CN116975517B - Sparse recovery method and system for partial weighted random selection strategy - Google Patents
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Abstract
The invention discloses a sparse recovery method and a system for a partial weighted random selection strategy, wherein the method comprises the following steps: s1, taking an underdetermined linear system as a target, simulating and generating a large-scale sparse signal and a corresponding perception matrix, randomly selecting a preset number of elements from the sparse signal to keep original values, returning values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix; s2, a greedy method for selecting indexes in the OMP algorithm is replaced by a partial weighted random selection strategy, and a sparse signal estimated value is obtained through calculation. The beneficial effects of the invention are as follows: the partial weighted random selection strategy is adopted to reduce a large amount of computation consumption caused by computation correlation in the iterative process, a random method is utilized to find a suboptimal solution, meanwhile, the reliability of the algorithm is ensured, and the aim of accelerating the sparse signal recovery algorithm in compressed sensing can be fulfilled.
Description
Technical Field
The invention relates to the technical field of compressed sensing signal processing, in particular to a sparse recovery method and system of a partial weighted random selection strategy.
Background
Big data includes not only traditional structured data (e.g., tabular data in a database), but also unstructured data such as text, images, audio, video, etc. These diverse data types make data analysis more complex and challenging.
The conventional deterministic algorithm, such as the orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm, is a well-known algorithm for solving the problem in the compressed sensing field, and can effectively recover sparse signals from an underdetermined linear system, for example, a sequential orthogonal matching pursuit algorithm based on compressed sensing disclosed in CN106487389a uses the algorithm. However, today, where the amount of data is increasing, applying deterministic algorithms to large-scale signal recovery typically consumes a significant amount of time, which is detrimental to improving the operating efficiency of the system.
Disclosure of Invention
Aiming at the problem of large-scale signal recovery under big data, the invention provides a sparse recovery method and a system of a partial weighted random selection strategy, which are used for reducing the time consumption of an algorithm by using a random method and accelerating the operation of the algorithm.
In order to solve the above technical problems, a first aspect of the present invention provides a sparse recovery method of a partial weighted random selection strategy, including the following steps:
s1, taking an underdetermined linear system as a target, simulating and generating a large-scale sparse signal and a corresponding perception matrix, randomly selecting a preset number of elements from the sparse signal to keep original values, returning values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix;
s2, a greedy method for selecting indexes in an OMP algorithm is replaced by a partial weighted random selection strategy, and the sparse signal estimated value is obtained through calculation.
In some embodiments, in S1, the method for calculating the underdetermined linear system is:
，
wherein,for the sense matrix +.>For sparse signals, ++>For observing signals, a sensing matrix->The number of lines and columns is respectivelySparsity of sparse signal is defined as +.>，/>，/>And->。
In some embodiments, in S2, the OMP algorithm is used as a skeleton, in an iterative process, a current residual is updated by using a matrix product of the sparse signal estimation value and the sensing matrix, the current residual is used for the next iteration, in a process of iterative computation of a preset number of times, a partial weighted random selection strategy is applied, a correlation between a column of the sensing matrix and the current residual is computed by randomly selecting a column index with the largest correlation in a self-adaptive number of times, the column index is selected as an estimation value of a non-zero element index in the sparse signal, and then the sparse signal estimation value is obtained by a least square method computation based on an estimation value of all previous iterations on the non-zero element index of the sparse signal.
In some embodiments, the number of iterations of the OMP algorithm is the sparsity of the sparse signal.
In some embodiments, the method for calculating the correlation is:
，
wherein,representing the perception matrix->Is>Column (S)/(S)>Indicate->Residual error of multiple iterations,/>Representing the inner product of both.
In some embodiments, further comprising S3, S3 comprises: and simultaneously acquiring a support set of the sparse signal and the sparse signal estimated value, carrying out intersection operation on the two support sets, acquiring a set base number of an obtained result, and taking the ratio of the set base number to the support set base number of the sparse signal as the recovery accuracy of the sparse signal.
In some embodiments, the method for calculating the recovery accuracy rate includes:
，
wherein,representing the passage->Said sparse signal estimate, < >>Representing the sparse signal,/->Representing the cardinality of the collection.
