CN104270158B - A cooperative reconstruction method with adaptive sparsity - Google Patents
A cooperative reconstruction method with adaptive sparsity Download PDFInfo
- Publication number
- CN104270158B CN104270158B CN201410122703.1A CN201410122703A CN104270158B CN 104270158 B CN104270158 B CN 104270158B CN 201410122703 A CN201410122703 A CN 201410122703A CN 104270158 B CN104270158 B CN 104270158B
- Authority
- CN
- China
- Prior art keywords
- supported collection
- signal
- collection
- supported
- init
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 29
- 230000003044 adaptive effect Effects 0.000 title claims abstract description 17
- 238000012937 correction Methods 0.000 claims abstract description 6
- 238000005070 sampling Methods 0.000 claims description 16
- 239000011159 matrix material Substances 0.000 claims description 7
- 238000004422 calculation algorithm Methods 0.000 abstract description 27
- 230000006978 adaptation Effects 0.000 abstract 1
- 230000007547 defect Effects 0.000 abstract 1
- 238000005259 measurement Methods 0.000 description 5
- 238000007906 compression Methods 0.000 description 3
- 230000006835 compression Effects 0.000 description 3
- 238000012545 processing Methods 0.000 description 3
- 238000007152 ring opening metathesis polymerisation reaction Methods 0.000 description 3
- BWSIKGOGLDNQBZ-LURJTMIESA-N (2s)-2-(methoxymethyl)pyrrolidin-1-amine Chemical compound COC[C@@H]1CCCN1N BWSIKGOGLDNQBZ-LURJTMIESA-N 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000012804 iterative process Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 230000005540 biological transmission Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 238000007418 data mining Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000009472 formulation Methods 0.000 description 1
- 230000014509 gene expression Effects 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 230000011664 signaling Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Abstract
The invention discloses a cooperative signal-reconstruction method with adaptation to the sparsity of a signal and the size of a support set, to overcome defects of a conventional algorithm based on orthogonal matching pursuit that sparsity prior information of an original signal needs to be input for signal reconstruction, the reconstruction precision is low and the like. The method described according to the invention reduces error estimation and error correction of the support set by predicting sparsity information and cooperatively updating and expanding the support set. Compared with the conventional orthogonal matching pursuit algorithm, the cooperative reconstruction method with adaptive sparsity of the invention can obtain higher reconstruction precision, especially for the reconstruction of a signal that has unknown sparsity.
Description
Technical field
The present invention relates to a kind of signal reconfiguring method, belongs to signal processing technology field.
Background technology
Compressed sensing (Compressed Sensing, CS) is a kind of brand-new letter for breaching nyquist sampling theorem
Number sampling theory, also referred to as compression sampling or sparse sampling.It is by American scholar David Donoho and Emmanuel
Candes et al. proposed in the literature in 2006, such as Donoho D L, Compressed Sensing, IEEE
Transaction on Information Theory；Candes E J, Compressed Sampling.Proceedings
ofthe International Congress of Mathematicians.Traditional sampling thheorem be simulated signal to
It is that the information for ensureing source signal does not lose, recovers source signal without distortions during data signal is changed, sample frequency should be big
2 times of bandwidth in the analog signal；And the thought of compressed sensing is with far below Nyquist sampling rate to sparse signal
Global sampling is carried out to source signal, source signal is reconstructed from sampled value by appropriate restructing algorithm.CS is theoretical right by tradition
The sampling of signal changes into the sampling to information, and sampling and compression are fused into a step, reduces signal processing time and calculating
Cost, while also reducing the sample frequency of signal, reduces data space and transmission cost.Therefore, CS it is theoretical once
Proposition is just widely used in fields such as message sink coding, data mining, Radar Signal Processings.
