CN104410423A - Backtracking genetic iterative reconstruction method in compressed sensing - Google Patents
Backtracking genetic iterative reconstruction method in compressed sensing Download PDFInfo
- Publication number
- CN104410423A CN104410423A CN201410584035.4A CN201410584035A CN104410423A CN 104410423 A CN104410423 A CN 104410423A CN 201410584035 A CN201410584035 A CN 201410584035A CN 104410423 A CN104410423 A CN 104410423A
- Authority
- CN
- China
- Prior art keywords
- atom
- support set
- sparse
- residual error
- compressed sensing
- 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.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 40
- 230000002068 genetic effect Effects 0.000 title claims abstract description 25
- 230000035772 mutation Effects 0.000 claims abstract description 24
- 125000004429 atom Chemical group 0.000 claims description 103
- 239000011159 matrix material Substances 0.000 claims description 16
- 238000001514 detection method Methods 0.000 claims description 15
- 210000000349 chromosome Anatomy 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 12
- 230000001174 ascending effect Effects 0.000 claims description 10
- 238000004364 calculation method Methods 0.000 claims description 8
- 230000009466 transformation Effects 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 4
- 238000005259 measurement Methods 0.000 claims description 4
- 238000012545 processing Methods 0.000 claims description 4
- 125000004434 sulfur atom Chemical group 0.000 claims description 4
- 230000006870 function Effects 0.000 claims description 2
- 229940050561 matrix product Drugs 0.000 claims description 2
- 230000007935 neutral effect Effects 0.000 claims description 2
- 108090000623 proteins and genes Proteins 0.000 claims description 2
- 230000003252 repetitive effect Effects 0.000 claims description 2
- 230000017105 transposition Effects 0.000 claims description 2
- 230000001502 supplementing effect Effects 0.000 claims 1
- 125000004122 cyclic group Chemical group 0.000 abstract 1
- 238000005070 sampling Methods 0.000 description 7
- 230000008901 benefit Effects 0.000 description 2
- 238000007906 compression Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 230000006835 compression Effects 0.000 description 1
- 239000012141 concentrate Substances 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000010353 genetic engineering Methods 0.000 description 1
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a backtracking genetic iterative reconstruction method in compressed sensing. The backtracking genetic iterative reconstruction method comprises the following steps of firstly, initializing a support set of a sparse signal to be solved, carrying out cyclic iterative approximation on optimal position information of the solved sparse signal through genetic operation, such as copying, multipoint crossing, selection and big mutation treatment, carrying out backtracking updating of the support set, and lastly, projecting by utilizing a least square method to obtain amplitude information of each nonzero element of the sparse signal to be solved so as to complete signal reconstruction. According to the backtracking genetic iterative reconstruction method in compressed sensing, the sparse signal to be solved can be precisely reconstructed under the condition of unknown sparseness.
Description
Technical field
The present invention relates to a kind of signal reconfiguring method, belong to signal processing technology field.
Background technology
Nyquist sampling theorem is pointed out, sampling rate must reach more than the twice of signal bandwidth could Accurate Reconstruction signal.Then, although the data of sampling in this manner can complete representation primary signal, there is larger redundancy in sample value data.Therefore the method image data often needs to carry out compression process to save memory space.Compressed sensing (Compressed Sensing, CS) is also referred to as compression sampling or sparse sampling, breaches the signal sampling theory of conventional Nyquist sampling thheorem.This theory is pointed out, as long as signal or be sparse on certain transform domain, so just can be projected to by this higher-dimension sparse signal with the incoherent calculation matrix of sparse base with one and a lower dimensional space completes sparse signal compress.Restructuring procedure is: from the projection value of low-dimensional, decompress(ion) restores higher-dimension sparse signal.In theory, if projection contain reconstruction signal enough information just can high probability, high-precisionly restore primary signal.Therefore, CS can be widely used in the exploitation etc. of Medical Image Processing, remote sensing image processing, wireless sensor network and image capture device.
