Sparse signal recovery method and device

Abstract

This application discloses a sparse signal recovery method and apparatus, comprising: performing signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario; and performing sparse signal recovery using an iterative detection method using N parallel processes based on the signal obtained from the signal measurement and the measurement matrix; wherein, during each iterative detection, each parallel process uses a distributed consensus algorithm (DCBA) to determine a signal detection vector, where N is the number of elements contained in the sparse signal to be recovered. This application can improve the efficiency of sparse signal recovery.

Description

Technical Field

[0001] The present invention relates to mobile communication technology, and in particular to a sparse signal recovery method and device. Background Art

[0002] Sparse signal recovery is a core problem in the theoretical and technical framework of compressed sensing. Sparse signals, where the vast majority of their elements are zero, have broad applications in interdisciplinary fields that exploit the sparse nature of signals or images, such as signal processing, medical imaging, and radar systems.

[0003] During the implementation of the present invention, the inventors discovered that existing sparse signal recovery schemes suffer from low recovery efficiency, making them inefficient on massively parallel platforms such as FPGAs and ASICs. Research revealed that the primary reason for the low recovery efficiency of existing sparse signal recovery schemes is that they are generally executed in a serial manner, resulting in extended processing time and low efficiency. Summary of the Invention

[0004] In view of this, the main purpose of the present invention is to provide a sparse signal recovery method and device, which can improve the recovery efficiency.

[0005] In order to achieve the above objectives, the technical solutions proposed in the embodiments of the present invention are as follows:

[0006] A sparse signal recovery method, comprising:

[0007] Performing signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario;

[0008] Based on the signal obtained by the signal measurement and the measurement matrix, sparse signal recovery is performed using N parallel processes and an iterative detection method; wherein, during each iterative detection, each parallel process uses a distributed consensus algorithm (DCBA) to determine a signal detection vector, where N is the number of elements contained in the sparse signal to be recovered.

[0009] Preferably, each iterative detection includes:

[0010] Each of the processes P that is currently running n , judge whether the current selected support set contains its own process number n, if yes, then end the running of its own process; otherwise, add its own process number n to the selected support set Λ s , get the process P n In this iteration, the corresponding support set is detected Based on the support set and the specified measurement matrix, for the process P nConstruct the measurement matrix used in this iterative detection Using the measurement matrix Solve using the distributed consensus method And from the signal detection vector obtained Select the vector element with the smallest absolute value In which, during the first iterative detection, the N parallel processes are all in a running state; N is the number of elements contained in the signal to be recovered; s is the current number of iterative detections; the initial state of the selected support set is an empty set; y is the signal obtained by the signal measurement;

[0011] The vector elements from all currently running processes In the example, select the vector element with the largest absolute value and set the current selected support set Λ s Update to sequence number n max Process Pn max The corresponding support set Among them, the n max is the process number corresponding to the vector element with the largest absolute value;

[0012] If the current iterative detection times s is less than the iterative detection times threshold K, then continue with the next iterative detection; otherwise, the selected support set Λ obtained by this iterative detection is s and the process Pn max The corresponding signal detection vector It is output as the sparse signal recovery result; the iterative detection number threshold K is the number of non-zero elements contained in the sparse signal to be restored.

[0013] Preferably, the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection include:

[0014] With the support set Each element in is used as the column number, and the corresponding column is obtained from the specified measurement matrix. All the obtained columns are combined to obtain the measurement matrix

[0015] Preferably, the measurement matrix is ​​used Solve using the distributed consensus method include:

[0016] x1, based on the measurement matrix calculate Get matrix X; Based on the matrix X, calculate Get the convergence rate parameter ρ; initialize the inner layer iteration number t to 1; where, for The conjugate transposed matrix of express The first line of express The pseudo-inverse of k(X) represents the condition number of the matrix X; M represents the measurement matrix number of rows;

[0017] x2, using parallel computing, based on the measurement matrix Each row in Calculate the corresponding and in accordance with Calculate the corresponding Wherein, the I s is the unit vector in s-dimensional space; The lth element of the signal obtained by measuring the signal; represents the square of the 2-norm; express The null space projection matrix of ;

[0018] x3. According to For all the above Performing average calculation, we get

[0019] x4, using parallel computing, based on the measurement matrix Each row corresponds to and as well as according to Calculate the corresponding rows in, μ max is the largest eigenvalue of matrix X; μ min is the minimum eigenvalue of matrix X;