At present, the classic algorithm of sparse signal reconfiguring problem have match tracing (Matching Pursuit, MP) algorithm and
Orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm.The basic thought of MP algorithms is each time
In iterative process, (perceive matrix) from over-complete dictionary of atoms and select the atom most matched with signal to build sparse bayesian learning,
And signal residual error is obtained, then proceed to find the atom matched the most with signal residual error, through certain number of times (signal degree of rarefication)
Iteration, signal may finally be by some atom linear expressions.But due to signal select atom (perceive matrix column to
Amount) nonorthogonality of projection closed of collection causes the result of each iteration possibly suboptimal.Therefore, with the atom collection for obtaining
Conjunction have during signal error to represent.OMP algorithms have continued to use the atom selection criterion in matching pursuit algorithm, each in reconstruct
Iteration obtains an atom of supported collection (atom set) F of x, simply by recurrence to selecting atom set to be orthogonalized
To ensure the optimality of iteration, so that supported collection can more accurately represent signal.Tropp J, Gilbert A exists
Table in Signal recovery from random Measurements via orthogonal matching pursuit
The bright N-dimensional discrete-time signal x to fixed K degree of rarefications, when being measured with Gaussian matrix, as long as measurement number M >=O (K log N), just
Friendship matching pursuit algorithm will be with maximum probability accurate reconstruction signal, and ratio adopts minimum l1The algorithm of norm optimization is faster.But,
Orthogonal matching pursuit algorithm reconstruct accuracy ratio adopts minimum l1Norm optimization algorithm is low.
Needlle et al. proposes regularization orthogonal matching pursuit (Regularized Orthogonal on the basis of OMP
Matching Pursuit, ROMP) algorithm, for the matrix and all sparse signals of all meet the constraint isometry conditions all may be used
With accurate reconstruction.In addition, Donaho proposes substep orthogonal matching pursuit (Stagewise Orthogonal Matching
Pursuit, StOMP) algorithm, iterative process is divided into several stages by it to be carried out.ROMP and StOMP algorithms are obtained in each iteration
To one group of atom of F, therefore speed is faster than OMP.The reconstruction complexity of these algorithms is O (KMN), far below the O of BP algorithm
(N3).They can obtain preferable quality reconstruction when M is larger.
Needlle et al. proposes the compression sampling matching pursuit algorithm (Compressive for introducing backtracking thought
Sample Matching Pursuit, CoSaMP) can also reconstruction signal well, there is provided than OMP, ROMP more fully
Theory ensures, and robustness is had more in sampling process.Follow the trail of (Subspace in the same subspace that also has for introducing backtracking thought
Persuit, SP) algorithm, a Candidate Set C was first set up before supported collection F of x is obtained, give up from C again afterwards unwanted
Atom, ultimately forms F, and their theoretical reconstruction accuracies are suitable with linear programming algorithm, while reconstruct complexity is low, but this kind of calculation
On the basis of method is all built upon known to degree of rarefication K.
But in practical application, K is often unknown, therefore occur in that sparse Adaptive matching adaptive to K is followed the trail of
(Sparsity Adaptive Matching Pursuit, SAMP) algorithm, it carries out weight by fixed step size s Step wise approximations
Structure, can obtain in the case where K is unknown preferably rebuild effect, and speed is also far faster than OMP algorithms.But SAMP fixed step sizes
Bring the deficiencies such as the inadequate and excessive estimation of precision.
The content of the invention
The degree of rarefication elder generation for being input into primary signal is needed in reconstruction signal for the existing algorithm based on orthogonal matching pursuit
Test information, and reconstruction accuracy it is relatively low the problems such as.The invention discloses a kind of have certainly to signal degree of rarefication and supported collection size
Adaptive cooperation reconstruction signal method.Method of the present invention：By predicting degree of rarefication information, cooperation updates and extension
Support collection, reduces the mistake to supported collection and estimates and error correction.Compared to existing orthogonal matching pursuit algorithm, the inventive method
Higher reconstruction accuracy can be obtained, especially to the reconstruct of degree of rarefication unknown signaling.
