CN103036576A - Two-value sparse signal reconstruction algorithm based on compressive sensing theory - Google Patents
Two-value sparse signal reconstruction algorithm based on compressive sensing theory Download PDFInfo
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- CN103036576A CN103036576A CN201210562420XA CN201210562420A CN103036576A CN 103036576 A CN103036576 A CN 103036576A CN 201210562420X A CN201210562420X A CN 201210562420XA CN 201210562420 A CN201210562420 A CN 201210562420A CN 103036576 A CN103036576 A CN 103036576A
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Abstract
The invention discloses a two-value sparse signal reconstruction algorithm based on the compressive sensing theory and belongs to the field of compressive sensing technology. Based on the matching track algorithm, through variable weighted processing of a measurement matrix, the two-value sparse signal reconstruction algorithm solves the problem that the matching track algorithm is poor in effect of two-value sparse signal reconstruction. Weighted reconstruction sparse signals are reconstructed according to obtained weighted measurement value and an unweighted sensing matrix. Original signals are obtained by a sparse substrate after weighing of the weighted reconstruction sparse signals is removed. Compared with an existing two-value sparse signal reconstruction algorithm, the two-value sparse signal reconstruction algorithm based on the compressive sensing theory has the advantages of being high in reconstruction successive rate, short in construction time, and simple in calculation, has universality, and can be used for sparse signals of other types.
Description
[technical field]
The present invention relates to a kind ofly based on the new method of matching pursuit algorithm for the two-value sparse signal reconfiguring, belong to the compressed sensing technical field.
[background technology]
The compressed sensing theory is since proposing, and this theory becomes the important idea that signal is processed educational circles, receives in the past few years very big concern.CS theoretical breakthrough tradition nyquist sampling theorem requires signal sampling rate must not be lower than the bottleneck of 2 times of signal bandwidths, will compress with the sampling merging and carry out, and the collection signal measured value then reconstructs original signal according to restructing algorithm.Restructing algorithm is the core of compressed sensing theory, has very high researching value.
Reconstructing in the compressed sensing theory in the original signal question essence is a NP-hard problem, and numerical computations is extremely unstable.Existing restructing algorithm mainly contains minimum l
1Norm method, greedy algorithm, iteration threshold method and the minimum full calculus of variations etc.Wherein greedy algorithm is again match tracing class algorithm, because the lower small scale signal of dimension is had low, the fireballing advantage of reconstruction calculations complexity, so receive more researchers' concern.Its basic thought is in each iterative process, at over-complete dictionary of atoms (namely
) in choose the atom that mates most with signal and make up sparse approaching, obtain the signal residual error and continue to iterate to and satisfy till the end condition.(the LP algorithm is based on minimum l with LP (Linear Programming) algorithm
1The norm method has high complexity, in most of practical applications and unrealistic) to compare, matching pursuit algorithm can reconstruct Gauss's sparse signal preferably, but bad to the reconstruct effect of two-value sparse signal.Main cause is that two-value class sparse signal has the same or analogous characteristics of nonzero value, matching pursuit algorithm is difficult to coupling and obtains the most relevant atom, for this problem, the present invention proposes a kind of based on the new method of matching pursuit algorithm for the two-value sparse signal reconfiguring.
The present invention is in the Signal Compression measuring process, to measure in advance matrix and carry out a kind of change weighting weight_ Φ=Φ (Ψ Q/ Ψ), obtain weighted measures, then utilize weighted measures and unweighted sensing matrix to be reconstructed, obtain the reconstruct sparse signal of weighting.Realized on this process nature that the rarefaction representation to primary signal is the weighting of x, thereby broken through matching pursuit algorithm to the bottleneck problem of two-value sparse signal reconfiguring.
[summary of the invention]
Purpose of the present invention has solved in the compressed sensing theory the bottleneck problem in the two-value sparse signal reconfiguring, proposes a kind of two-value sparse signal reconfiguring algorithm based on the compressed sensing theory.
The objective of the invention is to be achieved through the following technical solutions:
(1) but sparse signal f=Ψ x, x is sparse signal, measures matrix Φ, by to sensing matrix
Be weighted, obtain the weighting sensing matrix
Wherein weighting matrices Q is diagonal matrix;
(2) to the distortion of weighting sensing matrix,
Simultaneously weight_ Φ=Φ (Ψ Q/ Ψ) is defined as measuring the change weighting of matrix Φ;
(3) obtain weighted measures weight_y=weight_ Φ f according to becoming weighted measurement matrix weight_ Φ, make residual error r
0=weight_y;
(4) iterations k=1 calculates residual error and sensing matrix
In the inner product value of each column vector
Get wherein maximum L
K-1(L
0=1) index value corresponding to individual value deposits set P in
kIn;
(5) Candidate Set
Calculate
Wherein
Representative
Pseudo inverse matrix, ask maximum L
K-1Individual value manipulative indexing value deposits F in, and obtains residual error
(6) judge whether to satisfy outage threshold condition r
k≤ T, the satisfied iteration that stops, to step (8), otherwise, if || r
k||
2〉=|| r
K-1||
2, L=L+1 does not satisfy then and continues;
(7) upgrade F
k=F, k=k+1 continues step (4);
(8) obtain the reconstruct sparse signal of weighting
Weight_x is gone weighting, get the reconstruct sparse signal
According to sparse substrate Ψ, get reconstruct primary signal rec_f=Ψ rec_x.