[0020] x5. Based on the above and stated according to calculate in,

[0021] x6. Update the t according to t=t+1. If the t-th power of the convergence speed parameter ρ is greater than the preset maximum allowable error, return to step x4. Otherwise, determine the signal detection vector For the

[0022] An embodiment of the present invention further provides a sparse signal recovery device, comprising:

[0023] A signal measurement unit, configured to perform signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario;

[0024] A signal recovery unit is used to perform sparse signal recovery based on the signal obtained by the signal measurement and the measurement matrix using N parallel processes and an iterative detection method; wherein, during each iterative detection, each parallel process uses a distributed consensus method DCBA to determine a signal detection vector, and N is the number of elements contained in the sparse signal to be recovered.

[0025] Preferably, the signal recovery unit is specifically configured to utilize the N parallel processes to perform sparse signal recovery in an iterative detection manner, wherein each iterative detection includes:

[0026] Each of the processes P that is currently running n , judge whether the current selected support set contains its own process number n, if yes, then end the running of its own process; otherwise, add its own process number n to the selected support set Λ s , get the process P n In this iteration, the corresponding support set is detected Based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection Using the measurement matrix Solve using the distributed consensus method And from the signal detection vector obtained Select the vector element with the smallest absolute value In which, during the first iterative detection, the N parallel processes are all in a running state; N is the number of elements contained in the signal to be recovered; s is the current number of iterative detections; the initial state of the selected support set is an empty set; y is the signal obtained by the signal measurement;

[0027] The vector elements from all currently running processes In the example, select the vector element with the largest absolute value and set the current selected support set Λ s Update to sequence number n max Process Pn max The corresponding support set Among them, the n max is the process number corresponding to the vector element with the largest absolute value;

[0028] If the current iterative detection times s is less than the iterative detection times threshold K, then continue with the next iterative detection; otherwise, the selected support set Λ obtained by this iterative detection is s and the process Pn max The corresponding signal detection vector It is output as the sparse signal recovery result; the iterative detection number threshold K is the number of non-zero elements contained in the sparse signal to be restored.

[0029] Preferably, the signal recovery unit is specifically configured to recover the signal based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection include:

[0030] With the support set Each element in is used as the column number, and the corresponding column is obtained from the specified measurement matrix. All the obtained columns are combined to obtain the measurement matrix

[0031] Preferably, the signal recovery unit is specifically configured to utilize the measurement matrix Solve using the distributed consensus method include:

[0032] x1, based on the measurement matrix calculate Get matrix X; Based on the matrix X, calculate Get the convergence rate parameter ρ; initialize the inner layer iteration number t to 1; where, for The conjugate transposed matrix of express The first line of express The pseudo-inverse of κ(X) represents the condition number of matrix X; M represents the measurement matrix number of rows;

[0033] x2, using parallel computing, based on the measurement matrix Each row in Calculate the corresponding and in accordance with Calculate the corresponding Wherein, the I s is the unit vector in s-dimensional space; The lth element of the signal obtained by measuring the signal; represents the square of the 2-norm; express The null space projection matrix of ;

[0034] x3. According to For all the above Performing average calculation, we get

[0035] x4, using parallel computing, based on the measurement matrix Each row corresponds to and as well as according to Calculate the corresponding rows in, μ max is the largest eigenvalue of matrix X; μ min is the minimum eigenvalue of matrix X;

[0036] x5. Based on the above and stated according to calculate in,

[0037] x6. Update the t according to t=t+1. If the t-th power of the convergence speed parameter ρ is greater than the preset maximum allowable error, return to step x4. Otherwise, determine the signal detection vector For the

[0038] An embodiment of the present invention further provides a non-volatile computer-readable storage medium, wherein the non-volatile computer-readable storage medium stores instructions, which, when executed by a processor, enable the processor to perform the steps of the sparse signal recovery method described above.

[0039] An embodiment of the present invention further provides an electronic device, comprising the non-volatile computer-readable storage medium as described above, and the processor capable of accessing the non-volatile computer-readable storage medium.

