CN106817132B - Compressed sensing source signal reconstructing method based on tail support collection - Google Patents
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Abstract
The invention discloses a kind of compressed sensing source signal reconstructing method based on tail support collection, specific steps include: 1, acquisition signal, 2, it initializes, 3, the initial solution vector of compressed sensing source signal reconstruct is calculated, 4, tail support collection when the L times iteration is constructed, 5, calculate the solution vector 6 of the L time Iteration Contraction perception source signal reconstruct, update the number of iterations of compressed sensing source signal reconstruct, 7, judge the number of iterations, 8, the L times Iteration Contraction of output perceive the solution vector that source signal reconstructs.The present invention solves the disadvantages that prior art anti-noise ability is poor, and can not reconstruct source signal when source signal degree of rarefication is greater than the half of observation signal length, realizes the compressed sensing source signal reconstruct when source signal degree of rarefication is greater than observation signal length half.
Description
Technical field
The invention belongs to fields of communication technology, further relate to one of wireless communication signals processing technology field base
In the compressed sensing source signal reconstructing method of tail support collection.The present invention can compressed sensing observing matrix and observation signal
Under conditions of knowing, realize under white Gaussian noise environment to the Accurate Reconstruction of compressed sensing source signal.
Background technique
Compressed sensing (Compressed Sensing, CS) breaches traditional nyquist sampling theorem, can be with remote
Rate lower than Nyquist sampling rate samples signal, while being capable of the item known to perception matrix and observation signal
Under part, the high reconstructing method of, fast convergence rate low using complexity, reconstruction accuracy reconstructs source signal, therefore, studies compressed sensing
Source signal reconstructing method has very important significance.Currently, compressed sensing source signal reconstructing method mainly has based on orthogonal
The methods of reconstructing method with tracking, reconstructing method based on base tracking.
Paper " the Sparse representation based on redundant dic that Chen S et al. is delivered at it
tionary and basis pursuit denoising for wind turbine gearbox fault diagnosis”
It is proposed in (Int ernational Symposium on Flexible Automation (ISFA), 2016,103-107)
A kind of sparse reconstructing method based on base tracking.The convex relaxation of L0 norm problem is L1 norm problem by this method, using linear gauge
The method of drawing solves optimization problem, realizes the sparse reconstruct of source signal, the advantages of this method is that anti-noise ability is good.But the party
The shortcoming that method still has is, when compressed sensing source signal degree of rarefication is greater than the half of compressed sensing observation signal length
Source signal can not be reconstructed.
Patented technology " a kind of compressed sensing signal reconfiguring method " (application number that Nanjing Univ. of Posts and Telecommunications possesses
201210343893.0, applying date 2012.09.17, grant number 102882530B) in propose a kind of compressed sensing signal reconstruction side
Method.This method convert the Regularization Problem in the sparse domain of compressed sensing signal to by variable cracking technology it is of equal value with it,
The constraint Regularization Problem of signal sparse characteristic can be more embodied than Regularization Problem, so that signal is more sparse, therefore reconstruct letter
Number precision it is higher.But the shortcoming that this method still has is that anti-noise ability is poor, and compressed sensing source signal is sparse
Degree can not reconstruct source signal when being greater than the half of compressed sensing observation signal length.
Summary of the invention
It is an object of the invention to overcome the shortcomings of above-mentioned prior art, a kind of compression based on tail support collection is provided
Source signal reconstructing method is perceived, is realized when compressed sensing source signal degree of rarefication is greater than compressed sensing observation signal length half
Compressed sensing source signal reconstruct, improve the anti-noise ability of compressed sensing source signal reconstructing method.
Realizing the concrete thought of the object of the invention is: known to compressed sensing observing matrix and compressed sensing observation signal
Under the conditions of, one group of initial solution of compressed sensing source signal reconstruct, the method for recycling threshold value are found out using existing method first
Tail support collection is constructed, on this basis, the essence of compressed sensing source signal reconstruct is found out using linear programming method progressive alternate
Really solution realizes the compressed sensing source when compressed sensing source signal degree of rarefication is greater than compressed sensing observation signal length half and believes
Number reconstruct.