Compressed sensing mainly comprises the restructing algorithm of the sparse transformation of signal, the design of calculation matrix and signal.Traditional restructing algorithm mainly contains: greedy algorithm and base tracing algorithm.Greedy algorithm mainly obtains the support set of the x of primary signal by iteration, mainly comprise match tracing (Matching pursuit, MP), orthogonal matching pursuit (Or-thogonal matching pursuit, OMP) etc., greedy algorithm, the simple advantage of method for reconstructing fast with reconstruction speed obtained extensive use in engineering.Base tracing algorithm mainly comprises subspace and follows the trail of (Ba-sis pursuit, SP), gradient tracking (Gradient pursuit, GP) etc.MP and OMP algorithm all needs degree of rarefication K as the condition of Accurate Reconstruction, but the degree of rarefication K of signal is normally unknown in actual applications.In addition, MP and OMP algorithm idea concentrates on match tracing, needs effective subspace to follow the trail of and expands, once atom to be selected enters candidate's support set, then permanent interpolation can not be deleted, and the atom led to errors cannot be rejected, and lacks the thought of " backtracking ".Although SP has new atom to join support set at every turn, but quantitative assessment (namely increasing or delete the impact of atom pair error redundancy) is not carried out on the solution utilized calculated by least square closing when time support set, the theory being necessarily less than previous iteration residual error when time iteration residual error can not be provided simultaneously and ensure.Based on the shortcoming of these algorithms, cause reconstructed error comparatively large, become the key technology difficult problem that signal reconstruction needs solution badly.
Summary of the invention
The present invention needs known degree of rarefication K sum of subspace tracing algorithm cannot judge whether preferably problem to the atom newly added in support set to solve conventional greedy restructing algorithm, propose in a kind of compressed sensing and recall formula genetic iteration reconstructing method, its process and greedy restructing algorithm process contrary.Genetic algorithm is very effective for the np problem solved in Combinatorial Optimization, therefore the thought of backtracking formula genetic algorithm can be applied to the reconstruction of compressed sensing.Basic process is: build preferably initial support collection through optimization process; Carry out again copying, optimal location information that multiple-spot detection, selection, the genetic manipulation successive ignition such as Big mutation rate approach sparse signal to be asked, finally to be projected the amplitude information and final reconstruction result that obtain each position by least square method; Wherein by preserve eliminate atom carry out multiple-spot detection operation, then with support set in carry out the residual error ratio of the atom after multiple-spot detection operation comparatively, backtracking formula renewal support set, the loss of optimal solution can be prevented like this.The inventive method can be unknown at degree of rarefication K, and can reconstruct final sparse result efficiently under the condition not needing subspace to follow the trail of.
The present invention proposes in compressed sensing and recall formula genetic iteration reconstructing method, comprise the following steps:
Step one, required sparse signal θ is equivalent to chromosome carries out population setting, namely population is equivalent to the support set ψ of required sparse signal θ, and chromosome is the atom of support set ψ, input measurement value y, gaussian random calculation matrix Φ and sparse transformation matrix
, then by encoding scheme initialization support set ψ;
Step 2, by calculating the residual error size of support set ψ Atom and sort ascending, judge whether to eliminate the atom in support set ψ to preserve to the storehouse S arranged according to residual error size, if meet, then carry out eliminating operation, otherwise, atom is directly entered interlace operation; Judge again directly to enter in the atom of interlace operation and whether atom is carried out copying and saving operation, if meet, then carry out copy operation, otherwise, do not carry out other operations;
Step 3, random pair and multiple-spot detection operation is between two carried out to the part of atoms in support set ψ, and the atom of pairing is replaced by the atom newly produced, random pair and multiple-spot detection operation between two are also carried out to the part of atoms in storehouse S, and is replaced the atom of pairing by the atom newly produced;
Step 4, the atom preserved by copy operation expand support set ψ, calculate support set ψ and the residual extent of storehouse S Atom respectively and sort ascending, then compare and judge whether to upgrade support set;
Step 5, be carry out cataclysmic mutation according to Big mutation rate condition criterion, or common mutation operation, then judge whether to reach maximum genetic algebra, if reach, skip to step 6, otherwise, skip to step 2 and carry out loop iteration;
Step 6, obtained the amplitude of nonzero element in sparse result by least square method projection.