[0040] In summary, the sparse signal recovery scheme proposed in the embodiment of the present invention is based on the signal obtained by the signal measurement and the measurement matrix, and uses the same number of parallel processes as the number N of elements contained in the sparse signal to be recovered, and adopts an iterative detection method to perform sparse signal recovery, and in each iterative detection, each parallel process uses the DCBA method to determine the signal detection vector. In this way, by splitting the logical function of sparse signal recovery into two layers, that is, in the outer layer, N parallel processes are used to perform support set detection, and in the inner layer, each parallel process uses the DCBA method to determine the signal detection vector, so that both the outer layer and the inner layer can be parallelized on a large scale. In addition, when determining the signal detection vector, each parallel process is constructed based on DCBA. On the one hand, it can give full play to the parallel capability of DCBA while reducing the complex calculations in the core steps. On the other hand, it can utilize the sparsity of the signal to be recovered so that DCBA can iterate quickly. Therefore, the use of the embodiment of the present application can effectively improve the recovery efficiency of sparse signals. Moreover, the scenarios for signal measurement in the embodiments of the present application include scenarios with noise pollution, so that the embodiments of the present application can also perform sparse signal recovery under noise pollution conditions, thereby effectively expanding the application scenarios of the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of the device structure of an embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] Figure 1 FIG. 1 is a flow chart of a sparse signal recovery method according to an embodiment of the present invention. Figure 1 As shown, this embodiment mainly includes:

[0045] Step 101: Perform signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario.

[0046] It should be noted that, unlike existing sparse signal recovery schemes, signal measurement in this step is no longer limited by the noise in the scene. This means that signal measurement can be performed even in the presence of noise contamination, and the noise-contaminated signal measurement results can still be used for sparse signal recovery in subsequent steps. Specifically, the M-dimensional signal y obtained after signal measurement in this step can be expressed as:

[0047] y=Φx+n Formula (1)

[0048] Where n represents the M-dimensional measurement noise, Φ is the M×N-dimensional measurement matrix, x=[x1,x2,...,x N ] is the high-dimensional signal to be restored, N is the number of elements contained in the signal x. Assume that x is K-sparse, that is, |supp(x)|≤K, where supp(x)={i:x i ≠0} represents the support set of x, and |·| represents the size of the set.

[0049] Step 102: Based on the signal obtained by the signal measurement and the measurement matrix, N parallel processes are used to perform sparse signal recovery in an iterative detection manner.

[0050] In each iterative detection, each of the parallel processes adopts a distributed consensus algorithm (DCBA) to determine a signal detection vector, where N is the number of elements contained in the sparse signal to be restored.

[0051] In this step, N parallel processes are used to perform sparse signal recovery through iterative detection. This parallel processing can shorten the processing time of a single iterative detection, effectively improving the efficiency of iterative detection. Furthermore, during each iterative detection, DCBA is called in parallel, with each parallel process using the DCBA method to determine the signal detection vector. This DCBA-based approach not only fully utilizes DCBA's parallel capabilities while reducing complex computations in the core steps, but also leverages the sparsity of the signal to be recovered, enabling rapid DCBA iteration. Therefore, this step enables large-scale parallelization of sparse signal recovery logic, ensuring extremely low-latency processing and significantly improving sparse signal recovery efficiency.

[0052] In one embodiment, the specific implementation process of each iterative detection in this step may include the following steps:

[0053] Step 1021: Each process P currently in operation n , judge whether the current selected support set contains its own process number n, if yes, then end the running of its own process; otherwise, add its own process number n to the selected support set Λ s , get the process P n In this iteration, the corresponding support set is detected Based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection Using the measurement matrix Solve using the distributed consensus method And from the signal detection vector obtained Select the vector element with the smallest absolute value

[0054] Among them, the N parallel processes are all in running state during the first iterative detection; N is the number of elements contained in the signal to be recovered; s is the current number of iterative detections, which indicates that the current is the sth iterative detection; the initial state of the selected support set is an empty set, that is, the selected support set is an empty set during the first iterative detection; y is the signal obtained by the signal measurement.

[0055] In this step, each parallel process P that is currently running n , it is necessary to determine whether the currently selected support set contains the sequence number n of its own process. If so, it means that the parallel process P n The signal detection task has been completed and the iterative detection process can be exited. Therefore, it is necessary to end the operation of its own process. In this way, by introducing an early exit mechanism for parallel processes, the sparsity of the signal to be recovered can be utilized to effectively reduce the detection running time.