Realize that specific step is as follows for the object of the invention:
(1) signal is acquired:
The signal of communication that communication antenna acquires is stored in the compressed sensing observation signal vector of the dimension of P × 1, P indicates compression
Perceive the dimension of observation signal vector；
(2) it initializes:
The number of iterations L that compressed sensing source signal reconstructs is initialized as 1, location index set is initialized as empty set,
Compressed sensing observing matrix is initialized as M × N-dimensional Gaussian matrix, M indicates the row dimension of compressed sensing observing matrix, N table
Show the column dimension of compressed sensing observing matrix, M < N, M=P；
(3) the initial solution vector of compressed sensing source signal reconstruct is calculated；
(4) tail support collection when the L times iteration is constructed；
(4a) calculates the threshold value of the L-1 times iteration:
(4b) is searched in the solution vector of compressed sensing source signal reconstruct of the L-1 times iteration, and absolute value is greater than the L-1 times repeatedly
For the location index of the component of threshold value；
(4c) will search for resulting location index and be deposited into location index set；
The calculating position (4d) indexed set complement of a set, obtains tail support collection when the L times iteration；
(5) solution vector of the L times Iteration Contraction perception source signal reconstruct is calculated using linear programming method；
Wherein, f(L)Indicating the solution vector of the L times Iteration Contraction perception source signal reconstruct, min indicates operation of minimizing, |
|·||1Expression asks 1 norm of vector to operate,The corresponding compressed sensing source signal of tail support collection when indicating the L times iteration
The tail portion of vector, s.t. indicate that constraint condition symbol, y indicate that the compressed sensing observation signal vector that P × 1 is tieed up, P indicate compression sense
Know the dimension of observation signal vector, A indicates that M × N-dimensional compressed sensing observing matrix, M indicate the row of compressed sensing observing matrix
Dimension, N indicate the column dimension of compressed sensing observing matrix, M < N, M=P, and x indicates the compressed sensing source signal vector that R × 1 is tieed up, R
Indicate the dimension of compressed sensing source signal vector, N=R；
(6) the number of iterations that compressed sensing source signal reconstructs is added 1；
(7) judge whether the number of iterations of compressed sensing source signal reconstruct is greater than 10, if so, step (8) are executed, otherwise,
It executes step (4)；
(8) solution vector of the L times Iteration Contraction perception source signal reconstruct is exported.
Compared with the prior art, the present invention has the following advantages:
First, due to present invention employs the method construct tail support collection of threshold value, so that compressed sensing source signal
Tail portion very little, it is almost nil, therefore, the prior art is overcome when compressed sensing source signal degree of rarefication is greater than compressed sensing observation letter
The shortcomings that source signal can not be reconstructed when the half of number length, so that have can be big in compressed sensing source signal degree of rarefication by the present invention
The advantages of source signal is reconstructed when the half of compressed sensing observation signal length.
Second, since present invention employs linear programming methods, the solution vector of compressed sensing source signal reconstruct is solved, linearly
Planing method approaches accurate solution by successive ignition, and therefore, it is poor to overcome prior art anti-noise ability, and compressed sensing source signal
The shortcomings that degree of rarefication can not reconstruct source signal when being greater than the half of compressed sensing observation signal length, so that the present invention is with higher
Noise immunity, and can compressed sensing source signal degree of rarefication be greater than compressed sensing observation signal length half when reconstruct source believe
Number the advantages of.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is analogous diagram of the invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
Referring to attached drawing 1, the specific steps of the present invention are as follows.
Step 1, signal is acquired.
The signal of communication that communication antenna acquires is stored in the compressed sensing observation signal vector of the dimension of P × 1, P indicates compression
Perceive the dimension of observation signal vector.
Step 2, it initializes.
The number of iterations L that compressed sensing source signal reconstructs is initialized as 1, location index set is initialized as empty set,
Compressed sensing observing matrix is initialized as M × N-dimensional Gaussian matrix, M indicates the row dimension of compressed sensing observing matrix, N table
Show the column dimension of compressed sensing observing matrix, M < N, M=P.
Step 3, the initial solution vector of compressed sensing source signal reconstruct is calculated.
