CN107977680A - A kind of method of the sparse reconstruct of signal - Google Patents
A kind of method of the sparse reconstruct of signal Download PDFInfo
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Abstract
The invention discloses a kind of method of the sparse reconstruct of signal, including inner product value is calculated, and inner product value is normalized；Choose maximum inner product value inner product value is summed, it is supported collection to choose the corresponding position of maximum K value；By loop iteration, to being updated every time to supported collection, the precision of supported collection is improved；Final signal reconstruction result is obtained by least square method.The method of the sparse reconstruct of signal of the present invention can improve reconstruction accuracy and reconstruct efficiency with joint sparse characteristic signal, the present invention is directed to the signal reconstruction problem with joint sparse characteristic, it is proposed a kind of new reconstructing method, this method takes full advantage of the joint sparse characteristic of all signals during signal supported collection (nonzero element position) is found, more accurately supported collection information thus can be searched more preferably, faster, so as to improve the reconstruction property and efficiency of algorithm.
Description
Technical Field
The invention relates to the technical field of information, in particular to a signal sparse reconstruction method.
Background
In actual signal processing, echo signals generally have joint sparse characteristics, that is, in a certain sparse domain, the support set positions (non-zero element positions) of all signals are the same, and such signal models are generally referred to as joint sparse models. For the model, the distributed compressed sensing algorithm can fully utilize the structural characteristic during reconstruction, and a better sparse reconstruction result is obtained.
However, the currently commonly used Subspace tracking algorithm (SP) cannot utilize the joint sparse information of the signals to improve the sparse reconstruction performance. In addition, a Distributed Subspace tracking algorithm (DiSP) and a Distributed Parallel tracking algorithm (dispp) obtained based on the algorithm are both proposed for the mixed support set model, that is, echo signals have both a joint sparse part and a part unique to the echo signals. Therefore, when these two methods are used for reconstruction of joint sparse models, the reconstruction accuracy and efficiency are not ideal.
Disclosure of Invention
Based on the defects of the prior art, the technical problem to be solved by the invention is to provide a signal sparse reconstruction method, which makes full use of the joint sparse characteristics of all signals, better and faster searches for more accurate support set information, and improves the reconstruction performance and efficiency of the algorithm.
In order to solve the above technical problem, the present invention provides a method for signal sparse reconstruction, comprising the following steps:
1. calculating an inner product value and normalizing the inner product value;
2. selecting a maximum inner product value, summing the inner product values, and selecting a position corresponding to the maximum K values as a support set;
3. through loop iteration, the support set is updated each time, and the precision of the support set is improved;
4. and obtaining a final signal reconstruction result by a least square method.
As a preferred implementation manner of the foregoing technical solution, the method for signal sparse reconstruction provided in the embodiment of the present invention further includes some or all of the following technical features:
in the first step:
calculate the inner product value of each signal:
δ j,l ＝<y j ,Φ j >,j＝1,..,J (1)
wherein < represents inner product operation, y j Representing signals with joint sparseness, phi j Denotes the sparse radical, δ j,l Representing the inner product value of the jth signal.
In the second step:
selecting a support set, selecting the maximum K inner product values, and finding the position information corresponding to the K values:
γ l ＝max(z l ,K),j＝1,..,J (2)
Ω l ＝max_indices(γ l ),j＝1,..,J (3)
wherein gamma is l Represents the maximum K inner product values, Ω l The position of the nonzero element corresponding to the maximum inner product value, namely the information of the support set;
and (3) summing the inner product values of all signals:
z l ＝sum(abs(δ j,l )) (4)
where abs () represents an absolute value operation, sum () represents a sum operation, δ j,l Representing the inner product value of the jth signal.
In the third step:
the non-zero information obtained by first removing it from the signal is obtained by the following method:
in the formulaRepresenting the extraction of the support set omega from the sparse basis corresponding to the jth signal l Corresponding column, y j Representing signals having a joint sparsity characteristic,representsExtracting a support set omega from a sparse basis corresponding to the jth signal l The conjugate of the corresponding column.