The present invention is to the Signal Compression measuring process, to measure in advance matrix and carry out a kind of change weighting weight_ Φ=Φ (Ψ Q/ Ψ), realized that in fact the rarefaction representation to primary signal is the weighting of x, utilize weighted measures and unweighted sensing matrix to be reconstructed, obtain the reconstruct sparse signal of weighting, thereby eliminated matching pursuit algorithm to the poor reason of two-value type sparse signal reconfiguring.
The present invention introduces Weight Theory in the two-value sparse signal reconfiguring, wherein weighting matrices Q is diagonal matrix,
Be the inverse matrix of Q, require the equal non-zero of value on the leading diagonal of Q, and have certain amplitude difference.Nonzero value with two-value class sparse signal after the realization weighting is different or not close.
[advantage of the present invention and good effect]
Compared with prior art, the present invention has following advantage and good effect:
The first, by the change weighting of measuring matrix is processed, broken through the bottleneck problem of matching pursuit algorithm to the reconstruct of two-value sparse signal, do not strengthen simultaneously computational complexity, can apply to practical application.
The second, the reconstruct of two-value sparse signal had successfully the reconstruct rate is high, short, the simple characteristics of computing of reconstitution time, have simultaneously generality, also can be used for the other types sparse signal.In the situation of the sparse type of unknown signaling, do not affect the restructuring procedure to signal, more realistic signal is to the requirement of restructing algorithm.
[description of drawings]
Fig. 1 is the two-value sparse signal reconfiguring algorithm flow chart based on the compressed sensing theory that the present invention proposes;
Fig. 2 is the comparison diagram to two-value sparse signal reconfiguring effect of the present invention and OMP, ROMP, CoSaMP, SAMP, LP algorithm;
[embodiment]
For making embodiment of the present invention and meaning advantage explain more clearly, below in conjunction with accompanying drawing and reconstruct effect comparison diagram, the present invention is described in more detail.
Fig. 1 is the two-value sparse signal reconfiguring algorithm flow chart based on the compressed sensing theory that the present invention proposes, and the algorithm idiographic flow is as follows:
(1) but sparse signal f=Ψ x, x is sparse signal, measures matrix Φ, by to sensing matrix
Be weighted, obtain the weighting sensing matrix
Wherein weighting matrices Q is diagonal matrix;
(2) to the distortion of weighting sensing matrix,
Simultaneously weight_ Φ=Φ (Ψ Q/ Ψ) is defined as measuring the change weighting of matrix Φ;
(3) obtain weighted measures weight_y=weight_ Φ f according to becoming weighted measurement matrix weight_ Φ, make residual error r
0=weight_y;
(4) iterations k=1 calculates residual error and sensing matrix
In the inner product value of each column vector
Get wherein maximum L
K-1(L
0=1) index value corresponding to individual value deposits set P in
kIn;
(5) Candidate Set
Calculate
Wherein
Representative
Pseudo inverse matrix, ask maximum L
K-1Individual value manipulative indexing value deposits F in, and obtains residual error
(6) judge whether to satisfy outage threshold condition r
k≤ T, the satisfied iteration that stops, to step (8), otherwise, if || r
k||
2〉=|| r
K-1||
2, L=L+1 does not satisfy then and continues;
(7) upgrade F
k=F, k=k+1 continues step (4);
(8) obtain the reconstruct sparse signal of weighting
Weight_x is gone weighting, get the reconstruct sparse signal
According to sparse substrate Ψ, get reconstruct primary signal rec_f=Ψ rec_x.
Fig. 2 is the comparison diagram to two-value sparse signal reconfiguring effect of the present invention and OMP, ROMP, CoSaMP, SAMP, LP algorithm, signal is that length is 256 one dimension two-value sparse signal, K is the degree of rarefication of sparse signal, chooses respectively each point in 10 to 60 to be spaced apart 5.The original measurement matrix is the random matrix of 128 * 256 normal distribution, sets to stop iteration threshold T=10
-3, at each degree of rarefication, each algorithm all repeats 500 times and adds up the algorithm success reconstruct rate that draws.If set in the experiment || rec_f-f||
2＜10
-3, then restructing algorithm success, on the contrary then assert unsuccessfully.As can be seen from Figure, the present invention all is higher than OMP, ROMP, CoSaMP, SAMP, LP algorithm to the power that reconstitutes of two-value sparse signal on each degree of rarefication.Experimental results show that by numerical simulation the present invention has more advantage to the reconstruct of two-value sparse signal.