According to the following formula, the initial solution vector of compressed sensing source signal reconstruct is calculated:
Wherein, f(0)Indicate the initial solution vector of compressed sensing source signal reconstruct, min indicates operation of minimizing, and x indicates N
The compressed sensing source signal vector of × 1 dimension, | | | |1Expression asks 1 norm of vector to operate, and s.t. indicates constraint condition symbol, y
Indicate that the compressed sensing observation signal vector that P × 1 is tieed up, P indicate the dimension of compressed sensing observation signal vector, A indicates M × N-dimensional
Compressed sensing observing matrix, M indicate compressed sensing observing matrix row dimension, N indicate compressed sensing observing matrix column dimension
Degree, M < N, M=P, x indicate that the compressed sensing source signal vector that R × 1 is tieed up, R indicate the dimension of compressed sensing source signal vector, N=
R。
Step 4, tail support collection when the L times iteration is constructed.
The first step calculates the threshold value of the L-1 times iteration according to the following formula:
ρ(L-1)=0.2*max | f(L-1)|
Wherein, ρ(L-1)Indicating the threshold value of the L-1 times iteration, product operation is sought in * expression, and max indicates maximizing operation,
| | absolute value operation, f are asked in expression(L-1)Indicate the solution vector of the compressed sensing source signal reconstruct of the L-1 times iteration；
Second step is searched in the solution vector of compressed sensing source signal reconstruct of the L-1 times iteration, and absolute value is greater than L-1
The location index of the component of secondary iteration threshold value；
Third step will be searched for resulting location index and is deposited into location index set；
4th step, calculating position indexed set complement of a set obtain tail support collection when the L times iteration.
Step 5, using linear programming method, the solution vector of the L times Iteration Contraction perception source signal reconstruct is calculated:
Wherein, f(L)Indicating the solution vector of the L times Iteration Contraction perception source signal reconstruct, min indicates operation of minimizing, |
|·||1Expression asks 1 norm of vector to operate,The corresponding compressed sensing source signal of tail support collection when indicating the L times iteration
The tail portion of vector, s.t. indicate that constraint condition symbol, y indicate that the compressed sensing observation signal vector that P × 1 is tieed up, P indicate compression sense
Know the dimension of observation signal vector, A indicates that M × N-dimensional compressed sensing observing matrix, M indicate the row of compressed sensing observing matrix
Dimension, N indicate the column dimension of compressed sensing observing matrix, M < N, M=P, and x indicates the compressed sensing source signal vector that R × 1 is tieed up, R
Indicate the dimension of compressed sensing source signal vector, N=R.
Step 6, the number of iterations that compressed sensing source signal reconstructs is added 1.
Step 7, judge whether the number of iterations of compressed sensing source signal reconstruct is greater than 10, if so, step (8) are executed, it is no
Then, step (4) are executed.
Step 8, the solution vector of the L times Iteration Contraction perception source signal reconstruct is exported.
Below with reference to analogous diagram 2, the present invention will be further described.
1. simulated conditions:
Two emulation experiments of the method that the present invention and the prior art use are in operating system for Pentium (R)
Dual-Core CPU E5300@2.60GHz is carried out under the simulated conditions of 32-bit Windows operating system, and simulation software uses
MATLAB。
Two emulation experiments of the method that the present invention and the prior art use are generated using MATLAB software random dilute
Signal is dredged as compressed sensing source signal, noise is white Gaussian noise, and compressed sensing observing matrix is Gaussian matrix.The present invention with
Two emulation experiments of the method that the prior art uses are respectively to the existing reconstructing method based on base tracking, based on orthogonal matching
The reconstructing method and the present invention of tracking emulate.
2. emulation content and interpretation of result:
Emulation experiment 1:
In the case where the length of compressed sensing observation signal is 64, respectively using the weight based on base tracking of the prior art
Structure method, the reconstructing method based on orthogonal matching pursuit and three kinds of methods of the invention, carry out the emulation that source signal reconstructs
As a result as shown in Fig. 2 (a).Abscissa in Fig. 2 (a) indicates that degree of rarefication, ordinate indicate reconstruct probability.With triangle in Fig. 2 (a)
The curve of shape mark indicates that reconstruct probability of the invention with the change curve of degree of rarefication, indicates to be based on base with the curve that circle indicates
The reconstruct probability of the reconstructing method of tracking is indicated with the curve of square mark based on orthogonal matching with the change curve of degree of rarefication
The reconstructing method of tracking reconstructs probability with the change curve of degree of rarefication.