[0056] In one embodiment, the following method can be specifically used in step 1021: based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection

[0057] With the support set Each element in is used as the column number, and the corresponding column is obtained from the specified measurement matrix. All the obtained columns are combined to obtain the measurement matrix Thus, the measurement matrix That is, a subset of the specified measurement matrix.

[0058] In one embodiment, step 1021 may specifically adopt the following steps x1 to x6, using the measurement matrix Solve using the distributed consensus method

[0059] x1, based on the measurement matrix calculate Get matrix X; Based on the matrix X, calculate Get the convergence rate parameter ρ; initialize the number of inner layer iterations t to 1.

[0060] in, Right now is a 1×s-dimensional vector, for The conjugate transposed matrix of express The first line of express The pseudo-inverse of κ(X) represents the condition number of matrix X; M represents the measurement matrix number of rows.

[0061] x2, using parallel computing, based on the measurement matrix Each row in Calculate the corresponding and in accordance with Calculate the corresponding Wherein, the I s is the unit vector in s-dimensional space; The lth element of the signal obtained by measuring the signal; represents the square of the 2-norm; express The null space projection matrix of .

[0062] In this step, parallel computing is used and based on the measurement matrix Each row in Calculate the corresponding Can take full advantage of parallel processing to improve the solution efficiency.

[0063] x3. According to For all the above Performing average calculation, we get

[0064] x4, using parallel computing, based on the measurement matrix Each row corresponds to and as well as according to Calculate the corresponding rows

[0065] in, μ max is the largest eigenvalue of matrix X; μ min is the smallest eigenvalue of the matrix X.

[0066] In this step, parallel computing is used and based on the measurement matrix Each row corresponds to and as well as Calculate the corresponding rows Can take full advantage of parallel processing to improve the solution efficiency.

[0067] x5. Based on the above and stated according to calculate

[0068] in,

[0069] x6. Update the t according to t=t+1. If the t-th power of the convergence speed parameter ρ is greater than the preset maximum allowable error, return to step x4. Otherwise, determine the signal detection vector For the

[0070] In the above steps x4 and x5, the parameters and The optimization problem solving in the existing method can be avoided, thereby reducing the complexity of parameter setting.

[0071] From the above, we use the DCBA method to solve It can be seen from the process that the above method uses the DCBA method to solve the signal detection vector. On the one hand, it can give full play to the parallel capability of DCBA while reducing the complex operations in the core steps. For example, steps x4 and x5 do not have the least squares or matrix inversion operations in the orthogonal matching pursuit (OMP) algorithm. On the other hand, the sparsity of the signal to be recovered can be used to enable DCBA to iterate quickly.

[0072] Step 1022: From the vector elements of all processes currently in operation In the example, select the vector element with the largest absolute value and set the current selected support set Λ s Update to sequence number n max Process Pn max The corresponding support set

[0073] Among them, the n max is the process number corresponding to the vector element with the largest absolute value.

[0074] Step 1023: If the current iterative detection times s is less than the iterative detection times threshold K, continue with the next iterative detection; otherwise, the selected support set Λ obtained by the current iterative detection is s and the process Pn max The corresponding signal detection vector It is output as the sparse signal recovery result; the iterative detection number threshold K is the number of non-zero elements contained in the sparse signal to be restored.

[0075] In this step, when the number of iterative detections s reaches the iterative detection threshold K, the selected support set Λ obtained by the Kth iterative detection is s and process Pn max The corresponding signal detection vector The sparse signal recovery result is output, ending the iterative detection process.

[0076] Corresponding to the above method embodiment, the embodiment of the present invention further provides a sparse signal recovery device, such as Figure 2 As shown, the device mainly includes:

[0077] A signal measurement unit, configured to perform signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario;

[0078] A signal recovery unit is used to perform sparse signal recovery based on the signal obtained by the signal measurement and the measurement matrix using N parallel processes and an iterative detection method; wherein, during each iterative detection, each parallel process uses a distributed consensus method DCBA to determine a signal detection vector, and N is the number of elements contained in the sparse signal to be recovered.

