CN105513102B - EO-1 hyperion compressed sensing method for reconstructing based on non-local total variation and low-rank sparse - Google Patents
EO-1 hyperion compressed sensing method for reconstructing based on non-local total variation and low-rank sparse Download PDFInfo
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Abstract
The invention discloses a kind of EO-1 hyperion compressed sensing method for reconstructing based on non-local total variation and low-rank sparse mainly solves the problems, such as that the prior art rebuilds that accuracy is low, effect is poor after high-spectral data carries out compression sampling.It includes：1. inputting high-spectral data dyad；2. the high-spectral data of pair vectorization samples, sampled data is obtained；3. carrying out original reconstruction to sampled data；4. the data clusters of pair original reconstruction；5. classifying according to pixel classification to sampled data, all kinds of sampled datas are obtained；6. constructing secondary reconstruction model；7. solving secondary reconstruction model according to all kinds of sampled datas, the optimal data of secondary reconstruction is obtained, and rebuild data using the data as final.The present invention introduces non-local total variation and Clustering on the basis of low-rank sparse is rebuild, and has the advantages that reconstruction accuracy is high, effect is good, can be used for high-spectral data imaging.
Description
Technical field
The invention belongs to technical field of image processing, relate generally to a kind of high-spectral data compressed sensing method for reconstructing, can
For high light spectrum image-forming.
Background technique
High-spectral data is made of up to a hundred very narrow wave bands, and the high-resolution characteristic in space and wave band direction makes
High-spectral data has very big data dimension, storage, transmission and subsequent processing of the huge information content to high-spectral data
Bring difficulty.Traditional compressive sampling method carries out uniform or nonuniform sampling to signal using Nyquist sampling rate
Afterwards, it is compressed by prediction, transformation, vector quantization scheduling algorithm.The process of this highly redundant sampling recompression causes greatly
The wasting of resources, it is limited airborne to low-power consumption and resource or spaceborne application brings immense pressure.
Compressed sensing is theoretical as a kind of novel signal acquisition, has merged traditional sampling and compression process, with remote low
Measurement data is directly acquired in the mode of nyquist sampling rate, sampling cost is reduced, reduces storage resource.Compressed sensing
Method efficiently solves the problems, such as that high-spectral data calculates and amount of storage is big.It is rebuild in existing high-spectral data compressed sensing
In method, Wagadarikar A et al. proposes the data that total variation model is applied independently in each wave band, for constraining sky
Between flatness, but this method have ignored spectrum between correlation.Aravind N V et al. is in a distributed manner based on compressive sensing theory
Simultaneous OMP method is proposed, this process employs the joint sparse characteristics of high-spectral data, although when rebuilding
Between it is upper there is some superiority, but the quality of reconstruction image is lower, it is difficult to reach the requirement of subsequent applications.
What James E.Fowler was proposed is calculated principal component analysis PCA based on compression-projection principal component analysis CPPCA algorithm
Compression of the method for high-spectral data is rebuild.Former high-spectral data is projected to randomly selected lower-dimensional subspace first by the algorithm
Sampled data is obtained, PCA transformation then is carried out to sampled data.Base is converted by the PCA of sampled data, is alternately thrown using convex set
Shadow optimization algorithm approximation recovers the PCA transformation coefficient and transformation base of former data, and then the high-spectral data rebuild.The party
Although PCA dimensionality reduction step can be transferred to decoding end by coding side by method, and reconstruction time is shorter, the quality of reconstruction image
Lower, deficiency is to provide reliable data source for subsequent image procossing.
Summary of the invention
It is an object of the invention to be directed to the deficiency of above-mentioned prior art, propose a kind of based on non-local total variation and low-rank
Sparse EO-1 hyperion compressed sensing method for reconstructing meets subsequent answer to improve the reconstruction quality after high-spectral data compression sampling
It is required that.