Compared with prior art, the invention has the advantages that:
1, degree of rarefication K need not be predicted.
2, by comparing the method for storehouse and the residual extent of support set Atom, the renewal support set of backtracking formula is reached.
3, can not locally optimal solution be absorbed in, can better globally optimal solution be found.
Accompanying drawing explanation
Fig. 1 is the flow chart of recalling formula genetic iteration reconstructing method in compressed sensing of the present invention
Embodiment
According to an aspect of the present invention, as shown in Figure 1, the specific embodiment of the invention is as following steps:
Step one, setting population and encoding scheme:
1) sparse signal θ to be asked is equivalent to chromosome and carries out population setting, namely population is equivalent to the support set ψ of required sparse signal θ, and chromosome is the atom of support set ψ;
2) suppose that support set is the matrix of N row (N bar chromosome), M dimension (having M gene in every bar chromosome), input measurement value y, random Gaussian calculation matrix Φ ∈ R
n × Mwith sparse transformation matrix
3) sparse signal
transposition for random Gaussian calculation matrix and sparse transformation matrix product), x
1support set be ψ, element non-vanishing in the atom of support set ψ is put 1, obtains initial support collection and can be expressed as ψ
m × N={ θ
1, θ
2..., θ
n.
Step 2, to copy:
1) by residual error function
calculate support set ψ Atom residual error F
iand sort ascending, wherein i=1,2 ..., N;
2) set generation gap value GAP:GAP ∈ (0.8,1), judge whether atom residual error is greater than
if be greater than, will eliminate
the atom that individual residual error is larger is preserved in the storehouse S arranged, otherwise, directly enter multiple-spot detection operation;
The atom directly entering multiple-spot detection operation is judged whether the residual error of atom is less than
if be less than, copy
individual atom to atom collection K, otherwise, do not carry out other operation.
Step 3, multiple-spot detection:
1) two atoms in Stochastic choice support set ψ also match, and storehouse S also carries out random pair operation;
2) crossover probability p is set
c, by crossover probability p
cdetermine
individual atom carries out random pair and multiple-spot detection operation;
3) the random binary character string τ that a length is M is produced respectively
1and τ
2, τ
1corresponding with the atom that in support set ψ, two are matched, τ
2corresponding with the atom that in storehouse S, two are matched;
4) if τ
1, τ
2middle correspondence position element is 1, then match the correspondence position commutative element of atom, otherwise, do not exchange;
5) the new atom produced by pairing replaces the atom of pairing.
Step 4, selection:
1) the atom collection K copied is merged into support set ψ;
2) calculate residual error size and the sort ascending of support set ψ Atom, storehouse S Atom also carries out residual computations and sort ascending operation;
3) make the atom that in storehouse S, residual error is minimum be k, the atom that in support set ψ, residual error is maximum is m, if k is less than m, then k and m exchanges mutually, otherwise, do not exchange, this process of repetitive operation, until when the residual error of all atoms in storehouse S is all greater than the residual error of the atom that residual error is maximum in support set ψ.
Step 5, cataclysmic mutation:
Cataclysmic mutation can prevent the support set of iteration be absorbed in " precocity " phenomenon (namely when algorithm proceeds to certain iteration, in support set, the residual error of certain atom m is far smaller than the residual error of other any atom because the selected probability carrying out copying of atom by
formula is determined, a lot of atoms in next support set will be caused like this from same atom m, thus be similar to each other, and the limiting case of this phenomenon is exactly that all atoms are from same previous atom); Detailed process is:
1) intensive factor a:a ∈ (0.5,1) is set, Big mutation rate Probability p
bigwith common mutation probability p
m, and calculate the least residual F of the atom of support set ψ in this iteration
minwith mean residual F
avg;
2) if meet the condition a × F of Big mutation rate
min< F
avg, then
wherein
be the atom that the t time iteration has least residual, t=0,1,2 ..., n, is set to the form with least residual atom by atoms all in this support set, then to each element on support set ψ Atom, produces a random chance p
kif, p
kbe less than Big mutation rate Probability p
bigthen carry out inversion operation, otherwise, do not change;
3) if do not meet the condition a × F of Big mutation rate
mm< F
avg, then to each element on support set ψ Atom, a random chance p is produced
kif, p
kbe less than common mutation probability p
m, then carry out inversion operation, otherwise, do not change.
