CN102629374B - Image super resolution (SR) reconstruction method based on subspace projection and neighborhood embedding - Google Patents

Abstract

The invention discloses an image super resolution (SR) reconstruction method based on subspace projection and neighborhood embedding. The method is characterized by: using first and secondary subspace projection methods to project original high-dimensional data to a low-dimensional space, using dimension reduction feature vectors to show a feature of a low-resolution image block so that global structure information and local structure information of original data can be maintained; comparing a Euclidean distance between the dimension reduction feature vectors in the low-dimensional space, finding a neighborhood block which is most matched with the low-resolution image block to be reconstructed, using a similarity and a scale factor between the feature vectors to construct an accurate embedded weight coefficient so that a searching speed and matching precision can be increased; then constructing the similarity and the scale factor between the feature vectors, calculating the accurate weight coefficient and acquiring more high frequency information from a training database; finally, according to the weight coefficient and the neighborhood block, estimating the high-resolution image block with high precision, reconstructing the image which has the high similarity with a real object, which is good for later-stage real object identification processing.

Description

Based on the image super-resolution rebuilding method of subspace projection and neighborhood embedding

Technical field

The present invention relates to the method for image processing, relate in particular to a kind of image super-resolution rebuilding method based on subspace projection and neighborhood embedding.

Background technology

Image super-resolution (Super Resolution, SR) reconstruction technique refers to and utilize one or more low resolution (the Low Resolution capturing in the different observation angles of Same Scene, different observation time or different sensors situation, LR) mutual information in image, adopt the method for Digital Image Processing to reconstruct a panel height resolution (High Resolution, HR) image.Under the condition that this reconstruction technique can limit at hardware devices such as charge-coupled image sensors (Charge Coupled Device, CCD), estimate the high-frequency information of its loss by one or more low-resolution image.In fields such as remote sensing satellite, military surveillance, medical imaging, security monitoring and traffic administrations, image super-resolution rebuilding technology not only has important researching value, is also with a wide range of applications.

The essence of image super-resolution rebuilding is how to solve the accurate estimation problem of losing high-frequency information, this is a classical one-to-many ill-conditioning problem, theory to this problem and applied research are still in the exploratory stage, and the aspects such as the quality of the time efficiency of image super-resolution rebuilding method and super-resolution rebuilding image all need further to be improved.Existing image super-resolution rebuilding method is mainly divided into interpolation, reconstruct and study three major types.Method of interpolation is a kind of method of utilizing known neighbour's point value to estimate interpolation point value, and these class methods are difficult to estimate the high-frequency information of loss.Reconstruction Method is to utilize the mutual information between several low-resolution images comprehensively to estimate high-frequency information, and its reconstruction effect is better than method of interpolation.But, Reconstruction Method needs the low-resolution image after several accuracy registrations, and the precision of current most image registration algorithms is not very high, can affect the quality of super-resolution rebuilding image.Learning method is the corresponding relation between low-resolution image piece and high-definition picture piece in first learning training storehouse, and estimates the high-definition picture piece corresponding with low-resolution image piece to be reconstructed according to this relation.Learning method can be realized single image super-resolution rebuilding, does not need image to carry out registration, and can from training storehouse, get more high-frequency information, thereby obtain better rebuilding effect.Therefore, learning method is the study hotspot of current image super-resolution rebuilding technology.