To achieve the above object, technical solution of the present invention includes as follows：
(1) high-spectral data is inputtedWhereinIndicate that real number space, H and P respectively indicate high-spectral data and count in the both horizontally and vertically pixel of spatial domain, N indicates wave
Section sum, Xn={ Xi,j,n, i=1 ..., H, j=1 ..., P } indicate high-spectral data XoriN-th of wave band, Xi,j=
{Xi,j,1,...,Xi,j,NIndicate high-spectral data a pixel；By high-spectral data XoriCarry out vectorization processing, obtain to
The high-spectral data of quantization
(2) to dataUse the diagonal sampling matrix of blockIt is sampled, obtains sampled data
Wherein T indicates the sampled data dimension of single EO-1 hyperion pixel；
(3) original reconstruction is carried out as the following formula to sampled data Y：
Wherein, XLIndicate the low-rank component of reconstruction data, XSIndicate the sparse component of reconstruction data, XL' indicate original reconstruction
The low-rank component of data X ', XSThe sparse component of ' expression original reconstruction data X ', mat () indicate the matrix form of amount of orientation,
||·||*Expression takes the operation of matrix nuclear norm, | | | |1Indicate the operation of 1 norm of amount of orientation, μ1Indicate constraint low-rank item
Parameter, μ2Indicate the parameter of the sparse item of constraint, arg min indicates to take argument value when objective function being made to reach minimum value；
Original reconstruction data X ' is calculated according to above formula, X ' is vector XL′+XS' three-dimensional tensor form；
(4) M class data are obtained to the high-spectral data X ' carry out cluster operation of original reconstruction using K mean cluster method
Xclu(1),Xclu(2),...,Xclu(m),...,Xclu(M), wherein Xclu(m)Indicate m class data, m=1 ..., M；
(5) according to pixel Xi,jClassification, classify to sampled data Y, obtain M class sampled data Y(1),Y(2),...,
Y(m),...,Y(M), wherein Y(m)Indicate the sampled data of m class pixel, m=1 ..., M；
(6) according to the diagonal sampling matrix of high-spectral data X, block of vectorizationAnd sampled data Y, construct secondary reconstruction
Model is as follows：
Wherein, X1(m)Indicate X(m)Low-rank component, X2(m)Indicate X(m)Sparse component, X(m)Indicate the reconstruction number of m class
According to, m=1 ..., M, M indicate that cluster sum, X indicate that estimation high-spectral data, Y indicate sampled data,Indicate that block is diagonally adopted
Sample matrix,Indicate n-th of wave band X in XnNon-local total variation, X*Indicate the optimal high-spectral data of secondary reconstruction,
μ1Indicate the parameter of constraint low-rank item, μ2Indicate the parameter of the sparse item of constraint, μ indicates the parameter of constraint non-local total variation item.
(7) all kinds of sampled data Y obtained according to step (5)(m), the secondary reconstruction model in step (6) is iterated
It solves, and by the optimal high-spectral data X of secondary reconstruction*As final reconstruction data.
Compared with prior art, the present invention having the following advantages that：
First, the present invention considers the non local architectural characteristic of high-spectral data, and it is dilute that non-local total variation is introduced low-rank
Reconstruction model is dredged, the stronger Spectral correlation of EO-1 hyperion is not only utilized, but also the space non-local information in combined data, gram
Taken traditional TV and rebuild to easily cause and changed violent edge and rebuild fuzzy disadvantage so that in image details and edge weight
Structure effect gets a promotion.
Second, the present invention introduces clustering algorithm, by low-rank in view of the high similarity between similar pixel in high-spectral data
Sparse reconstruction model is applied in similar pixel, substantially increases the signal-to-noise ratio of reconstructed results, obtains reconstruction effect obviously
It improves.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is that the present invention emulates the 10th band image of high-spectral data IndianPines used；
Fig. 3 is the present invention and existing algorithm is respectively 0.2,0.3,0.4 in sample rate to high-spectral data IndianPines
The signal-to-noise ratio curve graph that Shi Jinhang is rebuild；
Fig. 4 is that the present invention and existing algorithm rebuild when sample rate is 0.2 to high-spectral data IndianPines
The 10th band image arrived.
Specific embodiment
With reference to the accompanying drawing, the present invention is described in further detail.
Referring to attached drawing 1, steps are as follows for realization of the invention：
Step 1, high-spectral data X is inputtedori, obtain the high-spectral data X of vectorization.
Input high-spectral dataWhereinTable
Show that real number space, H and P respectively indicate high-spectral data and count in the both horizontally and vertically pixel of spatial domain, N indicates that wave band is total
Number, Xn={ Xi,j,n, i=1 ..., H, j=1 ..., P } indicate high-spectral data XoriN-th of wave band, Xi,j=
{Xi,j,1,...,Xi,j,NIndicate high-spectral data a pixel；
By high-spectral data XoriEach pixel pile up column one by one, obtain the high-spectral data of vectorization
Step 2, the high-spectral data X of vectorization is sampled.