And then, the steps one to three are cycled until the inner product value is minimum, which indicates that a correct support set is obtained.
In the fourth step:
using the support set information obtained by the above search, and using a least square method to obtain a final sparse reconstruction result, which can be expressed as:
in the formulaFor the j-th reconstructed signal,support set, phi, representing the jth reconstructed signal j Denotes the sparse radical, l is the number of cycles, y j Representing signals with joint sparsity.
Therefore, the reconstruction precision and the reconstruction efficiency of the signal with the joint sparse feature can be improved by the signal sparse reconstruction method, the invention provides a new reconstruction method aiming at the signal reconstruction problem with the joint sparse feature, and the joint sparse feature of all signals is fully utilized in the process of searching the signal support set (non-zero element position), so that more accurate support set information can be searched better and faster, and the reconstruction performance and the reconstruction efficiency of the algorithm are improved.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following detailed description is given in conjunction with the preferred embodiments, together with the accompanying drawings.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly described below.
Fig. 1 is a flow chart of a method for sparse reconstruction of signals according to a preferred embodiment of the present invention.
Fig. 2 is a diagram of the effect of the signal reconstruction in the method for sparse signal reconstruction of the present invention.
Fig. 3a is a graph of signal sparse reconstruction results when the signal-to-noise ratio is 20 dB.
Fig. 3b is a graph of the signal sparse reconstruction result when the signal-to-noise ratio is 10 dB.
Fig. 3c is a graph of the reconstruction error for different algorithms under different signal-to-noise ratios.
Fig. 4a is a graph of the signal sparse reconstruction result when the sampling number is 40.
Fig. 4b is a graph of the signal sparse reconstruction result when the sampling number is 20.
Fig. 4c is a reconstruction error map for different algorithms at different sample numbers.
Detailed Description
Other aspects, features and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the invention and which, together with the description, serve to explain the principles of the invention. In the referenced drawings, the same or similar components in different drawings are denoted by the same reference numerals.
FIG. 1 is a schematic flow chart of a method for sparse reconstruction of signals according to a preferred embodiment of the present invention, in which y is a signal with joint sparse property 1 ，...，y j ，y J ]The corresponding sparse basis is [ phi ] 1 ，...，Φ j ，Φ J ]And K is the sparsity of the signal,is an initial support set;r j,0 ＝y j for initial residuals, l is the number of cycles.
The first step is as follows: calculating an inner product value of each signal, and normalizing the inner product values:
δ j,l ＝<y j ,Φ j >,j＝1,..,J (1)
wherein < represents inner product operation, y j Representing signals with joint sparsity, phi j Denotes the sparse radical, δ j,l Representing the inner product value of the j-th signal.
The second step: selecting a support set, selecting the maximum K inner product values, and finding the position information corresponding to the K values:
γ l ＝max(z l ,K),j＝1,..,J (2)
Ω l ＝max_indices(γ l ),j＝1,..,J (3)
wherein gamma is l Represents the maximum K inner product values, Ω l The position of the nonzero element corresponding to the maximum inner product value, namely the information of the support set;
and (3) summing the inner product values of all signals:
z l ＝sum(abs(δ j,l )) (4)
where abs () represents an absolute value operation, sum () represents a sum operation, δ j,l Representing the inner product value of the j-th signal.
The fourth step: cyclically updated support set
The non-zero information obtained by first removing it from the signal is obtained by the following method:
in the formulaRepresenting the extraction of the support set omega from the sparse basis corresponding to the jth signal l Corresponding column, y j Is shown as havingIn conjunction with the signals of the sparse nature,representing the extraction of the support set omega from the sparse basis corresponding to the jth signal l The conjugate of the corresponding column.
And then, circulating from the first step to the third step until the inner product value is minimum, so that a correct support set is obtained.
The fifth step: obtaining the final reconstruction result
Using the support set information obtained by the above search, and using a least square method to obtain a final sparse reconstruction result, which can be expressed as:
in the formulaFor the j-th reconstructed signal,support set, phi, representing the jth reconstructed signal j Denotes the sparse radical, l is the number of cycles, y j Representing signals with joint sparseness.