[0079] In one embodiment, the signal recovery unit is specifically configured to perform sparse signal recovery using the N parallel processes in an iterative detection manner, wherein each iterative detection includes:

[0080] Each of the processes P that is currently running n , judge whether the current selected support set contains its own process number n, if yes, then end the running of its own process; otherwise, add its own process number n to the selected support set Λ s , get the process P n In this iteration, the corresponding support set is detected Based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection Using the measurement matrix Solve using the distributed consensus method And from the signal detection vector obtained Select the vector element with the smallest absolute value In which, during the first iterative detection, the N parallel processes are all in a running state; N is the number of elements contained in the signal to be recovered; s is the current number of iterative detections; the initial state of the selected support set is an empty set; y is the signal obtained by the signal measurement;

[0081] The vector elements from all currently running processes In the example, select the vector element with the largest absolute value and set the current selected support set Λ s Update to sequence number n max Process Pn max The corresponding support set Among them, the n max is the process number corresponding to the vector element with the largest absolute value;

[0082] If the current iterative detection times s is less than the iterative detection times threshold K, then continue with the next iterative detection; otherwise, the selected support set Λ obtained by this iterative detection is s and the process Pn max The corresponding signal detection vector It is output as the sparse signal recovery result; the iterative detection number threshold K is the number of non-zero elements contained in the sparse signal to be restored.

[0083] In one embodiment, the signal recovery unit is specifically configured to recover the signal based on the support set. and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection include:

[0084] With the support set Each element in is used as the column number, and the corresponding column is obtained from the specified measurement matrix. All the obtained columns are combined to obtain the measurement matrix

[0085] In one embodiment, the signal recovery unit is specifically configured to utilize the measurement matrix Solve using the distributed consensus method include:

[0086] x1, based on the measurement matrix calculate Get matrix X; Based on the matrix X, calculate Get the convergence rate parameter ρ; initialize the inner layer iteration number t to 1; where, for The conjugate transposed matrix of express The first line of express The pseudo-inverse of κ(X) represents the condition number of matrix X; M represents the measurement matrix number of rows;

[0087] x2, using parallel computing, based on the measurement matrix Each row in Calculate the corresponding and in accordance with Calculate the corresponding Wherein, the I s is the unit vector in s-dimensional space; The lth element of the signal obtained by measuring the signal; represents the square of the 2-norm; express The null space projection matrix of ;

[0088] x3. According to For all the above Performing average calculation, we get

[0089] x4, using parallel computing, based on the measurement matrix Each row corresponds to and as well as according to Calculate the corresponding rows in, μ max is the largest eigenvalue of matrix X; μ min is the minimum eigenvalue of matrix X;

[0090] x5. Based on the above and stated according to calculate in,

[0091] x6. Update the t according to t=t+1. If the t-th power of the convergence speed parameter ρ is greater than the preset maximum allowable error, return to step x4. Otherwise, determine the signal detection vector For the

[0092] Based on the above-mentioned sparse signal recovery method embodiment, the embodiment of the present application also implements a sparse signal recovery electronic device, including a processor and a memory; an application program that can be executed by the processor is stored in the memory, which is used to enable the processor to execute the sparse signal recovery method as described above. Specifically, a system or device equipped with a storage medium can be provided, on which a software program code that implements the functions of any of the embodiments described above is stored, and the computer (or CPU or MPU) of the system or device reads out and executes the program code stored in the storage medium. In addition, the operating system operating on the computer can also be used to complete part or all of the actual operations based on the instructions of the program code. The program code read out from the storage medium can also be written to a memory provided in an expansion board inserted into the computer or to a memory provided in an expansion unit connected to the computer, and then based on the instructions of the program code, a CPU installed on the expansion board or expansion unit is made to perform part and all of the actual operations, thereby realizing the functions of any of the embodiments described above in the sparse signal recovery method implementation method.

[0093] Specifically, the memory may be implemented as various storage media such as electrically erasable programmable read-only memory (EEPROM), flash memory, and programmable read-only memory (PROM). The processor may be implemented as including one or more central processing units (CPUs) or one or more field programmable gate arrays (FPGAs), wherein the FPGAs integrate one or more CPU cores. Specifically, the CPU or CPU core may be implemented as a CPU or an MCU.

[0094] An embodiment of the present application implements a computer program product, including a computer program / instruction, which implements the steps of the sparse signal recovery method described above when executed by a processor.