According to the following formula, the diagonal sampling matrix of block is used to the high-spectral data X of vectorizationIt is sampled, obtains hits
According to Y：
Wherein, the diagonal sampling matrix of blockIt is by the sampling matrix Φ of HP pixel1,Φ2,...,Φi,...,ΦHPStructure
At being expressed as：
ΦiIndicate sampling matrix used in i-th of pixel, size is T × N
Random gaussian matrix, the value range of i is { 1 ..., HP }, and sampled data Y is the vector that size is THP × 1, and T indicates single
The sampled data dimension of a EO-1 hyperion pixel.
Step 3, original reconstruction is carried out to sampled data Y.
The realization of this step is carried out by solving to low-rank sparse reconstruction model as follows：
Wherein, XLIndicate the low-rank component of reconstruction data, XSIndicate the sparse component of reconstruction data, XL' indicate original reconstruction
The low-rank component of data X ', XSThe sparse component of ' expression original reconstruction data X ', mat () indicate the matrix form of amount of orientation,
||·||*Expression takes the operation of matrix nuclear norm, | | | |1Indicate the operation of 1 norm of amount of orientation, μ1Indicate constraint low-rank item
Parameter, μ1Value be set as 1500, μ2Indicate the parameter of the sparse item of constraint, μ2Value be set as 500, arg min expression and take and make mesh
Scalar functions reach argument value when minimum value；
Steps are as follows for specific original reconstruction：
The number of iterations initial value k=1, maximum number of iterations k 3a) are setmax=5, low-rank component is initialized respectivelyIt is dilute
Dredge componentAnd intermediate variable Yk；
3b) using following formula to intermediate variable YkIt is updated：
Wherein, Yk+1Indicate that the intermediate variable that+1 iteration of kth obtains, k are indicated for iteratively solving XLAnd XSUsed changes
Generation number,WithRespectively indicate low-rank component and sparse component that kth time iteration obtains；
3c) using following formula to low-rank componentWith sparse componentIt is updated：
3d) judge whether to meet iteration stopping condition：If k+1=kmax, stop iteration, at this time
Original reconstruction data X ' is vector XL′+XS' three-dimensional tensor form；Otherwise, k=k+1 returns to 3b).
Step 4, M class number is obtained to the high-spectral data X ' carry out cluster operation of original reconstruction using K mean cluster method
According to.
M pixel point 4a) is randomly selected from original reconstruction data X ' as initial cluster centre；
The pixel not clustered point 4b) is arbitrarily chosen from X ', is calculated separately in selected pixel point and M cluster
The Euclidean distance of the heart finds out the corresponding cluster centre of Euclidean distance minimum value, most with Euclidean distance by the pixel point of selected taking-up
It is small to be worth corresponding cluster centre as same class data；
4c) judge whether whole pixel points in original reconstruction data X ' all complete cluster, if so, executing 4d), otherwise,
Return to 4b)；
The mean value of every a kind of pixel point after clustering 4d) is calculated, and using the mean value as updated cluster centre；
4e) according to the following formula, the residual error that M cluster centre updates front and back is calculated separately out：
Cresi=| | fi-hi||2
Wherein, CresiIndicate that the i-th class cluster centre updates the residual error of front and back, the value range of i is { 1,2 ..., M }, M
Indicate cluster sum, | | | |2Indicate the operation of 2 norm of amount of orientation, fiIndicate the updated cluster centre of the i-th class, hiIndicate i-th
Cluster centre before class update；
4f) judge that calculated M cluster centre updates whether maximum value in the residual error of front and back is less than preset threshold
0.001, if so, cluster process terminates, obtain M class data Xclu(1),Xclu(2),...,Xclu(m),...,Xclu(M), and∪ expression takes collection union operation, m=1 ..., M；Otherwise, using updated M cluster centre as new
Cluster centre returns to 4b).
Step 5, according to pixel Xi,jClassification, classify to sampled data Y.
According to M class data Xclu(1),Xclu(2),...,Xclu(m),...,Xclu(M)Middle pixel Xi,jClassification, determine hits
According to the pixel X corresponded in Y on spatial positioni,jSampled data classification；
It is combined of a sort sampled data is belonged in sampled data Y, obtains M class sampled data Y(1),Y(2),...,
Y(m),...,Y(M), wherein Y(m)Indicate the sampled data of m class pixel, m=1 ..., M.