Assuming that the transmitted signal is a joint sparse signal, the sparsity of the transmitted signal is K =10, the preset sparsity K =15, the number of the transmitted signals J =256, the length of the signal N =200, and the signal amplitude and the position information are randomly generated, the reconstruction results of the SP algorithm, the DiPP algorithm and the DiSP algorithm are provided as comparison for embodying the beneficial effects of the invention.
Simulation 1: validation of new algorithms
Fig. 1 is a graph of the effect of a reconstructed signal, where the abscissa in fig. 1 represents the length of a sparse signal and the ordinate represents the magnitude of the amplitude of a non-zero element of the signal. It can be seen from fig. 1 that the method for sparse reconstruction of signals of the present invention can also correctly reconstruct the result as the conventional SP algorithm.
Simulation 2: performance comparison at different signal-to-noise ratios
In order to test the reconstruction performance of the method (NDSP algorithm) under different signal-to-noise ratios, a simulation 2 experiment is designed. Fig. 2 a-2 ab show the signal sparse reconstruction results under different signal-to-noise ratios, fig. 2c shows the reconstruction errors under different signal-to-noise ratios in different algorithms, the abscissa in fig. 2c shows the signal-to-noise ratio, the ordinate shows the reconstruction errors, and the error calculation method is as followsWhere x is the original signal and x' is the reconstructed signal.
From the result of the simulation 2, it can be seen that the reconstruction performance of the signal sparse reconstruction method (NDSP algorithm) of the present invention under the condition of low signal-to-noise ratio is obviously due to other algorithms.
Simulation 3: performance comparison at different sample numbers
This experiment was designed to examine the reconstruction performance of the method (NDSP algorithm) under different sample numbers. Fig. 3 (a) - (b) show the signal sparse reconstruction results under different sampling numbers, fig. 3 (c) shows the reconstruction errors of different algorithms under different sampling numbers, in the figure, the abscissa α is the sampling rate, and the calculation method is α = M/N, where M is the sampled signal length and N is the total signal length.
From the result of the simulation 3, it can be seen that the reconstruction performance of the signal sparse reconstruction method of the present invention under the condition of low sampling number is obviously due to other algorithms.
And (4) simulation: reconstructed velocity comparison
This experiment was designed to compare the reconstruction efficiency of the method. The computer used for simulation is configured with an Intel core E7500 processor and 2GB memory. The results of simulation comparison of the processing times of the above algorithms are shown in the following table, and it can be seen that the NDSP algorithm of the present invention has the least amount of running time.
TABLE 1 several Algorithm runtime comparison
| Algorithm | Operation time(s) | Algorithm | Operation time(s) |
| SP | 0.23 | DiSP | 10.51 |
| DiPP | 11.06 | NDSP | 0.22 |
The experimental results of simulation 4 fully illustrate the advantages of the present invention.
In conclusion, the signal sparse reconstruction method can improve the reconstruction precision and the reconstruction efficiency of the combined sparse characteristic signal. The invention provides a New reconstruction method aiming at the signal reconstruction problem with the joint sparse characteristic, namely a New Distributed Subspace tracking algorithm (NDSP). The method fully utilizes the joint sparse characteristic of all signals in the process of searching a signal support set (non-zero element position), so that more accurate support set information can be searched better and faster, and the reconstruction performance and efficiency of the algorithm are improved. The original signal in the above figures (fig. 1 to 4) is the original signal.
While the foregoing is directed to the preferred embodiment of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (5)
1. A method of sparse reconstruction of a signal, characterized by: the method comprises the following steps:
1. calculating an inner product value, and normalizing the inner product value;
2. selecting a maximum inner product value, summing the inner product values, and selecting a position corresponding to the maximum K values as a support set;
3. through loop iteration, the support set is updated each time, and the precision of the support set is improved;
4. and obtaining a final signal reconstruction result by a least square method.