The reconstructing method the invention provides a kind of adaptive sparse degree cooperates, comprises the following steps：
From known sampling matrix A and measured value b, the method for estimating primary signal x (formulation is expressed as b=Ax)
It is specific as follows：
Step one, using |input paramete A, b and initial residual error r0=x, initial support collectionPre-estimation supported collection
Tinit, method of estimation is：
1) i is calculatedk=arg max (| Ab |) obtain a supported collection element：
2) by ikIt is merged in the middle of acquired supported collection, obtains Tk=Tk-1∪ik；
3) residual error is calculated
4) relatively more adjacent residual error twice, if | | rk||2＞ | | rk-1||2Then by TkReturn to pre-estimation supported collection Tinit, it is no
Then, 1) -4 are repeated)；
Step 2, using subspace follow the trail of amendment supported collection Tinit, correction result is designated as Tre；
Step 3, cooperation update supported collection Tup, Tup=Tinit∩Tre；
Step 4, estimation initial signal v,
Step 5, cooperation extension supported collection Tex, TexIt is maximum in v middle molds | Tre|-|Tup| individual index, and these indexes
Not in TupIn；
Step 6, renewal supported collection T=Tup∪Tex；
Step 7, acquisition signal finally estimate xest,
Description of the drawings
Fig. 1：Adaptive sparse degree cooperation reconstructing method flow chart；
Fig. 2：Reconstruction signal contrasts Fig. 1 (signal length K=120, degree of rarefication s=K with primary signal1, measure number M=
30)；
Fig. 3：Reconstruction signal contrasts Fig. 2 (signal length K=120, degree of rarefication s=K with primary signal2(K2＜ K1), measurement
Number M=30)；
Fig. 4：Reconstructing method relative error comparison diagram (signal length K=120, degree of rarefication s=K2(K2＜ K1), measure number M
∈[20：2：40]) (AC represents the inventive method).
Specific embodiment
The present invention relates to from known sampling matrix A and measured value b, then the method for estimating primary signal x.
Comprise the following steps that with reference to Fig. 1 explanations；
Step one, using |input paramete pre-estimation supported collection Tinit, its estimating step is as follows：
1) i is calculatedk=arg max (| Ab |) obtain a supported collection element；
2) by ikIt is merged in the middle of acquired supported collection, obtains Tk=Tk-1∪ik；
3) residual error is calculated
4) relatively more adjacent residual error twice, if | | rk||2＞ | | rk-1||2Then by TkReturn to pre-estimation supported collection Tinit, it is no
Then, 1) -4 are repeated)；
Step 2, using subspace follow the trail of amendment supported collection Tinit, correction result is designated as Tre；
Step 3, cooperation update supported collection Tup, Tup=Tinit∩Tre；
Step 4, estimation initial signal v,
Step 5, cooperation extension supported collection Tex, TexIt is maximum in v middle molds | Tre|-|Tup| individual index, and these indexes
Not in TupIn；
Step 6, renewal supported collection T=Tup∪Tex；
Step 7, acquisition signal finally estimate xest,
Advantages of the present invention is further illustrated by following simulation result.From emulation content and result：
A kind of adaptive sparse degree cooperation reconstructing method reconstruction signal of the invention and primary signal are carried out to such as Fig. 2 and
Shown in Fig. 3.Fig. 2 is displayed in signal length K=120, degree of rarefication s=K1, in the case of measuring number M=30, the letter after reconstruct
Number and primary signal it is completely the same.Fig. 3 is displayed in signal length K=120, degree of rarefication s=K2(K2＜ K1), measure number M=30's
In the case of, the signal and primary signal after reconstruct is also completely the same.
Fig. 4 is the comparison diagram of a kind of adaptive sparse degree cooperation reconstructing method of the invention and OMP algorithm relative errors.Fig. 4
It is displayed in signal length K=120, degree of rarefication s=K2(K2＜ K1), measurement number M ∈ [20：2：40] in the case of, the inventive method
Reconstructed error reduce with the increase of measurement signal dimension, and downward trend becomes apparent from than OMP algorithm.
Tables 1 and 2 represents respectively the false code for invention.
Table 1 realizes the false code of the present invention
Table 2 is realized estimating supported collection T in the present inventioninitFalse code
In sum：The present invention improves reconstruction signal percent reduction, and has adaptivity to signal, is adapted to degree of rarefication
Unknown signal reconstruction.