Step 6, secondary reconstruction model is constructed.
According to the diagonal sampling matrix of high-spectral data X, block of vectorizationAnd sampled data Y, construct secondary reconstruction mould
Type is as follows：
Wherein, X1(m)Indicate X(m)Low-rank component, X2(m)Indicate X(m)Sparse component, X(m)Indicate the reconstruction number of m class
According to, m=1 ..., M, M indicate that cluster sum, X indicate that estimation high-spectral data, Y indicate sampled data,Indicate that block is diagonally adopted
Sample matrix,Indicate n-th of wave band X in XnNon-local total variation, X*Indicate the optimal high-spectral data of secondary reconstruction, μ
1 indicates the parameter of constraint low-rank item, μ1Value be set as 15000, μ2Indicate the parameter of the sparse item of constraint, μ2Value be set as
3500, μ indicate that the parameter of constraint non-local total variation item, the value of μ are set as 110.
Step 7, all kinds of sampled data Y obtained according to step 5(m), the secondary reconstruction model in step 6 is iterated
It solves, and using the optimal high-spectral data of secondary reconstruction as final reconstruction data.
The number of iterations initial value k=1, maximum number of iterations k 7a) are setmax=30；
7b) according to the following formula, every a kind of sampled data Y is calculated(m)Intermediate reconstructed data under low-rank sparse constraint：
Wherein, Y(m)Indicate the sampled data of m class,Indicate block diagonal matrix, the sampling as used in m class pixel
Matrix is constituted,Indicate the m class estimated data that kth time iteration obtains, XkIndicating willIt closes
And resulting three-dimensional reconstruction data, X "(m)Indicate the centre that m class data obtain under low-rank sparse constraint when+1 iteration of kth
Data are rebuild, m=1 ..., M, M indicate cluster sum, λ1Indicate constraint X(m)Penalize a parameter, λ1Value be set as 1；
7c) by intermediate reconstructed data X "(m)It is playbacked and is merged by former pixel position, obtain three-dimensional intermediate data X "；
7d) according to the following formula, non-local total variation amendment is carried out to each wave band of three-dimensional intermediate data X ", obtains amendment data
Wherein, XnN-th of wave band of " indicating X ",Indicate n-th of wave band Z in high-spectral data ZnIt is non local complete
It is deteriorated,Indicate Xn" reconstructed results that the amendment data under non-local total variation constraint, i.e.+1 iteration of kth obtain, λ2
Indicate constraint ZnPenalize a parameter, λ2Value be set as 1,Expression takes the square operation of 2 norms.
7e) judge whether to meet iteration stopping condition：If k+1=kmax, stop iteration, obtain the non-office of each wave band at this time
Portion's total variation corrects dataExecute 7f)；Otherwise, the non-local total variation of each wave band is corrected into dataCombination obtains three
Dimension data Xk+1, k=k+1, return 7b).
The non-local total variation of each wave band 7f) is corrected into dataMerge, obtains the optimal EO-1 hyperion number of secondary reconstruction
According to X*, which is final reconstruction data.
Effect of the invention is described further below with reference to emulation experiment.
1. simulated conditions
It is Inter (R) Core (TM) i5-4200U 2.30GHZ, carried out in 7 system of memory 4G, WINDOWS in CPU
Emulation.
2. emulating data
Data used in this experiment are U.S. AVIRIS high-spectral data IndianPines, and size of the data in airspace is
145 × 145, share 21025 pixel points, 220 spectral bands.For convenience of experiment, taken in original image size be 128 ×
128, the data of 1-100 wave band carry out emulation experiment, and initial position of the image block in original image is (1,1).Fig. 2 shows experiment
The grayscale image of the 10th wave band of IndianPines used.
3. emulation content
Utilize the present invention and existing compression-projection principal component analysis CPPCA algorithm and its innovatory algorithm KCPPCA algorithm
When sample rate K/N is respectively 0.2,0.3,0.4, compression sampling and reconstruction are carried out to IndianPines data, reconstructed results
Signal-to-noise ratio is as shown in table 1.
