number and the atom index number corresponding to the transformation matrix; The probability that each atom in the transformation matrix is ​​an atom missed during the first-stage reconstruction is determined based on the minimum distance. The weight matrix of the transformation matrix is ​​calculated based on the probability.

6. The method according to any one of claims 1-4, characterized in that, The second target matrix is ​​calculated based on the weight matrix, the transformation matrix, and the current second residual, including: Multiply the weight matrix, the conjugate transpose of the transformation matrix, and the current second residual to generate the second initial vector; Calculate the modulus of each element in the second initial vector, select the maximum preset number of moduli from the moduli of each element, and obtain the second atom index number corresponding to the preset number of moduli; The atom corresponding to the second atom index number is selected from the transformation matrix according to the second atom index number, and used as the second target matrix.

7. A sparse signal reconstruction device, characterized in that, The device includes: An acquisition module is used to acquire a compressed signal and a transformation matrix corresponding to the compressed signal; the compressed signal is a signal generated by compressing the original sparse signal using the transformation matrix; the transformation matrix includes multiple atoms. The first reconstruction module is used to extract multiple candidate matrices sequentially from the transformation matrix using a sliding window method, determine the first target matrix based on the correlation between the multiple candidate matrices and the first residual, and perform a first-stage reconstruction on the original sparse signal to generate a first-stage target reconstruction signal. The second reconstruction module includes: a weight matrix calculation unit, used to calculate the weight matrix of the transformation matrix based on the index numbers of the remaining atoms in the transformation matrix excluding the first target matrix and the index numbers of the first atoms corresponding to the first target matrix; the weight matrix is ​​used to characterize the probability that each atom in the transformation matrix is ​​an atom missed in the first stage reconstruction process; a target matrix calculation unit, used to calculate a second target matrix based on the weight matrix, the transformation matrix, and the current second residual; the current second residual is the latest first residual in the first stage reconstruction process; a second reconstruction unit, used to perform a second stage reconstruction on the original sparse signal based on the first target matrix, the second target matrix, and the compressed signal, generating a second stage reconstruction signal; and a second iteration calculation unit, used to update the current second residual based on the second stage reconstruction signal, generate a new current second residual, use the new current second residual as the current second residual, iteratively calculate the second stage reconstruction signal until a second preset iteration stop condition is met, and use the second stage reconstruction signal that meets the second preset iteration stop condition as the second stage target reconstruction signal; the second preset iteration stop condition includes that the L2 norm of the current second residual is less than or equal to a preset threshold. The generation module is used to generate a target reconstruction signal based on the first-stage target reconstruction signal and the second-stage target reconstruction signal.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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