In step 6, sparse result, the amplitude of each nonzero element is determined:
1) setting maximum genetic algebra is MAXGEN, if reach MAXGEN loop iteration, just can converge to optimum atom, i.e. the optimal solution of sparse result, otherwise, skip to step 2; Wherein optimum atom is still made up of " 1 " and " 0 ", and wherein " 1 " represents that original sparse signal is nonzero element, and " 0 " represents that original sparse signal is neutral element;
2), on the basis that each nonzero element positional information has been determined in sparse result, least square method is utilized to project to determine its amplitude information in each position; Suppose on q position, have a nonzero element in sparse result, then the amplitude p of this nonzero element is:
wherein T
qrepresent the q row of T, <> represents inner product operation; Recover matrix
Claims (7)
1. in compressed sensing, recall formula genetic iteration reconstructing method, it is characterized in that the population support set in compressed sensing be equivalent in genetic algorithm, by copying, intersecting, select and the operation such as Big mutation rate, make the optimum support set of initial support collection Step wise approximation and final reconstruction result, described method at least comprises the following steps:
Step one, required sparse signal θ is equivalent to chromosome carries out population setting, namely population is equivalent to the support set ψ of required sparse signal θ, and chromosome is the atom of support set ψ, input measurement value y, gaussian random calculation matrix Φ and sparse transformation matrix
again by encoding scheme initialization support set ψ;
Step 2, by calculating the residual error size of support set ψ Atom and sort ascending, judge whether to eliminate the atom in support set ψ to preserve to the storehouse S arranged according to residual error size, if meet, then carry out eliminating operation, otherwise, atom is directly entered interlace operation; Judge again directly to enter in the atom of interlace operation and whether atom is carried out copying and saving operation, if meet, then carry out copy operation, otherwise, do not carry out other operations;
Step 3, random pair and multiple-spot detection operation is between two carried out to the part of atoms in support set ψ, and the atom of pairing is replaced by the atom newly produced, random pair and multiple-spot detection operation between two are also carried out to the part of atoms in storehouse S, and is replaced the atom of pairing by the atom newly produced;
Step 4, the atom preserved by copy operation expand support set ψ, calculate support set ψ and the residual extent of storehouse S Atom respectively and sort ascending, then compare and judge whether to upgrade support set;
Step 5, be carry out cataclysmic mutation according to Big mutation rate condition criterion, or common mutation operation, then judge whether to reach maximum genetic algebra, if reach, skip to step 6, otherwise, skip to step 2 and carry out loop iteration;
Step 6, obtained the amplitude of nonzero element in sparse result by least square method projection.
2. recall formula genetic iteration reconstructing method in compressed sensing according to claim 1, it is characterized in that the support set by sparse signal θ required in compressed sensing is equivalent to the colony of genetic algorithm, and by encoding scheme, initialized process is carried out to support set, concrete steps at least also comprise:
1) required sparse signal θ is equivalent to chromosome and carries out population setting, namely population is equivalent to the support set ψ of required sparse signal θ, and chromosome is the atom of support set ψ;
2) suppose that support set is the matrix that N arranges that (N bar chromosome) M ties up (having M gene in every bar chromosome), input measurement value y, random Gaussian calculation matrix Φ ∈ R
n × Mwith sparse transformation matrix
3) sparse signal
(wherein
transposition for calculation matrix and sparse transformation matrix product), x
1support set be ψ, element non-vanishing in the atom of support set ψ is put 1, obtains initial support collection and can be expressed as ψ
m × N: ψ
m × N={ θ
1, θ
2..., θ
n.
3. according to claim 1, recall the process that formula genetic iteration reconstructing method is characterized in that processing the atom in initial support collection ψ in compressed sensing, concrete steps at least also comprise:
1) by residual error function
calculate support set ψ Atom residual error F
iand sort ascending, wherein i=1,2 ..., N;
2) set generation gap value GAP:GAP ∈ (0.8,1), judge whether atom residual error is greater than
if be greater than, will eliminate
the atom that individual residual error is larger is preserved in the storehouse S arranged, otherwise, directly enter multiple-spot detection operation;
3) atom directly entering multiple-spot detection operation is judged whether the residual error of atom is less than
if be less than, copy
individual atom to atom collection K, otherwise, do not carry out other operation.
4. recall formula genetic iteration reconstructing method in compressed sensing according to claim 1, it is characterized in that, to the process of the interior atoms in support set ψ and storehouse S panmixia and multiple-spot detection between two, at least also comprising:
1) two atoms in Stochastic choice support set ψ also match, and storehouse S also carries out random pair operation;
2) crossover probability p is set
c, by crossover probability p
cdetermine
individual atom carries out random pair and multiple-spot detection operation;
3) the random binary character string τ that a length is M is produced respectively
1and τ
2, τ
1corresponding with the atom that in support set ψ, two are matched, τ
2corresponding with the atom that in storehouse S, two are matched;
4) if τ
1, τ
2middle correspondence position element is 1, then match the correspondence position commutative element of atom, otherwise, do not exchange;
5) the new atom produced by pairing replaces the atom that first wife is right.
5. recall formula genetic iteration reconstructing method in compressed sensing according to claim 1, it is characterized in that carrying out to support set ψ the process supplementing and upgrade, concrete steps at least also comprise:
1) the atom collection K copied is merged into support set ψ;
2) calculate the residual sum sort ascending of support set ψ Atom, storehouse S Atom also carries out residual computations and sort ascending;
3) make the atom that in storehouse S, residual error is minimum be k, the atom that in support set ψ, residual error is maximum is m, if k is less than m, then k and m exchanges mutually, otherwise, do not exchange, this process of repetitive operation, until when the residual error of all atoms in storehouse S is all greater than the residual error of the atom that residual error is maximum in support set ψ.
6. recall formula genetic iteration reconstructing method in compressed sensing according to claim 1, it is characterized in that judging whether to meet Big mutation rate condition, then definitive variation action type; Concrete steps at least also comprise:
1) intensive factor a:a ∈ (0.5,1) is set, Big mutation rate Probability p
bigwith common mutation probability p
m, and calculate the least residual F of the atom of support set ψ in this iteration
mmwith mean residual F
avg;
2) if meet the condition a × F of Big mutation rate
min< F
avg, then
wherein
be the atom that the t time iteration has least residual, t=0,1,2 ..., n, is set to the form with least residual atom by atoms all in this support set, then to each element on support set ψ Atom, produces a random chance p
kif, p
kbe less than Big mutation rate Probability p
bigthen carry out inversion operation, otherwise, do not change;
3) if do not meet the condition a × F of Big mutation rate
min< F
avg, then to each element on support set ψ Atom, a random chance p is produced
kif, p
kbe less than common mutation probability p
m, then carry out inversion operation, otherwise, do not change.
7. recall formula genetic iteration reconstructing method in compressed sensing according to claim 1, it is characterized in that the position and the amplitude information that are obtained nonzero element in support set by the heredity process in genetic algorithm, concrete steps at least also comprise:
1) setting maximum genetic algebra is MAXGEN, if reach MAXGEN loop iteration, just can converge to optimum atom, i.e. the optimal solution of sparse result, otherwise, skip to step 2; Wherein optimum atom is still made up of " 1 " and " 0 ", and wherein " 1 " represents that original sparse signal is nonzero element, and " 0 " represents that original sparse signal is neutral element;
2), on the basis that each nonzero element positional information has been determined in sparse result, least square method is utilized to project to determine its amplitude information in each position; Suppose on q position, have a nonzero element in sparse result, then the amplitude p of this nonzero element is:
wherein T
qrepresent the q row of T, <> represents inner product operation; Recover matrix
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410584035.4A CN104410423B (en) | 2014-10-23 | 2014-10-23 | Formula genetic iteration reconstructing method is recalled in compressed sensing |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410584035.4A CN104410423B (en) | 2014-10-23 | 2014-10-23 | Formula genetic iteration reconstructing method is recalled in compressed sensing |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104410423A true CN104410423A (en) | 2015-03-11 |
| CN104410423B CN104410423B (en) | 2018-12-28 |
Family
ID=52648024
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410584035.4A Expired - Fee Related CN104410423B (en) | 2014-10-23 | 2014-10-23 | Formula genetic iteration reconstructing method is recalled in compressed sensing |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104410423B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102148987A (en) * | 2011-04-11 | 2011-08-10 | 西安电子科技大学 | Compressed sensing image reconstructing method based on prior model and 10 norms |
| CN103198500A (en) * | 2013-04-03 | 2013-07-10 | 西安电子科技大学 | Compressed sensing image reconstruction method based on principal component analysis (PCA) redundant dictionary and direction information |
-
2014
- 2014-10-23 CN CN201410584035.4A patent/CN104410423B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102148987A (en) * | 2011-04-11 | 2011-08-10 | 西安电子科技大学 | Compressed sensing image reconstructing method based on prior model and 10 norms |
| CN103198500A (en) * | 2013-04-03 | 2013-07-10 | 西安电子科技大学 | Compressed sensing image reconstruction method based on principal component analysis (PCA) redundant dictionary and direction information |
Non-Patent Citations (2)
| Title |
|---|
| JOEL A. TROPP ET AL.: "Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit", 《IEEE TRANSACTIONS ON INFORMATION THEORY》 * |
| 朱丰 等: "一种新的基于遗传算法的压缩感知重构方法及其在SAR高分辨距离像重构中的应用", 《控制与决策》 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104410423B (en) | 2018-12-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Zenil et al. | Low-algorithmic-complexity entropy-deceiving graphs | |
| Higgott et al. | Improved decoding of circuit noise and fragile boundaries of tailored surface codes | |
| Pedarsani et al. | Phasecode: Fast and efficient compressive phase retrieval based on sparse-graph codes | |
| Liu et al. | Robust recovery of subspace structures by low-rank representation | |
| Kutyniok | Theory and applications of compressed sensing | |
| Watson et al. | Fast fault-tolerant decoder for qubit and qudit surface codes | |
| Chou et al. | Efficient computation of robust average of compressive sensing data in wireless sensor networks in the presence of sensor faults | |
| JP6487931B2 (en) | Method and apparatus for reconstructing data blocks | |
| Konishi et al. | Iterative partial matrix shrinkage algorithm for matrix rank minimization | |
| CN109543842A (en) | The Distribution estimation method of higher-dimension intelligent perception data with local secret protection | |
| CN109769080B (en) | Encrypted image cracking method and system based on deep learning | |
| Peter et al. | Damping noise-folding and enhanced support recovery in compressed sensing | |
| Liu et al. | Fault diagnosability of Bicube networks under the PMC diagnostic model | |
| Shi et al. | Robust l‐Isomap with a novel landmark selection method | |
| Orsucci et al. | Estimation of coherent error sources from stabilizer measurements | |
| Hu et al. | Binary sparse signal recovery algorithms based on logic observation | |
| Delgosha et al. | A universal low complexity compression algorithm for sparse marked graphs | |
| Aloshious et al. | Decoding toric codes on three dimensional simplical complexes | |
| CN105162472A (en) | Block sparse signal reconstruction method based on greedy iteration | |
| Li et al. | An active learning framework using sparse-graph codes for sparse polynomials and graph sketching | |
| Mazumdar et al. | Associative memory via a sparse recovery model | |
| CN104410423A (en) | Backtracking genetic iterative reconstruction method in compressed sensing | |
| Bernárdez et al. | Topological network traffic compression | |
| Xia et al. | A new analysis for support performance with block generalized orthogonal matching pursuit | |
| Li et al. | Reliable data transmission in wireless sensor networks with data decomposition and ensemble recovery |
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 | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20181228 |