The reconstructed results signal-to-noise ratio (dB) of 1 algorithms of different of table
| The present invention | KCPPCA | CPPCA | |
| K/N=0.2 | 32.95 | 28.11 | 26.76 |
| K/N=0.3 | 36.06 | 30.11 | 28.07 |
| K/N=0.4 | 38.65 | 30.58 | 28.67 |
From table 1 it follows that reconstructed results of the invention are all best in three kinds of algorithms under different sample rates
's.When sample rate is respectively 0.2,0.3,0.4, signal-to-noise ratio of the invention is respectively increased compared with KCPPCA algorithm
4.84dB, 5.95dB, 8.07dB, signal-to-noise ratio promotion amplitude is larger, and it is good thus to embody present invention reconstruction accuracy height, effect
Feature.
Signal-to-noise ratio result in table 1 is depicted as curve, obtain the present invention from two kinds of existing algorithms under different sample rates
Reconstruction signal-to-noise ratio curve graph, as shown in Figure 3.From figure 3, it can be seen that signal-to-noise ratio curve of the invention is located at extreme higher position,
It is that reconstructed results are best in three kinds of algorithms.And compared with two kinds of existing algorithms, signal-to-noise ratio is promoted with the increase of sample rate
Amplitude has apparent increase, it can be seen that the present invention has the characteristics that reconstruction accuracy is high, effect is good.
Utilize the present invention and existing compression-projection principal component analysis CPPCA algorithm and its innovatory algorithm KCPPCA algorithm
When sample rate K/N is 0.2, compression sampling and reconstruction are carried out to IndianPines data, rebuild the 10th band image of data
As shown in figure 4, wherein 4 (a) indicating reconstruction image of the present invention, 4 (b) indicate KCPPCA algorithm reconstruction image, and 4 (c) indicate CPPCA
Algorithm reconstruction image.
Figure 4, it is seen that in visual effect, reconstructed results of the present invention to high-spectral data IndianPines
It is best in three kinds of algorithms.The present invention not only has preferable reconstruction to the bulk smooth region in image, while to some thin
Also there are a more visible recovery in section and edge, and overall gray value is closer to original image.It is rebuild it can be seen that the present invention has
The feature that accuracy is high, effect is good.
Claims (4)
1. a kind of EO-1 hyperion compressed sensing method for reconstructing based on non-local total variation and low-rank sparse, includes the following steps：
(1) high-spectral data is inputtedWhereinIt indicates
Real number space, H and P respectively indicate high-spectral data and count in the both horizontally and vertically pixel of spatial domain, and N indicates that wave band is total
Number, Xn={ Xi,j,n, i=1 ..., H, j=1 ..., P } indicate high-spectral data XoriN-th of wave band, Xi,j=
{Xi,j,1,...,Xi,j,NIndicate high-spectral data a pixel；By high-spectral data XoriCarry out vectorization processing, obtain to
The high-spectral data of quantization
(2) to dataUse the diagonal sampling matrix of blockIt is sampled, obtains sampled dataWherein T
Indicate the sampled data dimension of single EO-1 hyperion pixel；
(3) original reconstruction is carried out as the following formula to sampled data Y：
Wherein, XLIndicate the low-rank component of reconstruction data, XSIndicate the sparse component of reconstruction data, XL' indicate original reconstruction data
The low-rank component of X ', XSThe sparse component of ' expression original reconstruction data X ', mat () indicate the matrix form of amount of orientation, | |
||*Expression takes the operation of matrix nuclear norm, | | | |1Indicate the operation of 1 norm of amount of orientation, μ1Indicate the parameter of constraint low-rank item,
μ2Indicate the parameter of the sparse item of constraint, argmin indicates to take argument value when objective function being made to reach minimum value；
Original reconstruction data X ' is calculated according to above formula, X ' is vector XL′+XS' three-dimensional tensor form；
(4) M class data X is obtained to the high-spectral data X ' carry out cluster operation of original reconstruction using K mean cluster methodclu(1),
Xclu(2),...,Xclu(m),...,Xclu(M), wherein Xclu(m)Indicate m class data, m=1 ..., M；
(5) according to pixel Xi,jClassification, classify to sampled data Y, obtain M class sampled data Y(1),Y(2),…,
Y(m),…,Y(M), wherein Y(m)Indicate the sampled data of m class pixel, m=1 ..., M；
(6) according to the diagonal sampling matrix of high-spectral data X, block of vectorizationAnd sampled data Y, construct secondary reconstruction model
It is as follows：
Wherein, X1(m)Indicate X(m)Low-rank component, X2(m)Indicate X(m)Sparse component, X(m)Indicate the reconstruction data of m class, m
=1 ..., M, M indicate that cluster sum, X indicate that estimation high-spectral data, Y indicate sampled data,Indicate that block diagonally samples square
Battle array, ▽NLXnIndicate n-th of wave band X in XnNon-local total variation, X*Indicate the optimal high-spectral data of secondary reconstruction, μ1It indicates
Constrain the parameter of low-rank item, μ2Indicate the parameter of the sparse item of constraint, μ indicates the parameter of constraint non-local total variation item；
(7) all kinds of sampled data Y obtained according to step (5)(m), the secondary reconstruction model in step (6) is iterated and is asked
Solution, and by the optimal high-spectral data X of secondary reconstruction*As final reconstruction data.