The second aspect of the present invention provides a sparse recovery system with a partial weighted random selection strategy, comprising;
the data preprocessing module is used for simulating and generating a large-scale sparse signal and a corresponding perception matrix by taking an underdetermined linear system as a target, randomly selecting a preset number of elements from the sparse signal to keep original values, resetting the values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix;
and the sparse signal estimated value output module is used for adopting a partial weighted random selection strategy to replace the greedy method of the original selection index in the OMP algorithm, and calculating to obtain the sparse signal estimated value.
The third aspect of the present invention proposes an electronic device, where the electronic device includes a processor and a memory, where at least one instruction, at least one section of program, a code set, or an instruction set is stored in the memory, where the at least one instruction, the at least one section of program, the code set, or the instruction set is loaded and executed by the processor, so as to implement the sparse recovery method of the partial weighted random selection policy described above.
In a fourth aspect, the present invention proposes a computer readable storage medium, where at least one instruction, at least one program, a code set, or an instruction set is stored, where the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor, so as to implement a sparse recovery method of the above-mentioned partial weighted random selection policy.
The beneficial effects of the invention are as follows: the partial weighted random selection strategy is adopted to reduce a large amount of computation consumption caused by computation correlation in the iterative process, a random method is utilized to find a suboptimal solution, meanwhile, the reliability of the algorithm is ensured, and the aim of accelerating the sparse signal recovery algorithm in compressed sensing can be fulfilled.
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Fig. 1 is a flowchart of a sparse recovery method of a partial weighted random access strategy according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the architecture of an underdetermined linear system;
FIG. 3 is a flowchart of an OMP algorithm according to an embodiment of the invention;
FIG. 4 is a flowchart of a sparse recovery method of a partially weighted random access strategy according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of an electronic device according to a third embodiment of the present invention.
Detailed Description
Some of the terms in the embodiments of the present application are explained below to facilitate understanding by those skilled in the art.
Underdetermined linear system: in the compressed sensing field, the number of rows of the sensing matrix is far smaller than the number of columns, i.e. the number of equations of the linear equation is far smaller than the number of unknowns. Based on linear algebraic knowledge, the system of equations has an infinite number of solutions. In general, the mathematical formula for compressed sensing can be expressed asWherein->Is a sense matrix +.>Is a sparse signal, i.e. a signal that needs to be recovered, < ->Is the observed signal.
Sparse signal: in the field of compressed sensing, sparse signals refer to signals in which the non-zero elements in the signal are much less than zero elements. In other words, the value of most elements in the signal is 0.
Sparseness: in the compressed sensing field, sparsity is used to measure the number of non-zero elements of a sparse signal. If the sparsity of one sparse signal is said to beThat is to say the number of non-zero elements of the sparse signal does not exceed +.>And each.
Index: the index is typically taken from a natural number starting from 0, referring to the number of element positions in the vector or matrix. The natural number is directly used as position information in the vector, and the row and column positions where the elements are located are expressed in the matrix by a pair of groups.
Support set: in the compressed sensing field, most elements in a signal are 0 due to sparsity of the signal. Taking indexes (positions) of non-zero elements in the signals as elements, forming a set of all indexes meeting the above conditions, and naming the set as a support set. The support set is a set of indices, the elements in the set, i.e., the indices in the signal, corresponding to the indices of all non-zero elements in the signal.
Residual and correlation: in OMP algorithms, residuals are typically usedIndicating that the residual is updated once in each iteration, in general, +.>The residual of the second iteration is denoted->. The calculation formula of the residual initial value before the iteration starts is as follows. Each subsequent step of iterative residual updating formula is +.>. Correlation refers to each iterationWherein, the inner product of the current residual error and each column of the perception matrix, specifically, the correlation calculation formula is as follows. It is noted that the index of the algorithm that takes the highest correlation refers to the one that takes the highest absolute value of the correlation.
The present invention will be described in further detail with reference to the drawings and the detailed description below, in order to make the objects, technical solutions and advantages of the present invention more clear and distinct. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting thereof. It should be further noted that, for convenience of description, only some, but not all of the matters related to the present invention are shown in the accompanying drawings.
Example 1
The embodiment provides a sparse recovery method of a partial weighted random selection strategy, which reduces a large amount of computation consumption caused by computation correlation in an iterative process by adopting the partial weighted random selection strategy, searches for a suboptimal solution by utilizing a random method, ensures the reliability of an algorithm, and can achieve the aim of accelerating a sparse signal recovery algorithm in compressed sensing.