By Fig. 2 (a) as it can be seen that with degree of rarefication increase, the reconstruct probability of three kinds of methods reduces, due to observation signal
Length is 64, when degree of rarefication be greater than 32 when, the prior art based on base tracking sparse reconstructing method and based on it is orthogonal matching chase after
The reconstruct probability of the sparse reconstructing method of track is respectively less than 0.1, and reconstruct failure, still, reconstruct probability of the invention is about 0.7.By
This is as it can be seen that the present invention can realize source signal reconstruct under conditions of degree of rarefication is greater than compressed sensing observation signal length half.
By Fig. 2 (a) simultaneously it can also be seen that reconstruct probability of the invention is far longer than the prior art using based on base tracking
Reconstructing method and the reconstructing method based on orthogonal matching pursuit reconstruct probability, when degree of rarefication is less than 25, the present invention can
100% reconstruct source signal, and the prior art uses the reconstructing method tracked based on base being capable of 100% weight when degree of rarefication is less than 14
Structure source signal, the reconstruct probability of the reconstructing method based on orthogonal matching pursuit is always below 90%.
Emulation experiment 2:
Compressed sensing observation signal length be 64 compressed sensing source signals degree of rarefication be 28 in the case where, use
The reconstructing method based on base tracking, the reconstructing method based on orthogonal matching pursuit and the three kinds of methods of the invention of the prior art, point
Not carry out source signal reconstruct, shown in obtained simulation result such as Fig. 2 (b).Abscissa in Fig. 2 (b) indicates signal-to-noise ratio, ordinate
Indicate signal interference ratio.In Fig. 2 (b) with the curve that triangle indicates indicate signal interference ratio of the invention with the change curve of signal-to-noise ratio, with
The curve of circle mark indicates the signal interference ratio for the reconstructing method tracked based on base with the change curve of signal-to-noise ratio, with square mark
Curve indicate the reconstructing method based on orthogonal matching pursuit signal interference ratio with signal-to-noise ratio change curve.
From Fig. 2 (b): with the increase of signal-to-noise ratio, the signal interference ratio of three kinds of methods is increase accordingly, and letter of the invention
The signal interference ratio of the dry reconstructing method tracked than being consistently greater than the prior art based on base and the reconstructing method based on orthogonal matching pursuit,
Therefore anti-noise ability of the invention is better than the reconstructing method of the prior art tracked based on base and based on the weight of orthogonal matching pursuit
Structure method.When input signal-to-noise ratio is 10dB, signal interference ratio of the invention is improved relative to based on the reconstructing method that base is tracked
10dB improves about 11dB relative to the reconstructing method based on orthogonal matching pursuit.
In conclusion by two obtained of two emulation experiments the result shows that, using method of the invention, it is possible to pressing
Contracting perception source signal degree of rarefication reconstructs source signal, and anti-noise of the invention when being greater than the half of compressed sensing observation signal length
Ability is fine.