[0095] It should be noted that not all steps and modules in the above processes and structure diagrams are required, and certain steps or modules can be omitted based on actual needs. The execution order of the steps is not fixed and can be adjusted as needed. The division of the modules is merely for the convenience of describing the functional division adopted. In actual implementation, a module can be implemented by multiple modules, and the functions of multiple modules can be implemented by the same module. These modules can be located in the same device or in different devices.

[0096] The hardware modules in each embodiment can be implemented mechanically or electronically. For example, a hardware module may include a specially designed permanent circuit or logic device (such as a dedicated processor, such as an FPGA or ASIC) for performing a specific operation. The hardware module may also include a programmable logic device or circuit (such as a general-purpose processor or other programmable processor) temporarily configured by software to perform a specific operation. As for whether to implement the hardware module mechanically, or using a dedicated permanent circuit, or using a temporarily configured circuit (such as configured by software), it can be decided based on cost and time considerations.

[0097] In this document, "schematic" means "serving as an example, instance or illustration", and any diagram or embodiment described as "schematic" in this document should not be interpreted as a more preferred or more advantageous technical solution. In order to keep the drawings simple, each figure only schematically shows the parts related to the present invention, and does not represent its actual structure as a product. In addition, in order to keep the drawings simple and easy to understand, in some figures, only one of the components with the same structure or function is schematically drawn, or only one of them is marked. In this document, "one" does not mean that the number of relevant parts of the present invention is limited to "only one", and "one" does not mean excluding the situation where the number of relevant parts of the present invention is "more than one". In this document, "upper", "lower", "front", "back", "left", "right", "inside", "outside" and the like are only used to indicate the relative positional relationship between the relevant parts, rather than to limit the absolute positions of these relevant parts.

[0098] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A sparse signal recovery method, characterized in that: include: Performing signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario; Based on the signal obtained by the signal measurement and the measurement matrix, sparse signal recovery is performed using N parallel processes in an iterative detection manner; wherein, during each iterative detection, each parallel process uses a distributed consensus method (DCBA) to determine a signal detection vector, where N is the number of elements contained in the sparse signal to be recovered; Each iterative detection includes: Each of the processes P that is currently running n , judge whether the current selected support set contains its own process number n, if yes, then end the running of its own process; otherwise, add its own process number n to the selected support set Λ s , get the process P n In this iteration, the corresponding support set is detected Based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection Using the measurement matrix Solve using the distributed consensus method And from the signal detection vector obtained Select the vector element with the smallest absolute value In which, during the first iterative detection, the N parallel processes are all in a running state; N is the number of elements contained in the signal to be recovered; s is the current number of iterative detections; the initial state of the selected support set is an empty set; y is the signal obtained by the signal measurement; The vector elements from all currently running processes In the example, select the vector element with the largest absolute value and set the current selected support set Λ s Update to sequence number n max Process The corresponding support set Among them, the n max is the process number corresponding to the vector element with the largest absolute value; If the current iterative detection times s is less than the iterative detection times threshold K, then continue with the next iterative detection; otherwise, the selected support set Λ obtained by this iterative detection is s and the process The corresponding signal detection vector It is output as the sparse signal recovery result; the iterative detection number threshold K is the number of non-zero elements contained in the sparse signal to be restored.