2. The method of signal sparse reconstruction of claim 1, wherein: in the first step:
calculate the inner product value of each signal:
δ j,l ＝<y j ,Φ j >,j＝1,..,J (1)
wherein < represents inner product operation, y j Representing signals with joint sparsity, phi j Denotes a sparse radical, δ j , l Representing the inner product value of the jth signal.
3. The method for signal sparse reconstruction as claimed in claim 1, wherein: in the second step:
selecting a support set, firstly selecting the maximum K inner product values, and then finding the position information corresponding to the K values:
γ l ＝max(z l ,K),j＝1,..,J (2)
Ω l ＝max_indices(γ l ),j＝1,..,J (3)
wherein gamma is l Represents the maximum K inner product values, Ω l Is non-zero corresponding to the maximum inner product valueThe position of the element, i.e. the support set information;
and (3) summing the inner product values of all signals:
z l ＝sum(abs(δ j,l )) (4)
where abs () represents an absolute value operation, sum () represents a sum operation, δ j,l Representing the inner product value of the jth signal.
4. The method of signal sparse reconstruction of claim 1, wherein: in the third step:
the non-zero element information obtained by first removing from the signal is as follows:
in the formulaRepresenting the extraction of the support set omega from the sparse basis corresponding to the jth signal l Corresponding column, y j Representing signals having a joint sparsity characteristic,representing the extraction of the support set omega from the sparse basis corresponding to the jth signal l The conjugate of the corresponding column;
and then, the steps one to three are cycled until the inner product value is minimum, which indicates that a correct support set is obtained.
5. The method of signal sparse reconstruction of claim 1, wherein: in the fourth step:
using the support set information obtained by the above search, and using a least square method to obtain a final sparse reconstruction result, which can be expressed as:
in the formulaFor the j-th reconstructed signal,support set, phi, representing the jth reconstructed signal j Denotes the sparse radical, l is the number of cycles, y j Representing signals with joint sparseness.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109995376A (en) * | 2019-04-28 | 2019-07-09 | 哈尔滨工业大学 | Signal reconfiguring method based on joint block sparse model |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102662171A (en) * | 2012-04-23 | 2012-09-12 | 电子科技大学 | Synthetic aperture radar (SAR) tomography three-dimensional imaging method |
| CN103532567A (en) * | 2013-11-01 | 2014-01-22 | 哈尔滨工业大学 | Signal reconstruction method of OMP (orthogonal matching pursuit) based on rapid inner product calculation under distributed type CS (compressed sensing) framework |
| CN103746703A (en) * | 2013-12-23 | 2014-04-23 | 哈尔滨工程大学 | Segmented self-adaptive regularized matching pursuit reconstruction method based on threshold |
-
2017
- 2017-12-15 CN CN201711353274.9A patent/CN107977680A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102662171A (en) * | 2012-04-23 | 2012-09-12 | 电子科技大学 | Synthetic aperture radar (SAR) tomography three-dimensional imaging method |
| CN103532567A (en) * | 2013-11-01 | 2014-01-22 | 哈尔滨工业大学 | Signal reconstruction method of OMP (orthogonal matching pursuit) based on rapid inner product calculation under distributed type CS (compressed sensing) framework |
| CN103746703A (en) * | 2013-12-23 | 2014-04-23 | 哈尔滨工程大学 | Segmented self-adaptive regularized matching pursuit reconstruction method based on threshold |
Non-Patent Citations (2)
| Title |
|---|
| ZHOU MING ET AL.: "A new distributed subspace pursuit algorithm and its performance analysis", 《2017 IEEE INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING, COMMUNICATIONS AND COMPUTING(ICSPCC)》 * |
| 黄成周: "基于压缩感知的轨道移频信号压缩加密技术研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109995376A (en) * | 2019-04-28 | 2019-07-09 | 哈尔滨工业大学 | Signal reconfiguring method based on joint block sparse model |
| CN109995376B (en) * | 2019-04-28 | 2023-02-03 | 哈尔滨工业大学 | Signal reconstruction method based on joint block sparse model |
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