Claims (4)
1. a kind of compressed sensing source signal reconstructing method based on tail support collection, includes the following steps:
(1) signal is acquired:
The signal of communication that communication antenna acquires is stored in the compressed sensing observation signal vector of the dimension of P × 1, P indicates compressed sensing
The dimension of observation signal vector；
(2) it initializes:
The number of iterations L that compressed sensing source signal reconstructs is initialized as 1, location index set is initialized as empty set, will be pressed
Contracting perception observing matrix is initialized as M × N-dimensional Gaussian matrix, and M indicates the row dimension of compressed sensing observing matrix, and N indicates pressure
The column dimension of contracting perception observing matrix, M < N, M=P；
(3) the initial solution vector of compressed sensing source signal reconstruct is calculated；
(4) tail support collection when the L times iteration is constructed；
(4a) calculates the threshold value of the L-1 times iteration:
(4b) is searched in the solution vector of compressed sensing source signal reconstruct of the L-1 times iteration, and absolute value is greater than the L-1 times iteration door
The location index of the component of limit value；
(4c) will search for resulting location index and be deposited into location index set；
The calculating position (4d) indexed set complement of a set, obtains tail support collection when the L times iteration；
(5) solution vector of the L times Iteration Contraction perception source signal reconstruct is calculated using linear programming method；
S.t.y=Ax
Wherein, f(L)Indicating the solution vector of the L times Iteration Contraction perception source signal reconstruct, min indicates operation of minimizing, | | |
|1Expression asks 1 norm of vector to operate,The corresponding compressed sensing source signal vector of tail support collection when indicating the L times iteration
Tail portion, s.t. indicate constraint condition symbol, y indicate P × 1 tie up compressed sensing observation signal vector, P indicate compressed sensing see
The dimension of signal vector is surveyed, A indicates that M × N-dimensional compressed sensing observing matrix, M indicate the row dimension of compressed sensing observing matrix,
N indicates the column dimension of compressed sensing observing matrix, M < N, M=P, and x indicates that the compressed sensing source signal vector that R × 1 is tieed up, R indicate
The dimension of compressed sensing source signal vector, N=R；
(6) the number of iterations that compressed sensing source signal reconstructs is added 1；
(7) judge whether the number of iterations of compressed sensing source signal reconstruct is greater than 10, if so, executing step (8), otherwise, execute
Step (4)；
(8) solution vector of the L times Iteration Contraction perception source signal reconstruct is exported.
2. the compressed sensing source signal reconstructing method according to claim 1 based on tail support collection, it is characterised in that: step
Suddenly the initial solution vector of the reconstruct of compressed sensing source signal described in (3) is calculated according to following formula:
S.t.y=Ax
Wherein, f(0)Indicate the initial solution vector of compressed sensing source signal reconstruct, min indicates operation of minimizing, and x indicates N × 1
The compressed sensing source signal vector of dimension, | | | |1Expression asks 1 norm of vector to operate, and s.t. indicates constraint condition symbol, y table
Show that the compressed sensing observation signal vector that P × 1 is tieed up, P indicate the dimension of compressed sensing observation signal vector, A indicates M × N-dimensional
Compressed sensing observing matrix, M indicate the row dimension of compressed sensing observing matrix, and N indicates the column dimension of compressed sensing observing matrix,
M < N, M=P, x indicate that the compressed sensing source signal vector that R × 1 is tieed up, R indicate the dimension of compressed sensing source signal vector, N=R.
3. the compressed sensing source signal reconstructing method according to claim 1 based on tail support collection, it is characterised in that: step
Suddenly the threshold value of the L-1 times iteration described in (4a) is calculated according to following formula:
ρ(L-1)=0.2*max | f(L-1)|
Wherein, ρ(L-1)Indicating the threshold value of the L-1 times iteration, product operation is sought in * expression, and max indicates maximizing operation, | |
Absolute value operation, f are asked in expression(L-1)Indicate the solution vector of the compressed sensing source signal reconstruct of the L-1 times iteration.
4. the compressed sensing source signal reconstructing method according to claim 1 based on tail support collection, it is characterised in that: step
Suddenly location index collection complement of a set described in (4d) is calculated according to following formula:
TL←{1,2,…,N}\G
Wherein, TLIndicate tail support collection when the L times iteration, ← indicate that assignment operation symbol, N indicate that compressed sensing observes square
Battle array columns, indicate ask set supplementary set operation；G indicates location index set.
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| CN101908889B (en) * | 2010-07-30 | 2013-03-20 | 哈尔滨工业大学 | Compressed sensing reconstructing method of sparse signal with unknown block sparsity |
| CN102882530B (en) * | 2012-09-17 | 2015-04-08 | 南京邮电大学 | Compressed sensing signal reconstruction method |
| US10073701B2 (en) * | 2013-07-29 | 2018-09-11 | The Regents Of The University Of California | Scalable and parameterized VLSI architecture for compressive sensing sparse approximation |
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| CN105846826B (en) * | 2016-03-22 | 2018-11-16 | 西安电子科技大学 | Compressed sensing signal reconfiguring method based on approximate smooth L0 norm |
| CN105743511A (en) * | 2016-04-05 | 2016-07-06 | 西安电子科技大学 | Compressed sensing signal reconstruction method based on conjugate gradient method |
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