2. The method according to claim 1, characterized in that Based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection include: With the support set Each element in is used as the column number, and the corresponding column is obtained from the specified measurement matrix. All the obtained columns are combined to obtain the measurement matrix 3. The method according to claim 1, characterized in that The use of the measurement matrix Solve using the distributed consensus method include: x1, based on the measurement matrix calculate Get matrix X; Based on the matrix X, calculate Get the convergence rate parameter ρ; initialize the inner layer iteration number t to 1; where, is α l The conjugate transpose of α l express The first line of Represents α l The pseudo-inverse of κ(X) represents the condition number of the matrix X; M represents the measurement matrix number of rows; x2, using parallel computing, based on the measurement matrix Each row in Calculate P corresponding to each row l , and in accordance with Calculate the z corresponding to each row l (0); wherein said I s is the unit vector of s-dimensional space; y l The lth element of the signal obtained by measuring the signal; represents the square of the 2-norm; P l Represents α l The null space projection matrix of ; x3. According to For all the above l (0) Perform average calculation and get x4, using parallel computing, based on the measurement matrix Each row in the P l and z l (t-1) and according to Calculate the z corresponding to the corresponding rows respectively l (t); where μ max is the largest eigenvalue of matrix X; μ min is the minimum eigenvalue of matrix X; x5. Based on the z l (t) and according to calculate in, x6. Update the t according to t=t+1. If the t-th power of the convergence speed parameter ρ is greater than the preset maximum allowable error, return to step x4. Otherwise, determine the signal detection vector For the 4. A sparse signal recovery device, characterized in that: include: A signal measurement unit, configured to perform signal measurement based on a specified measurement matrix; wherein the signal measurement scenario includes a noise-contaminated scenario; a signal recovery unit, configured to perform sparse signal recovery based on the signal obtained by the signal measurement and the measurement matrix using N parallel processes and an iterative detection method; wherein, during each iterative detection, each parallel process uses a distributed consensus method (DCBA) to determine a signal detection vector, where N is the number of elements contained in the sparse signal to be recovered; The signal recovery unit is specifically configured to perform sparse signal recovery using the N parallel processes in an iterative detection manner, wherein each iterative detection includes: Each of the processes P that is currently running n , judge whether the current selected support set contains its own process number n, if yes, then end the running of its own process; otherwise, add its own process number n to the selected support set Λ s , get the process P n In this iteration, the corresponding support set is detected Based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection Using the measurement matrix Solve using the distributed consensus method And from the signal detection vector obtained Select the vector element with the smallest absolute value In which, during the first iterative detection, the N parallel processes are all in a running state; N is the number of elements contained in the signal to be recovered; s is the current number of iterative detections; the initial state of the selected support set is an empty set; y is the signal obtained by the signal measurement; The vector elements from all currently running processes In the example, select the vector element with the largest absolute value and set the current selected support set Λ s Update to sequence number n max Process The corresponding support set Among them, the n max is the process number corresponding to the vector element with the largest absolute value; If the current iterative detection times s is less than the iterative detection times threshold K, then continue with the next iterative detection; otherwise, the selected support set Λ obtained by this iterative detection is s and the process The corresponding signal detection vector It is output as the sparse signal recovery result; the iterative detection number threshold K is the number of non-zero elements contained in the sparse signal to be restored.

5. The device according to claim 4, characterized in that The signal recovery unit is specifically configured to recover the signal based on the support set and the specified measurement matrix, for the process P n Construct the measurement matrix used in this iterative detection include: With the support set Each element in is used as the column number, and the corresponding column is obtained from the specified measurement matrix. All the obtained columns are combined to obtain the measurement matrix 6. The device according to claim 4, characterized in that The signal recovery unit is specifically configured to utilize the measurement matrix Solve using the distributed consensus method include: x1, based on the measurement matrix calculate Get matrix X; Based on the matrix X, calculate Get the convergence rate parameter ρ; initialize the inner layer iteration number t to 1; where, is α l The conjugate transpose of α l express The first line of Represents α l The pseudo-inverse of κ(X) represents the condition number of the matrix X; M represents the measurement matrix number of rows; x2, using parallel computing, based on the measurement matrix Each row in Calculate P corresponding to each row l , and in accordance with Calculate the z corresponding to each row l (0); wherein said I s is the unit vector of s-dimensional space; y l The lth element of the signal obtained by measuring the signal; represents the square of the 2-norm; P l Indicates a l The null space projection matrix of ; x3. According to For all the above l (0) Perform average calculation and get x4, using parallel computing, based on the measurement matrix Each row in the P l and z l (t-1) and according to Calculate the z corresponding to the corresponding rows respectively l (t); where μ max is the largest eigenvalue of matrix X; μ min is the minimum eigenvalue of matrix X; x5. Based on the z l (t) and according to calculate in, x6. Update the t according to t=t+1. If the t-th power of the convergence speed parameter ρ is greater than the preset maximum allowable error, return to step x4. Otherwise, determine the signal detection vector For the 7. A non-volatile computer-readable storage medium storing instructions, characterized in that: When the instructions are executed by a processor, the processor is caused to perform the steps of the sparse signal recovery method according to any one of claims 1 to 3.

8. An electronic device, characterized in that: The method comprises the non-volatile computer-readable storage medium of claim 7 and the processor capable of accessing the non-volatile computer-readable storage medium.

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