Claims (3)
1. two-value sparse signal reconfiguring algorithm based on the compressed sensing theory may further comprise the steps:
(1) but sparse signal f=Ψ x, x is sparse signal, measures matrix Φ, by to sensing matrix
Be weighted, obtain the weighting sensing matrix
Wherein weighting matrices Q is diagonal matrix;
(2) to the distortion of weighting sensing matrix,
Simultaneously weight_ Φ=Φ (Ψ Q/ Ψ) is defined as measuring the change weighting of matrix Φ;
(3) obtain weighted measures weight_y=weight_ Φ f according to becoming weighted measurement matrix weight_ Φ, make residual error r
0=weight_y;
(4) iterations k=1 calculates residual error and sensing matrix
In the inner product value of each column vector
Get wherein maximum L
K-1(L
0=1) index value corresponding to individual value deposits set P in
kIn;
(5) Candidate Set
Calculate
Wherein
Representative
Pseudo inverse matrix, ask maximum L
K-1Individual value manipulative indexing value deposits F in, and obtains residual error
(6) judge whether to satisfy outage threshold condition r
k≤ T, the satisfied iteration that stops, to step (8), otherwise, if || r
k||
2〉=|| r
K-1||
2, L=L+1 does not satisfy then and continues;
(7) upgrade F
k=F, k=k+1 continues step (4);
(8) obtain the reconstruct sparse signal of weighting
Weight_x is gone weighting, get the reconstruct sparse signal
According to sparse substrate Ψ, get reconstruct primary signal rec_f=Ψ rec_x.
2. a kind of two-value sparse signal reconfiguring algorithm based on the compressed sensing theory according to claim 1, it is characterized in that to the Signal Compression measuring process, to measure in advance matrix and carry out a kind of change weighting weight_ Φ=Φ (Ψ Q/ Ψ), realized that in fact the rarefaction representation to primary signal is the weighting of x, utilize weighted measures and unweighted sensing matrix to be reconstructed, obtain the reconstruct sparse signal of weighting, thereby eliminated matching pursuit algorithm to the poor reason of two-value type sparse signal reconfiguring.
3. a kind of two-value sparse signal reconfiguring algorithm based on the compressed sensing theory according to claim 1 and 2 is characterized in that weighting matrices Q is diagonal matrix,
Be the inverse matrix of Q, require the equal non-zero of value on the leading diagonal of Q, and have certain amplitude difference, to realize that the nonzero value of two-value class sparse signal is different or not close after the weighting.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104574450A (en) * | 2014-12-31 | 2015-04-29 | 南京邮电大学 | Image reconstruction method based on compressed sensing |
| CN105472657A (en) * | 2015-12-14 | 2016-04-06 | 南开大学 | Data reconstruction method for wireless sensor network based on low-rank tensor |
| CN107516301A (en) * | 2017-08-30 | 2017-12-26 | 中国科学院光电技术研究所 | It is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method |
| CN108734191A (en) * | 2017-05-25 | 2018-11-02 | 湖北工业大学 | Deep learning is applied to the data training method that compressed sensing is rebuild |
| CN116975517A (en) * | 2023-09-21 | 2023-10-31 | 暨南大学 | Sparse recovery method and system for partial weighted random selection strategy |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110116724A1 (en) * | 2009-11-19 | 2011-05-19 | The University Of Arizona | Method for Exploiting Structure in Sparse Domain for Magnetic Resonance Image Reconstruction |
| CN102624399A (en) * | 2012-03-30 | 2012-08-01 | 北京邮电大学 | Reconfiguration method for compression sensing signal |
-
2012
- 2012-12-20 CN CN201210562420XA patent/CN103036576A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110116724A1 (en) * | 2009-11-19 | 2011-05-19 | The University Of Arizona | Method for Exploiting Structure in Sparse Domain for Magnetic Resonance Image Reconstruction |
| CN102624399A (en) * | 2012-03-30 | 2012-08-01 | 北京邮电大学 | Reconfiguration method for compression sensing signal |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104574450A (en) * | 2014-12-31 | 2015-04-29 | 南京邮电大学 | Image reconstruction method based on compressed sensing |
| CN105472657A (en) * | 2015-12-14 | 2016-04-06 | 南开大学 | Data reconstruction method for wireless sensor network based on low-rank tensor |
| CN105472657B (en) * | 2015-12-14 | 2019-03-15 | 南开大学 | Data reconstruction method in a kind of wireless sensor network based on low-rank tensor |
| CN108734191A (en) * | 2017-05-25 | 2018-11-02 | 湖北工业大学 | Deep learning is applied to the data training method that compressed sensing is rebuild |
| CN108734191B (en) * | 2017-05-25 | 2020-11-06 | 湖北工业大学 | Data training method for applying deep learning to compressed sensing reconstruction |
| CN107516301A (en) * | 2017-08-30 | 2017-12-26 | 中国科学院光电技术研究所 | It is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method |
| CN116975517A (en) * | 2023-09-21 | 2023-10-31 | 暨南大学 | Sparse recovery method and system for partial weighted random selection strategy |
| CN116975517B (en) * | 2023-09-21 | 2024-01-05 | 暨南大学 | Sparse recovery method and system for partial weighted random selection strategy |
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Application publication date: 20130410 |