Claims (5)
1. a kind of adaptive sparse degree cooperates reconstructing method, it is characterised in that methods described is at least comprised the following steps：
From known sampling matrix A and measured value b, according to metering system b=Ax, a kind of adaptive of primary signal x is estimated
Degree of rarefication cooperation reconstructing method is answered, be it is characterized in that, it is realized by following steps：
Step one, using |input paramete A, b and initial residual error r0=x, initial support collectionPre-estimation supported collection Tinit, estimate
Meter method is：
1) i is calculatedk=arg max (| Ab |) obtain a supported collection element；
2) by ikIt is merged in the middle of acquired supported collection, obtains Tk=Tk-1∪ik；
3) residual error is calculated
4) relatively more adjacent residual error twice, if | | rk||2＞ | | rk-1||2Then by TkReturn to pre-estimation supported collection Tinit, otherwise,
Repeat 1) -4)；
Step 2, using subspace follow the trail of amendment supported collection Tinit, correction result is designated as Tre；
Step 3, cooperation update supported collection Tup, Tup=Tinit∩Tre；
Step 4, estimation initial signal v,
Step 5, cooperation extension supported collection Tex, TexIt is maximum in v middle molds | Tre|-|Tup| individual index, and these indexes do not exist
TupIn；
Step 6, renewal supported collection T=Tup∪Tex；
Step 7, acquisition signal finally estimate xest,
2. a kind of adaptive sparse degree according to claim 1 cooperates reconstructing method, it is characterised in that to dilute in step one
The adaptivity of degree is dredged, the wherein adaptivity in step one mainly has the following estimation to degree of rarefication to complete：
1) i is calculatedk=arg max (| Ab |) obtain a supported collection element；
2) by ikIt is merged in the middle of acquired supported collection, obtains Tk=Tk-1∪ik；
3) residual error is calculated
4) relatively more adjacent residual error twice, if | | rk||2＞ | | rk-1||2Then by TkReturn to pre-estimation supported collection Tinit, otherwise,
Repeat step 1) -4).
3. a kind of adaptive sparse degree according to claim 1 cooperates reconstructing method, it is characterised in that in step 3 to
The cooperation of support collection updates, and obtains the common factor of supported collection in step one and step 2, eliminates mistake that may be present in step one
Estimate and error correction that may be present in step 2.
4. a kind of adaptive sparse degree according to claim 1 cooperates reconstructing method, it is characterised in that in step 5 to
The cooperation extension of support collection, it is in step 4 in the modulus value manipulative indexing of estimated signal, not in T to extend supported collectionupIn before |
Tre|-|Tup| individual index.
5. a kind of adaptive sparse degree according to claim 1 cooperates reconstructing method, it is characterised in that in step 6, to first
Beginning valuation supported collection takes union, it is ensured that supported collection size is constant.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410122703.1A CN104270158B (en) | 2014-03-26 | 2014-03-26 | A cooperative reconstruction method with adaptive sparsity |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410122703.1A CN104270158B (en) | 2014-03-26 | 2014-03-26 | A cooperative reconstruction method with adaptive sparsity |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104270158A CN104270158A (en) | 2015-01-07 |
| CN104270158B true CN104270158B (en) | 2017-05-03 |
Family
ID=52161659
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410122703.1A Expired - Fee Related CN104270158B (en) | 2014-03-26 | 2014-03-26 | A cooperative reconstruction method with adaptive sparsity |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104270158B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104767535B (en) * | 2015-03-31 | 2018-08-10 | 电子科技大学 | A kind of low complex degree bulk sparse signal reconfiguring method |
| CN108712173B (en) * | 2017-12-21 | 2021-12-24 | 湘潭大学 | Reconstruction method of multiple index extension mechanism |
| CN109995376B (en) * | 2019-04-28 | 2023-02-03 | 哈尔滨工业大学 | Signal reconstruction method based on joint block sparse model |
| CN116208169B (en) * | 2023-03-02 | 2023-08-22 | 哈尔滨工程大学 | Distributed compressed sensing reconstruction method based on joint matching criterion |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101908889A (en) * | 2010-07-30 | 2010-12-08 | 哈尔滨工业大学 | Compressed sensing reconstructing method of sparse signal with unknown block sparsity |