2. the EO-1 hyperion compressed sensing method for reconstructing according to claim 1 based on non-local total variation and low-rank sparse,
Wherein to data in step (2)Use the diagonal sampling matrix of blockSampled, be by such as down-sampling formula into
Row：
Wherein, the diagonal sampling matrix of blockIt is by the sampling matrix Φ of HP pixel1,Φ2,...,Φi,...,ΦHPIt constitutes,
It is expressed as：
ΦiIndicate sampling matrix used in i-th of pixel, size is the random of T × N
Gaussian matrix, the value range of i are { 1 ..., HP }, and sampled data Y is the vector that size is THP × 1, and T indicates single bloom
Compose the sampled data dimension of pixel.
3. the EO-1 hyperion compressed sensing method for reconstructing according to claim 1 based on non-local total variation and low-rank sparse,
Wherein in step (4) using K mean cluster method to the high-spectral data X ' carry out cluster operation of original reconstruction, steps are as follows：
(4a) randomly selects M pixel point as initial cluster centre from original reconstruction data X '；
(4b) arbitrarily chooses the pixel not clustered point from X ', calculates separately selected pixel point and M cluster centre
Euclidean distance, find out the corresponding cluster centre of Euclidean distance minimum value, the pixel point of selected taking-up and Euclidean distance is minimum
It is worth corresponding cluster centre as same class data；
(4c) judges whether whole pixel points in original reconstruction data X ' all complete cluster, otherwise returns if so, executing (4d)
It returns (4b)；
(4d) calculates the mean value of every a kind of pixel point after cluster, and using the mean value as updated cluster centre；
(4e) according to the following formula, calculates separately out the residual error that M cluster centre updates front and back：
Cresi=| | fi-hi||2
Wherein, CresiIndicate that the i-th class cluster centre updates the residual error of front and back, the value range of i is { 1,2 ..., M }, and M indicates poly-
Class sum, | | | |2Indicate the operation of 2 norm of amount of orientation, fiIndicate the updated cluster centre of the i-th class, hiIndicate that the i-th class updates
Preceding cluster centre；
(4f) judges that calculated M cluster centre updates whether maximum value in the residual error of front and back is less than preset threshold 0.001, if
It is that then cluster process terminates, obtains M class data Xclu(1),Xclu(2),...,Xclu(m),...,Xclu(M), and
∪ expression takes collection union operation, m=1 ..., M；Otherwise, it is returned updated M cluster centre as new cluster centre
(4b)。
4. the EO-1 hyperion compressed sensing method for reconstructing according to claim 1 based on non-local total variation and low-rank sparse,
Wherein according to pixel X in step (5)i,jClassification, to sampled data Y carry out sort operation, be according to M class data Xclu(1),
Xclu(2),...,Xclu(m),...,Xclu(M)Middle pixel Xi,jClassification, determine the pixel corresponded on spatial position in sampled data Y
Xi,jSampled data classification, and be combined of a sort sampled data is belonged in sampled data Y, obtain M class sampled data
Y(1),Y(2),...,Y(m),...,Y(M), wherein Y(m)Indicate the sampled data of m class pixel, m=1 ..., M.
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| CN106023273B (en) * | 2016-05-27 | 2018-12-07 | 西安交通大学 | A kind of non-local low rank regularized image compressed sensing method for reconstructing |
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| CN108876884B (en) * | 2018-06-21 | 2022-06-14 | 汕头大学 | Hyperspectral image reconstruction method based on non-local tensor low-rank regularization |
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