As shown in fig. 1, the method mainly comprises the following steps S1-S3:
s1, taking an underdetermined linear system as a target, simulating and generating a large-scale sparse signal and a corresponding perception matrix, randomly selecting a preset number of elements from the sparse signal to keep original values, returning values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix.
In S1, the problem of compressed sensing is built on the underdetermined linear system and the sparse signal, which is difficult to solve in the actual situation, but has a problem of practical significance, so that a certain requirement is required for the sensing matrix and the sparse signal. Let the sensing matrix beThe number of rows and columns are->Wherein->Sparse signal is defined as +.>Is +.>Is a column vector with sparsity of +.>. Typically, a gaussian matrix is used as the perception matrix, in particular, a gaussian matrix refers to a gaussian distribution in which each element of the perception matrix follows an independent co-distribution, i.e. Each element of the sparse signal is subjected to standard Gaussian distribution with independent same distribution, namely normal distribution with a mean value of 0 and a variance of 1. Then, to satisfy the sparse condition, choose +.>The individual elements retain the original values, after which the values of the other elements are zeroed. After completion of the sensing matrix->And sparse signal->After generation of (a) the observation signal is calculated using matrix multiplication +.>. The parameters needed by the algorithm are obtained so far: perception matrix->Observing signal->And sparsity->Let the algorithm derived sparse signal estimator be +.>The use of sparse signals is required>To measure +.>Is accurate. The present model is shown in fig. 2.
Therefore, the calculation method of the underdetermined linear system is as follows:
，
wherein,for the sense matrix +.>For sparse signals, ++>For observing signals, a sensing matrix->The number of lines and columns is respectivelySparsity of sparse signal is defined as +.>，/>，/>And->。
S2, a greedy method for selecting indexes in the OMP algorithm is replaced by a partial weighted random selection strategy, and a sparse signal estimated value is obtained through calculation.
In S2, using OMP algorithm as skeleton, in iterative process, using matrix product of estimated value of sparse signal and perception matrix to update current residual error, and using current residual error to make next iteration, in iterative calculation process of preset times, applying partial weighted random selection strategy, using self-adaptive times to randomly select column of perception matrix and current residual error to calculate correlation, selecting column index with maximum correlation, using column index as estimated value of non-zero element index in sparse signal, then calculating to obtain estimated value of sparse signal by least square method based on estimated value of non-zero element index of sparse signal in previous iteration. Specifically, the partial weighted random access strategy requires a preset maximum number of comparisons, typically usingTo represent. In each iteration, randomly selecting one column of the sensing matrix, recording the index of the current column, performing inner product with the current residual error to obtain correlation, randomly selecting another column which is not selected in the iteration, performing inner product with the current residual error to obtain correlation, discarding the index of the column if the correlation of the column is larger, recording the index of the column of the correlation, recording the comparison times, otherwise, performing no change, and continuing random selection. If the number of comparisons reaches the maximum number of comparisons +.>Or no columns of the sensing matrix which can be selected exist, namely the correlation between all columns of the sensing matrix and the current residual error is calculated, the partial weighted random selection strategy is finished, the currently recorded column index is used as an estimated value for the non-zero element index, the subsequent step of the OMP algorithm is continued, namely the sparse signal estimation is calculated through a least square method, the residual error is updated, and the next iteration is carried out. The general steps of the OMP algorithm are shown in fig. 3. The process of this step is shown in FIG. 4。
It should be noted in particular that the partial weighted random selection strategy proposed by the present invention only records column indexes that are more relevant than the current one for each random selection and selects multiple times. The method can adaptively select a plurality of times, thereby ensuring that the finally selected index is more similar to the index of the greedy method. More importantly, the method can greatly save the time for calculating the correlation due to the random method, effectively save the operand in the calculation process and reduce the time consumption of the algorithm. The iteration number of the OMP algorithm is the sparsity of the sparse signal.
The correlation calculation method comprises the following steps:
，
wherein,representing the perception matrix->Is>Column (S)/(S)>Indicate->Residual error of multiple iterations,/>Representing the inner product of both. It is believed that the greater the correlation, the more likely the index corresponding to the column is to be the index of the non-zero element in the sparse signal.