| CN102045118A (en) * | 2010-10-22 | 2011-05-04 | 清华大学 | Compressed sensing reconstruction algorithm based on pseudo-inverse multiplication |
| CN103595414A (en) * | 2012-08-15 | 2014-02-19 | 王景芳 | Sparse sampling and signal compressive sensing reconstruction method |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8811700B2 (en) * | 2009-04-15 | 2014-08-19 | Virginia Tech Intellectual Properties, Inc. | Exact local computed tomography based on compressive sampling |
| US20120259590A1 (en) * | 2011-04-11 | 2012-10-11 | Jong Chul Ye | Method and apparatus for compressed sensing with joint sparsity |
-
2014
- 2014-03-26 CN CN201410122703.1A patent/CN104270158B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101908889A (en) * | 2010-07-30 | 2010-12-08 | 哈尔滨工业大学 | Compressed sensing reconstructing method of sparse signal with unknown block sparsity |
| CN102045118A (en) * | 2010-10-22 | 2011-05-04 | 清华大学 | Compressed sensing reconstruction algorithm based on pseudo-inverse multiplication |
| CN103595414A (en) * | 2012-08-15 | 2014-02-19 | 王景芳 | Sparse sampling and signal compressive sensing reconstruction method |
Non-Patent Citations (3)
| Title |
|---|
| A Robust Sparse Signal Recovery Method for Perturbed Compressed Sensing Based;Rongzong Kang etc.;《3rd International Conference on Electric and Electronics (EEIC 2013)》;20131231;第199-202页 * |
| 一种自适应正则化总空间追踪算法;徐泽芳，刘顺兰;《计算机工程与应用》;20130123;第1-5页 * |
| 基于子空间的块稀疏信号压缩感知重构算法;付宁等;《电子学报》;20111031;第39卷(第10期);第2338-2342页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104270158A (en) | 2015-01-07 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Kutyniok | Theory and applications of compressed sensing | |
| CN104270158B (en) | A cooperative reconstruction method with adaptive sparsity | |
| CN104320144B (en) | Degree of rarefication self-adapting signal reconstructing method | |
| CN105513026A (en) | Compressed sensing reconstruction method based on image nonlocal similarity | |
| CN105827250A (en) | Electric-energy quality data compression and reconstruction method based on self-adaptive dictionary learning | |
| Wang et al. | A reducing iteration orthogonal matching pursuit algorithm for compressive sensing | |
| CN107527371B (en) | Approximating smoothness L in compressed sensing0Design and construction method of norm image reconstruction algorithm | |
| CN108536657B (en) | Method and system for processing similarity of artificially filled address texts | |
| CN105488767B (en) | A kind of compressed sensing image fast reconstructing method based on Least-squares minimization | |
| Haltmeier | Stable signal reconstruction via $\ell^ 1$-minimization in redundant, non-tight frames | |
| CN111667444A (en) | Image compressed sensing reconstruction method based on multi-channel residual error network | |
| CN107547088A (en) | Enhanced self-adapted segmentation orthogonal matching pursuit method based on compressed sensing | |
| CN109905129B (en) | Low-overhead power data acquisition method based on distributed compressive sensing | |
| CN103391099B (en) | Be applicable to the random sampler of one dimension tempolabile signal | |
| CN106548780B (en) | A kind of compressed sensing reconstructing method of voice signal | |
| Ambat et al. | Fusion of greedy pursuits for compressed sensing signal reconstruction | |
| CN105447894B (en) | Compressed sensing reconstruction algorithm based on Quasi Newton formula | |
| CN103036576A (en) | Two-value sparse signal reconstruction algorithm based on compressive sensing theory | |
| CN105490682A (en) | Compressive sensing signal recovery algorithm based on SVD (singular value decomposition) and OMP (orthogonal matching pursuit) | |
| Gao et al. | A Robust Orthogonal Matching Pursuit Based on L 1 Norm | |
| CN107403628A (en) | A kind of voice signal reconstructing method based on compressed sensing | |
| CN111177646A (en) | Inversion optimization method for karst aquifer permeable field | |
| CN111082973B (en) | Network delay estimation method based on lever sampling | |
| Zhang et al. | Distributed compressive sensing via LSTM-aided sparse bayesian learning | |
| Xueyuan | Sparsity Adaptive-based Stagewise Orthogonal Matching Pursuit Algorithm for Image Reconstruction. |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20170503 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |