CN107809253A - Compressed sensing data reconstruction method based on random Kaczmarz iteration - Google Patents
Compressed sensing data reconstruction method based on random Kaczmarz iteration Download PDFInfo
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Abstract
The invention discloses a kind of compressed sensing data reconstruction method based on random Kaczmarz iteration, including：First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；Secondly, in a manner of sparse random Kaczmarz iteration, original data vector to be reconstructed is updated using the calculation matrix row after weighting；Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains the individual elements of preceding k ' of maximum absolute value, and by remaining element zero setting；Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained.The present invention is according to the adaptive weight for adjusting calculation matrix of data characteristics, and utilize the calculation matrix renewal reconstruct vector after weighting, so as to strengthen the quality reconstruction of key element in primary signal, the precision of compressed sensing data reconstruction is improved, accelerates the speed of compressed sensing data reconstruction.
Description
Technical field
The present invention relates to a kind of compressed sensing data reconstruction method based on random Kaczmarz iteration, belong to compressed sensing
Data reconstruction technical field.
Background technology
With the fast development of information technology, need to gather in the application fields such as signal transacting, image procossing and transmit
Substantial amounts of observation data.Higher sample rate not only has higher requirement to sensor, analog-to-digital conversion circuit etc., is passing
Defeated and storage observation data can also consume larger network bandwidth and memory space.Therefore, energy-efficient compression how is realized
Data acquisition, and accurately reconstruct initial data has great importance.
The patent application of Application No. 201510062912.6 discloses one kind and is based on Kaczmarz algebraically iterative approximation side
The bridge mobile vehicle Load Identification Methods of method, it carries out data reconstruction using traditional Kaczmarz iterative algorithms, and applies
In the scene of bridge mobile vehicle load identification, but use the speed of this method progress data reconstruction slower, and data weight
Structure precision is relatively low.
Compressive sensing theory can be with sample rate of twice less than signal bandwidth specified in Shannon's sampling theorem to original
Signal is compressed sampling, and using data reconstruction algorithm reconstruct primary signal, is widely used to signal transacting, image procossing
Etc. application field.But above-mentioned traditional Kaczmarz iterative algorithms are not particularly suited for the reconstruct of compressed sensing data, and it is existing
A kind of other compressed sensing data reconstruction algorithm (" bases as disclosed in the patent application of Application No. 201510172344.5
In the adaptive resolution data reconstruction method of compressed sensing ", and " a kind of base disclosed in Application No. 201610841846.7
In the power line channel method of estimation of compressed sensing "), remained on when recovering primary signal exist data reconstruction speed it is relatively slow and
The problem of precision is relatively low, thus design quick high accuracy compressed sensing data reconstruction algorithm have important practical significance with it is huge
Big application value.
The content of the invention
It is an object of the present invention to provide a kind of compressed sensing data reconstruction method based on random Kaczmarz iteration,
It can effectively solve problems of the prior art, and the speed that especially compressed sensing data are reconstructed is relatively slow and smart
The problem of degree is not high.
In order to solve the above technical problems, the present invention adopts the following technical scheme that：Pressure based on random Kaczmarz iteration
Contracting perception data reconstructing method, comprises the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value
The maximum individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained.
Preferably, the weight in described adaptively changing calculation matrix per a line comprises the following steps：
S11, calculate the Frobenius norms square with calculation matrix of the L2 norms of each row vector of calculation matrix
Square ratio；
S12, using the ratio as probability, randomly select certain a line of calculation matrix；
S13, position the supported collection S=supp of original data vector to be reconstructedmax{k′,n-j}(x(j)), that is, calculate and treat weight
The original data vector x of structure(j)In take absolute value after descending arrangement preceding max { k ', n-j } individual element corresponding to index
Set；Wherein, j is cyclic variable, and n is the columns of calculation matrix；
S14, weighing vector w is calculated, if during the index l ∈ S of element, w is setl=1, otherwise set
Because original data vector to be reconstructed is sparse, by each in above method adaptively changing calculation matrix
Capable weight, so as to will be progressively isolated in calculation matrix with the row corresponding to neutral element in original data vector reconstruction cycle it
Outside, and then the reconstructed velocity of compressed sensing data is further increased.
Preferably, the calculation matrix row after described calculating weighting, even ai'=w ⊙ ai, by vectorial w and aiIn element
Carry out by element multiplication；Wherein, ai' for weighting after calculation matrix row, aiFor certain a line of the calculation matrix randomly selected, w is
Weighing vector.
By the above method, the value of calculation matrix is progressively corrected according to data reconstruction result, it is weak in a manner of comparing mitigation
Change with neutral element in original data vector corresponding to be listed in data reconstruction process and influence, so as to further increase data weight
The precision of structure.
Preferably, it is described in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting
Original data vector to be reconstructed includes：Calculate wait the original data vector reconstructed by the calculation matrix row a after weightingi' institute
Projection on the hyperplane of composition, and as the reconstruct vector after renewal, even
Wherein, x(j+1)Represent the reconstruct vector after renewal, x(j)Represent the reconstruct vector before renewal, yiRepresent measurement signal.
Original data vector to be reconstructed is updated by above method, without seeking inverse of a matrix (matrix inversion operation
Amount of calculation it is very big, be O (n3), and when data dimension is higher, matrix can not be put into the internal memory of computing device completely
In directly calculate), enormously simplify calculating, further increase the speed of data reconstruction.
The compressed sensing data reconstruction method based on random Kaczmarz iteration of the present invention, specifically includes following steps：
S1. parameter initialization, ifFor calculation matrix, wherein aiFor the of matrix A
I rows, x ∈ RnFor original data vector to be reconstructed, the degree of rarefication of the original data vector to be reconstructed is k ', y ∈ RmTo survey
Signal is measured, i.e. y=Ax, j are cyclic variable, and s is signal magnitude measurement, and η is threshold parameter, x(j)∈RnIt is restructing algorithm in jth
The reconstruction signal obtained during secondary iteration；Make j=0, x(0)=0, s=yTy/m；
S2. for calculation matrix A every a line a1,...,am, calculate respectively's
Value, wherein | | A | |FFor A Frobenius norms,For row vector amL2 norms square；And it will be calculated
Ratio randomly selects certain a line of calculation matrix, is designated as a as probabilityi；
S3. the supported collection S=supp of reconstruction signal is positionedmax{k′,n-j}(x(j)), that is, calculate and reconstruction signal x(j)In take absolutely
To the index set corresponding to preceding max { k ', n-j } individual element of descending arrangement after value；
S4. weighing vector w is calculated, if during the index l ∈ S of element, w is setl=1, otherwise set
S5. the calculation matrix row a after weighting is calculatedi', even ai'=w ⊙ ai, wherein ⊙ expression vectors are by element multiplication；
S6. calculate wait the original data vector reconstructed by the calculation matrix row a after weightingiOn ' the hyperplane formed
Projection, and as renewal after reconstruct vector, even
S7. cyclic variable is updated, makes j=j+1；
S8. when j is to m remainder non-zeros, then jump to step S2 and continue executing with, otherwise jump to step S9；
S9. the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value most
The big individual elements of preceding k ', and by remaining element zero setting；Even x(j)=Hk′(x(j)), wherein Hk′() is hard -threshold operator；
S10. as the difference (y-Ax of the adjacent resultant error of data reconstruction twice(j-m))-(y-Ax(j)) when being less than threshold value η s, then
Make x(j)For final reconstruction result；Otherwise step S2 is jumped to.
In the above method, n value is determined that m value is determined by compression ratio by original data vector x length, i.e. m is equal to pressure
Shrinkage is multiplied by n.
By using the above method, so that the reconstructed velocity of compressed sensing data is most fast, and precision highest.
Compared with prior art, the present invention devises a kind of improved Kaczmarz iterative algorithms, by the way that this is improved
Kaczmarz iterative algorithms are combined with the IHT algorithms (make use of hard -threshold operator therein) in compressed sensing, so as to real
Show the reconstruct of compressed sensing data, specifically, the weight of adjustment calculation matrix of the present invention according to data characteristics adaptively,
And original data vector to be reconstructed is updated using the calculation matrix after weighting, so as to strengthen key element in primary signal
Quality reconstruction, and then the precision of compressed sensing data reconstruction is improved, accelerate the speed of compressed sensing data reconstruction.According to a large amount of
Data statistics shows, after the present invention is improved to Kaczmarz iterative algorithms, relative to traditional compressed sensing data reconstruction
Method, when carrying out data reconstruction, reconstructed velocity is improved up to 25%, and reconstruction accuracy, which improves, reaches 8dB.
Brief description of the drawings
Fig. 1 is a kind of method flow diagram of embodiment of the present invention；
Fig. 2 is the effect contrast figure tested using the present invention.
The present invention is further illustrated with reference to the accompanying drawings and detailed description.
Embodiment
Embodiments of the invention 1：Based on the compressed sensing data reconstruction method of random Kaczmarz iteration, as shown in figure 1,
Comprise the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value
The maximum individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained.
Specifically include following steps：
S1. parameter initialization, ifFor calculation matrix, wherein aiFor the of matrix A
I rows, x ∈ RnFor original data vector to be reconstructed, the degree of rarefication of the original data vector to be reconstructed is k ', y ∈ RmTo survey
Signal is measured, i.e. y=Ax, j are cyclic variable, and s is signal magnitude measurement, and η is threshold parameter, x(j)∈RnIt is restructing algorithm in jth
The reconstruction signal obtained during secondary iteration；Make j=0, x(0)=0, s=yTy/m；
S2. for calculation matrix A every a line a1,...,am, calculate respectivelyValue,
Wherein | | A | |FFor A Frobenius norms,For row vector amL2 norms square；And the ratio that will be calculated
As probability, certain a line of calculation matrix is randomly selected, is designated as ai；
S3. the supported collection S=supp of reconstruction signal is positionedmax{k′,n-j}(x(j)), that is, calculate and reconstruction signal x(j)In take absolutely
To the index set corresponding to preceding max { k ', n-j } individual element of descending arrangement after value；
S4. weighing vector w is calculated, if during the index l ∈ S of element, w is setl=1, otherwise set
S5. the calculation matrix row a after weighting is calculatedi', even ai'=w ⊙ ai, wherein ⊙ expression vectors are by element multiplication；
S6. calculate wait the original data vector reconstructed by the calculation matrix row a after weightingiOn ' the hyperplane formed
Projection, and as renewal after reconstruct vector, even
S7. cyclic variable is updated, makes j=j+1；
S8. when j is to m remainder non-zeros, then jump to step S2 and continue executing with, otherwise jump to step S9；
S9. the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value most
The big individual elements of preceding k ', and by remaining element zero setting；Even x(j)=Hk′(x(j)), wherein Hk′() is hard -threshold operator；
S10. as the difference (y-Ax of the adjacent resultant error of data reconstruction twice(j-m))-(y-Ax(j)) when being less than threshold value η s, then
Make x(j)For final reconstruction result；Otherwise step S2 is jumped to.
Embodiment 2：Based on the compressed sensing data reconstruction method of random Kaczmarz iteration, comprise the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value
The maximum individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained.
Wherein, can in the following manner in adaptively changing calculation matrix each row vector weight：
Various ways can be used in the weight of each row vector in calculating calculation matrix, as calculated calculation matrix
The ratio of the L1 norms of each row vector and the L2,1 norms of calculation matrix；Wherein, the L1 norms of row vector are the row vector
In each element absolute value summation, the L2 of matrix A, 1 norm sums again for the L2 norms of each row element of matrix, i.e.,
The calculation matrix row after weighting can be calculated in the following manner：Such as the thought by hard threshold algorithm, will be with
Some big powers' systems in calculation matrix A in weight vector corresponding to smaller element value set to 0 (or reducing certain ratio), from
And weaken the effect being listed in data reconstruction process corresponding to neutral element in original data vector.
Embodiment 3：Based on the compressed sensing data reconstruction method of random Kaczmarz iteration, comprise the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value
The maximum individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained；
Weight in described adaptively changing calculation matrix per a line comprises the following steps：
S11, calculate the Frobenius norms square with calculation matrix of the L2 norms of each row vector of calculation matrix
Square ratio；
S12, using the ratio as probability, randomly select certain a line of calculation matrix；
S13, position the supported collection S=supp of original data vector to be reconstructedmax{k′,n-j}(x(j)), that is, calculate and treat weight
The original data vector x of structure(j)In take absolute value after descending arrangement preceding max { k ', n-j } individual element corresponding to index
Set；Wherein, j is cyclic variable, and n is the columns of calculation matrix；
S14, weighing vector w is calculated, if during the index l ∈ S of element, w is setl=1, otherwise set
Embodiment 4：Based on the compressed sensing data reconstruction method of random Kaczmarz iteration, comprise the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value
The maximum individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained；
Calculation matrix row after described calculating weighting, even ai'=w ⊙ ai, by vectorial w and aiIn element carry out by
Element multiplication；Wherein, ai' for weighting after calculation matrix row, aiFor certain a line of the calculation matrix randomly selected, w for weighting to
Amount.
Described updates original data vector to be reconstructed using the calculation matrix row after weighting, can utilize formula x=
(ATA)-1ATY direct solutions, wherein A are the calculation matrix after weighting.
Embodiment 5：Based on the compressed sensing data reconstruction method of random Kaczmarz iteration, comprise the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains absolute value
The maximum individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained；
It is described in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed
Original data vector includes：Calculate wait the original data vector reconstructed by the calculation matrix row a after weightingi' formed it is super
Projection in plane, and as the reconstruct vector after renewal, even
Wherein, x(j+1)Represent that the reconstruct after renewal is vectorial, x (j) represent the reconstruct vector before renewal, yiRepresent measurement signal.
In order to verify the effect of the present invention, inventor has carried out tests below research：
Make calculation matrix A ∈ R256×512To obey the gaussian random matrix of N (0,1) distributions, x ∈ R512It is 30 for degree of rarefication
Primary signal to be reconstructed, the position of its nonzero element selectes at random, and corresponding element value obeys N (0,1) Gaussian Profile, measurement
Signal y=Ax, threshold parameter η are arranged to 0.00001.
Utilize comprising the following steps that for the compressed sensing data reconstruction method based on random Kaczmarz iteration of the invention：
1) parameter initialization, j=0, x are made(0)=0, s=yTy/m；
2) for every a line a of matrix A1,…,a256, calculate respectivelyValue, and with
The numerical value randomly selects A certain a line as probability, is designated as ai(when it is implemented, using the randsample in matlab
Function realizes the function, and population parameters therein are vector)；
3) the supported collection S=supp of positioning reconstruct vectormax{30,512-j}(x(j)), that is, calculate and x(j)In take absolute value after by
The index set corresponding to preceding max { 30,512-j } individual element of small sequence is arrived greatly；
(such as x(j)=[1-3 6-7-2 0 9], the then supported collection comprising 3 elements are S={ 3,4,7 })
4) weighing vector w is calculated, as element index l ∈ S, then w is setl=1, otherwise set
(such as S={ 3,4,7 }, then w3、w4、w71 is all entered as, remaining element is entered as)
5) the calculation matrix row a after weighting is calculatedi', even ai'=w ⊙ ai, wherein ⊙ represent vector by element multiplication (i.e.
W and aiThe element multiplication of middle correspondence position, such as [1 2 3] and [2 3 4] obtain [1*2 2*3 3*4] by element multiplication,
The function can be realized in matlab with .*)；
6) reconstruct vector is calculated by ai' projection on hyperplane is formed, and as the reconstruct vector after renewal, even
7) cyclic variable is updated, makes j=j+1；
8) when j is to 256 remainder non-zero, jump to and 2) continue executing with, otherwise perform 9)；
9) hard -threshold operator H is utilized30() renewal reconstruct vector, even x(j)=H30(x(j)), retain after taking absolute value by big
To preceding 30 elements of small sequence, and by remaining element zero setting；
10) when continuous two groups of circulations reconstructed error difference (y-Ax(j-m))-(y-Ax(j)) when being more than threshold value η s,
Then jump to and 2) continue executing with；Otherwise x is made(j)For final reconstruction result.
The reconstruct of perception data is compressed by using the above method of the present invention, compared to traditional compressed sensing data
Reconstructing method, data reconstruction speed improve about 25%；The schematic diagram of compressed sensing data reconstruction result is as shown in Fig. 2 by Fig. 2
Understand, after the compressed sensing data reconstruction method using the present invention, the accuracy rate of data reconstruction is also very high, compared to traditional pressure
Contracting perception data reconstructing method, the accuracy rate of data reconstruction improve 8dB.
Claims (5)
1. the compressed sensing data reconstruction method based on random Kaczmarz iteration, it is characterised in that comprise the following steps：
First, in adaptively changing calculation matrix each row vector weight, and calculate weighting after calculation matrix row；
Secondly, in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed original
Data vector；
Again, the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains maximum absolute value
The individual elements of preceding k ', and by remaining element zero setting；Described k ' is the degree of rarefication of original data vector to be reconstructed；
Finally, when the difference of the adjacent resultant error of data reconstruction twice is less than threshold value, then final reconstruction result is obtained.
2. the compressed sensing data reconstruction method according to claim 1 based on random Kaczmarz iteration, its feature exist
In the weight in described adaptively changing calculation matrix per a line comprises the following steps：
S11, calculate the Frobenius norm squareds square with calculation matrix of the L2 norms of each row vector of calculation matrix
Ratio；
S12, using the ratio as probability, randomly select certain a line of calculation matrix；
S13, position the supported collection S=supp of original data vector to be reconstructedmax{k′,n-j}(x(j)), that is, calculate and to be reconstructed
Original data vector x(j)In take absolute value after descending arrangement preceding max { k ', n-j } individual element corresponding to index set；
Wherein, j is cyclic variable, and n is the columns of calculation matrix；
S14, weighing vector w is calculated, if during the index l ∈ S of element, w is setl=1, otherwise set
3. the compressed sensing data reconstruction method according to claim 1 based on random Kaczmarz iteration, its feature exist
In the calculation matrix row after described calculating weighting, even ai'=w ⊙ ai, by vectorial w and aiIn element carry out by element phase
Multiply；Wherein, ai' for weighting after calculation matrix row, aiFor certain a line of the calculation matrix randomly selected, w is weighing vector.