As an optional step in this embodiment, S3 is further included: and simultaneously acquiring a support set of the sparse signal and the sparse signal estimated value, performing intersection operation on the two support sets, acquiring a set base number from an obtained result, and taking the ratio of the set base number to the support set base number of the sparse signal as the recovery accuracy of the sparse signal.
The calculation method of the recovery accuracy rate comprises the following steps:
，
wherein,representing the passage->Said sparse signal estimate, < >>Representing the sparse signal,/->Representing the cardinality of the collection.
Example two
Based on the same inventive concept, the embodiment of the invention also provides a sparse recovery system of a partial weighted random selection strategy, which comprises the following steps of;
the data preprocessing module is used for simulating and generating a large-scale sparse signal and a corresponding perception matrix by taking the underdetermined linear system as a target, randomly selecting a preset number of elements from the sparse signal to keep original values, resetting the values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix;
and the sparse signal estimated value output module is used for adopting a partial weighted random selection strategy to replace the greedy method of the original selection index in the OMP algorithm, and calculating to obtain the sparse signal estimated value.
The recovery verification module is used for simultaneously acquiring the sparse signal and the support set of the sparse signal estimated value, carrying out intersection operation on the two support sets, obtaining a set base number as an obtained result, and taking the ratio of the set base number to the support set base number of the sparse signal as the recovery accuracy of the sparse signal.
The program executed by the hardware module in this embodiment may refer to S1 to S3 described in embodiment one.
Example III
Referring to fig. 5, based on the same inventive concept, an embodiment of the present invention further provides an electronic device, where the electronic device includes a processor and a memory, where at least one instruction, at least one section of program, a code set, or an instruction set is stored in the memory, where the at least one instruction, the at least one section of program, the code set, or the instruction set is loaded and executed by the processor, so as to implement the sparse recovery method of the partial weighted random access policy described in the embodiment.
It is understood that the Memory may include random access Memory (Random Access Memory, RAM) or Read-Only Memory (RAM). Optionally, the memory includes a non-transitory computer readable medium (non-transitory computer-readable storage medium). The memory may be used to store instructions, programs, code sets, or instruction sets. The memory may include a stored program area and a stored data area, wherein the stored program area may store instructions for implementing an operating system, instructions for at least one function, instructions for implementing the various method embodiments described above, and the like; the storage data area may store data created according to the use of the server, etc.
The processor may include one or more processing cores. The processor uses various interfaces and lines to connect various portions of the overall server, perform various functions of the server, and process data by executing or executing instructions, programs, code sets, or instruction sets stored in memory, and invoking data stored in memory. Alternatively, the processor may be implemented in hardware in at least one of digital signal processing (Digital Signal Processing, DSP), field programmable gate array (Field-Programmable Gate Array, FPGA), programmable logic array (Programmable Logic Array, PLA). The processor may integrate one or a combination of several of a central processing unit (Central Processing Unit, CPU) and a modem etc. Wherein, the CPU mainly processes an operating system, application programs and the like; the modem is used to handle wireless communications. It will be appreciated that the modem may not be integrated into the processor and may be implemented by a single chip.
Because the electronic device is an electronic device corresponding to the sparse recovery method of the partial weighted random selection strategy according to the embodiment of the present invention, and the principle of the electronic device for solving the problem is similar to that of the method, the implementation of the electronic device can refer to the implementation process of the first or second embodiment, and the repetition is omitted.
Example IV
Based on the same inventive concept, the embodiments of the present invention further provide a computer readable storage medium, where at least one instruction, at least one section of program, a code set, or an instruction set is stored, where the at least one instruction, the at least one section of program, the code set, or the instruction set is loaded and executed by a processor to implement the sparse recovery method of the partial weighted random selection policy described in the embodiment.
Those of ordinary skill in the art will appreciate that all or part of the steps of the various methods of the above embodiments may be implemented by a program that instructs associated hardware, the program may be stored in a computer readable storage medium including Read-Only Memory (ROM), random access Memory (Random Access Memory, RAM), programmable Read-Only Memory (Programmable Read-Only Memory, PROM), erasable programmable Read-Only Memory (Erasable Programmable Read Only Memory, EPROM), one-time programmable Read-Only Memory (OTPROM), electrically erasable programmable Read-Only Memory (EEPROM), compact disc Read-Only Memory (Compact Disc Read-Only Memory, CD-ROM) or other optical disk Memory, magnetic disk Memory, tape Memory, or any other medium that can be used for carrying or storing data that is readable by a computer.
Because the storage medium is a storage medium of the sparse recovery method of the partial weighted random access policy according to the embodiment of the present invention, and the principle of the storage medium for solving the problem is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the first embodiment of the method, and the repetition is omitted.
In some possible implementations, the aspects of the method of the embodiments of the present invention may also be implemented in the form of a program product comprising program code for causing a computer device to carry out the steps of the sparse signal recovery method according to the various exemplary embodiments of the present application as described above in this specification, when the program product is run on a computer device. Wherein executable computer program code or "code" for performing the various embodiments may be written in a high-level programming language such as C, C ++, c#, smalltalk, java, javaScript, visual Basic, structured query language (e.g., act-SQL), perl, or in a variety of other programming languages.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, and are not intended to limit the scope of the present invention. All equivalent changes or modifications made in accordance with the essence of the present invention should be included in the scope of the present invention.
The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, and are not intended to limit the scope of the present invention. All equivalent changes or modifications made in accordance with the essence of the present invention are intended to be included within the scope of the present invention.
Claims (9)
1. The sparse recovery method of the partial weighted random selection strategy is characterized by comprising the following steps of:
s1, taking an underdetermined linear system as a target, simulating and generating a large-scale sparse signal and a corresponding perception matrix, randomly selecting a preset number of elements from the sparse signal to keep original values, returning values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix;
s2, a greedy method for selecting indexes in an OMP algorithm is replaced by a partial weighted random selection strategy, and a sparse signal estimated value is obtained through calculation; in S2, using the OMP algorithm as a skeleton, in an iterative process, updating a current residual by using a matrix product of the sparse signal estimation value and the sensing matrix, and performing the next iteration by using the current residual, in a process of iterative computation of a preset number of times, applying a partial weighted random selection strategy, randomly selecting a column of the sensing matrix and the current residual to compute a correlation by using an adaptive number of times, selecting a column index with the largest correlation, taking the column index as an estimation value of a non-zero element index in the sparse signal, and then calculating to obtain the sparse signal estimation value by a least square method based on an estimation value of all previous iterations on the non-zero element index of the sparse signal.
2. The sparse recovery method of claim 1, wherein in S1, the calculation method of the underdetermined linear system is:
wherein,for the sense matrix +.>For sparse signals, ++>For observing signals, a sensing matrix->The number of lines and columns is +.>Sparsity of sparse signal is defined as +.>，/>，/>,/>And->。
3. The method for sparse recovery of a partially weighted random selection strategy of claim 1, wherein the number of iterations of the OMP algorithm is the sparsity of the sparse signal.
4. The sparse recovery method of a partially weighted random access strategy of claim 1, wherein the correlation calculation method is:
，
wherein the method comprises the steps of，Representing the perception matrix->Is>Column (S)/(S)>Indicate->Residual error of multiple iterations,/>Representing the inner product of both.
5. The sparse recovery method of claim 1, further comprising S3, S3 comprising: and simultaneously acquiring a support set of the sparse signal and the sparse signal estimated value, carrying out intersection operation on the two support sets, acquiring a set base number of an obtained result, and taking the ratio of the set base number to the support set base number of the sparse signal as the recovery accuracy of the sparse signal.
6. The sparse recovery method of claim 5, wherein the recovery accuracy calculation method is as follows:
wherein,representing the passage->Said sparse signal estimate, < >>Representing the sparse signal,/->Representing the cardinality of the collection.
7. The sparse recovery system of a partial weighted random selection strategy is characterized by comprising the following components;
the data preprocessing module is used for simulating and generating a large-scale sparse signal and a corresponding perception matrix by taking an underdetermined linear system as a target, randomly selecting a preset number of elements from the sparse signal to keep original values, resetting the values of other elements to zero, and calculating an observation signal according to the sparse signal and the perception matrix;
the sparse signal estimation value output module is used for replacing the greedy method of the original selection index in the OMP algorithm by adopting a partial weighted random selection strategy, and calculating to obtain the sparse signal estimation value; and in the iterative process, updating a current residual error by using the matrix product of the sparse signal estimated value and the perception matrix, carrying out the next iteration by using the current residual error, applying a partial weighted random selection strategy in the iterative calculation process of preset times, randomly selecting the column of the perception matrix and the current residual error by using self-adaptive times to calculate the correlation, selecting the column index with the largest correlation, taking the column index as the estimated value of the non-zero element index in the sparse signal, and then calculating the sparse signal estimated value by a least square method based on the estimated value of the non-zero element index of the sparse signal in all previous iterations.