4. the compressed sensing data reconstruction method according to claim 1 based on random Kaczmarz iteration, its feature exist
In, it is described in a manner of sparse random Kaczmarz iteration, updated using the calculation matrix row after weighting to be reconstructed original
Data vector includes：Calculate wait the original data vector reconstructed by the calculation matrix row a after weightingi' the hyperplane formed
On projection, and as renewal after reconstruct vector, evenWherein, x(j+1)
Represent the reconstruct vector after renewal, x(j)Represent the reconstruct vector before renewal, yiRepresent measurement signal.
5. the compressed sensing data reconstruction method according to claim 1 based on random Kaczmarz iteration, its feature exist
In specifically including following steps：
S1. parameter initialization, ifFor calculation matrix, wherein aiFor the i-th row of matrix A, x
∈RnFor original data vector to be reconstructed, the degree of rarefication of the original data vector to be reconstructed is k ', y ∈ RmBelieve for measurement
Number, i.e. y=Ax, j are cyclic variable, and s is signal magnitude measurement, and η is threshold parameter, x(j)∈RnChanged for restructing algorithm in jth time
For when obtained reconstruction signal；Make j=0, x(0)=0, s=yTy/m；
S2. for calculation matrix A every a line a1,...,am, calculate respectivelyValue, its
In | | A | |FFor A Frobenius norms,For row vector amL2 norms square；And the ratio being calculated is made
For probability, certain a line of calculation matrix is randomly selected, is designated as ai；
S3. the supported collection S=supp of reconstruction signal is positionedmax{k′,n-j}(x(j)), that is, calculate and reconstruction signal x(j)In take absolute value
Index set corresponding to preceding max { k ', n-j } individual element of descending arrangement afterwards；
S4. weighing vector w is calculated, if during the index l ∈ S of element, w is setl=1, otherwise set
S5. the calculation matrix row a after weighting is calculatedi', even ai'=w ⊙ ai, wherein ⊙ expression vectors are by element multiplication；
S6. calculate wait the original data vector reconstructed by the calculation matrix row a after weightingiThrowing on the ' hyperplane formed
Shadow, and as the reconstruct vector after renewal, even
S7. cyclic variable is updated, makes j=j+1；
S8. when j is to m remainder non-zeros, then jump to step S2 and continue executing with, otherwise jump to step S9；
S9. the original data vector to be reconstructed after renewal is handled using hard -threshold operator, retains maximum absolute value
The preceding individual elements of k ', and by remaining element zero setting；Even x(j)=Hk′(x(j)), wherein Hk′() is hard -threshold operator；
S10. as the difference (y-Ax of the adjacent resultant error of data reconstruction twice(j-m))-(y-Ax(j)) when being less than threshold value η s, then make x(j)For final reconstruction result；Otherwise step S2 is jumped to.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111541572A (en) * | 2020-04-26 | 2020-08-14 | 武汉理工大学 | Accurate reconstruction method of random opportunity network graph under low constraint condition |
| CN115412102A (en) * | 2022-10-31 | 2022-11-29 | 人工智能与数字经济广东省实验室(广州) | Sparse signal recovery method, system, device and medium based on sparse random Kaczmarz algorithm |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111541572A (en) * | 2020-04-26 | 2020-08-14 | 武汉理工大学 | Accurate reconstruction method of random opportunity network graph under low constraint condition |
| CN111541572B (en) * | 2020-04-26 | 2021-08-17 | 武汉理工大学 | Accurate reconstruction method of random opportunity network graph under low constraint condition |
| CN115412102A (en) * | 2022-10-31 | 2022-11-29 | 人工智能与数字经济广东省实验室(广州) | Sparse signal recovery method, system, device and medium based on sparse random Kaczmarz algorithm |
| CN115412102B (en) * | 2022-10-31 | 2023-02-03 | 人工智能与数字经济广东省实验室(广州) | Sparse signal recovery method, system, device and medium based on sparse random Kaczmarz algorithm |
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Application publication date: 20180316 |