8. An electronic device comprising a processor and a memory, wherein the memory stores at least one instruction, at least one program, a set of codes, or a set of instructions, the at least one instruction, the at least one program, the set of codes, or the set of instructions being loaded and executed by the processor to implement the sparse recovery method of the partially weighted random access policy of any one of claims 1-6.
9. A computer readable storage medium having stored therein at least one instruction, at least one program, code set, or instruction set, the at least one instruction, the at least one program, the code set, or instruction set being loaded and executed by a processor to implement the sparse recovery method of the partially weighted random access policy of any of claims 1-6.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103036576A (en) * | 2012-12-20 | 2013-04-10 | 南开大学 | Two-value sparse signal reconstruction algorithm based on compressive sensing theory |
| CN103117819A (en) * | 2013-01-18 | 2013-05-22 | 宁波大学 | Pulse ultra wide band signal detection method based on compressed sensing |
| CN103399292A (en) * | 2013-07-22 | 2013-11-20 | 西安电子科技大学 | Soft sparse representation-based direction of arrival (DOA) estimation method |
| CN103944579A (en) * | 2014-04-10 | 2014-07-23 | 东华大学 | Coding and decoding system for compressed sensing reconstitution |
| KR101874259B1 (en) * | 2017-10-26 | 2018-07-03 | 인하대학교 산학협력단 | Method and system for performing random access based on compressive sensing for machine type communications considering tradeoff between link performance and latency |
| CN112234994A (en) * | 2020-09-29 | 2021-01-15 | 西南石油大学 | Compressed sensing reconstruction signal processing method and system, computer equipment and application |
| CN115412102A (en) * | 2022-10-31 | 2022-11-29 | 人工智能与数字经济广东省实验室(广州) | Sparse signal recovery method, system, device and medium based on sparse random Kaczmarz algorithm |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2014144306A1 (en) * | 2013-03-15 | 2014-09-18 | Arizona Board Of Regents On Behalf Of Arizona State University | Ensemble sparse models for image analysis and restoration |
| US20140337017A1 (en) * | 2013-05-09 | 2014-11-13 | Mitsubishi Electric Research Laboratories, Inc. | Method for Converting Speech Using Sparsity Constraints |
-
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- 2023-09-21 CN CN202311218518.8A patent/CN116975517B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103036576A (en) * | 2012-12-20 | 2013-04-10 | 南开大学 | Two-value sparse signal reconstruction algorithm based on compressive sensing theory |
| CN103117819A (en) * | 2013-01-18 | 2013-05-22 | 宁波大学 | Pulse ultra wide band signal detection method based on compressed sensing |
| CN103399292A (en) * | 2013-07-22 | 2013-11-20 | 西安电子科技大学 | Soft sparse representation-based direction of arrival (DOA) estimation method |
| CN103944579A (en) * | 2014-04-10 | 2014-07-23 | 东华大学 | Coding and decoding system for compressed sensing reconstitution |
| KR101874259B1 (en) * | 2017-10-26 | 2018-07-03 | 인하대학교 산학협력단 | Method and system for performing random access based on compressive sensing for machine type communications considering tradeoff between link performance and latency |
| CN112234994A (en) * | 2020-09-29 | 2021-01-15 | 西南石油大学 | Compressed sensing reconstruction signal processing method and system, computer equipment and application |
| CN115412102A (en) * | 2022-10-31 | 2022-11-29 | 人工智能与数字经济广东省实验室(广州) | Sparse signal recovery method, system, device and medium based on sparse random Kaczmarz algorithm |
Non-Patent Citations (3)
| Title |
|---|
| Compressed Sensing Method for Health Monitoring of Pipelines Based on Guided Wave Inspection;Zhe Wang et.al;《IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT》;第4722-4732页 * |
| 噪声干扰下m2OLS 算法的稀疏重构分析;李海锋等;《中国科学》(第9期);第1451-1460页 * |
| 稀疏重构的压缩感知语声增强模型与算法;李洋等;《信号处理》(第9期);第1120-1126页 * |
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