The image super-resolution rebuilding embedding based on neighborhood is an important branch in learning method, obtains in recent years good achievement in research.(the document 1:H.Chang such as Chang, D.-Y.Yeung, and Y.Xiong, " Super-resolution through neighbor embedding ", IEEE Conference on Computer Vision Pattern Recognition, pp.275-282, 2004) first propose to utilize the thought of neighborhood embedding to realize image super-resolution rebuilding, this method is to have under the prerequisite of similar local geometric features hypothesis at low-resolution image piece and corresponding high-definition picture piece, for each low-resolution image piece to be reconstructed, utilize local linear to embed (Locally Linear Embedding, LLE) algorithm calculates the embedding weight coefficient of several training low-resolution image pieces similar to low-resolution image piece to be reconstructed, each similar training low-resolution image piece is as a neighborhood piece, and then embed weight coefficients and corresponding neighborhood piece comprehensively estimates the high-definition picture piece after reconstruction with these.But, the method is not considered image block type and the impact of neighborhood piece number on super-resolution rebuilding effect.Subsequently, (the document 2:T.-M.Chan such as Chan, J.Zhang, J.Pu, and H.Huang, " Neighbor embedding based super-resolution algorithm through edge detection and feature selection ", Pattern Recognition Letters, vol.30, pp.494-502, 2009) propose a kind of neighborhood based on rim detection and Feature Selection and embed algorithm, this method can be determined the number that will choose neighborhood piece according to the type of image block (He Fei edge, edge), but, in the time there is serious blurring effect in input low-resolution image to be reconstructed, this algorithm can be difficult to judge the type of image block, make super-resolution rebuilding poor effect.(the document 3:K.Zhang such as Zhang, X.Gao, X.Li, and D.Tao, " Partially supervised neighbor embedding for example-based image super-resolution ", IEEE Journal of Selected Topics in Signal Processing, vol.5, no.2, pp.230-239, 2011) utilize class label information to construct a semi-supervised distance function, can from training storehouse, select the neighborhood piece that low-resolution image piece more and to be reconstructed mates according to this semi-supervised distance function, the super-resolution rebuilding effect of the method depends on the accuracy of identification of sorter to a certain extent.Algorithm described in document 1～3 is all on original high-dimensional feature space, to find several neighborhood pieces, because the dimension of original feature vector is very large, only rely on certain distance function to find neighborhood piece, the similarity between the neighborhood piece searching out and low-resolution image piece to be reconstructed is not high.Feature Dimension Reduction is a kind of feasible method addressing the above problem, based on this thinking, (the document 4:X.Gao such as Gao, K.Zhang, D.Tao, and X.Li, " Joint learning for single image super-resolution via coupled constraint ", IEEE Transactions on Image Processing, 2011) proposition is low by training by combination learning method, high-resolution features vector projects on a low-dimensional proper subspace simultaneously, and then on this low-dimensional proper subspace, find out the neighborhood piece that several mate with low-resolution image piece to be reconstructed.Although document 4 has been used the method for Feature Dimension Reduction, but when original low, high-resolution features is vectorial while projecting on unified low-dimensional proper subspace simultaneously, due to large than original low resolution proper vector of the dimension of original high resolution proper vector, inevitably can damage the useful information in original high-resolution features vector, also can produce harmful effect to the neighborhood piece of finding coupling.In addition, the algorithm of document 1～4 is all to adopt local linear to embed algorithm in the time calculating embedding weight coefficient, the embedding weight coefficient calculating is likely negative value, this can affect neighbour and train high-definition picture piece that the degree of high-frequency information can be provided, and the computation complexity of this algorithm is high, and arithmetic speed is slow.

Summary of the invention

The object of the present invention is to provide a kind of image super-resolution rebuilding method based on subspace projection and neighborhood embedding, the method realizes more effective Feature Dimension Reduction, estimate more accurately and rebuild rear high-definition picture piece, similarity between reconstruction image and real-world object is higher, super-resolution rebuilding better effects if.

The present invention solves its technical matters, and the technical scheme adopting is:

A, training:

Using high-definition picture identical L width resolution, that size is identical as training high-definition picture

l=1,2 ..., L, L=3～80; To every width training high-definition picture

carry out obtaining N after overlap partition ₁individual size is the training high-definition picture piece of z*z, N ₁=1000～7000, z=6,9,12,15, obtain altogether N=L*N ₁individual training high-definition picture piece, extract after the standardization brightness of each training high-definition picture piece as a training high resolving power standardization brightness image block, i training high resolving power standardization brightness image block is converted to i by an order being listed as and trains high-resolution features vector

i=1,2 ..., N, each training high-resolution features vector

dimension be d ₁=z ², all training high-resolution features vectors

training high-resolution features matrix of (1≤i≤N) composition

To l (1≤l≤L) width training high-definition picture

do a times of down-sampling processing, a=2,3,4,5, obtain corresponding l width training low-resolution image

again to every width training low-resolution image

do after a times of up-sampling processed and obtain corresponding training interpolation image

extract every width training interpolation image

the vertical and second order level of single order level, single order, second order VG (vertical gradient) feature, this four width Gradient Features image is carried out to overlap partition, every width training interpolation image simultaneously

after overlap partition, obtain 4*N ₁individual size is the training low resolution Gradient Features image block of z*z, obtain altogether 4*N training low resolution Gradient Features image block, every four training low resolution Gradient Features image blocks, as a training low resolution Gradient Features image block group, are converted to i training low resolution proper vector by i training low resolution Gradient Features image block group by an order being listed as

each training low resolution proper vector dimension be d ₂=4*z ², all training low resolution proper vectors

training low resolution eigenmatrix of (1≤i≤N) composition $X^s=[x_1^s,x_2^s,\·\·\·,x_N^s];$

B, pre-service:

Input low-resolution image R to be reconstructed ^d, its resolution and all training low-resolution images

the resolution of (1≤l≤L) is identical, by low-resolution image R to be reconstructed ^dcarry out after a times of up-sampling processed obtaining interpolation image R to be reconstructed ^c, extract interpolation image R to be reconstructed ^cthe vertical and second order level of single order level, single order, second order VG (vertical gradient) feature, this four width Gradient Features image is carried out obtaining altogether 4*N after overlap partition simultaneously ₂individual size is the low resolution Gradient Features image block to be reconstructed of z*z, N ₂=1000～7000, every four low resolution Gradient Features image blocks to be reconstructed, as a low resolution Gradient Features image block group to be reconstructed, are converted to j low resolution proper vector to be reconstructed by j low resolution Gradient Features image block group to be reconstructed by an order being listed as j=1,2 ..., N ₂, each low resolution proper vector to be reconstructed

dimension and all training low resolution proper vectors

the dimension of (1≤i≤N) is identical, is d ₂=4*z ², all low resolution proper vectors to be reconstructed

(1≤j≤N ₂) a low resolution eigenmatrix to be reconstructed of composition $X^t=[x_1^t,x_2^t,\·\·\·,x_{N_2}^t];$

C, super-resolution rebuilding:

C1, subcharacter matrix generate: to the low resolution proper vector each to be reconstructed obtaining in step B

(1≤j≤N ₂), the training low resolution eigenmatrix obtaining in steps A successively in find out and j low resolution proper vector to be reconstructed

between n-1=100～300 the training low resolution proper vector of Euclidean distance minimum, by j low resolution proper vector to be reconstructed

as subcharacter vector x _1j, and by the n-1 searching out a training low resolution proper vector by with j low resolution proper vector to be reconstructed

between Euclidean distance from small to large successively as subcharacter vector x _2j, x _3j..., x _nj, form thus j sub-eigenmatrix

C2, dimensionality reduction eigenmatrix generate: adopt I and II subspace projection method, by j sub-eigenmatrix carry out Feature Dimension Reduction, each subcharacter vector x _{i ' j}(1≤i '≤n) project on a low n-dimensional subspace n, obtain altogether n dimensionality reduction proper vector

each dimensionality reduction proper vector

dimension be m < d ₂; Each subcharacter vector x _{i ' j}with corresponding dimensionality reduction proper vector

form mapping relations one by one, after I and II subspace projection, dimension is d ₂subcharacter vector x _{i ' j}converting dimension to is the dimensionality reduction proper vector of m

realization character dimensionality reduction, all dimensionality reduction proper vectors (1≤i '≤n) j dimensionality reduction eigenmatrix of composition $X_j^m={\left\{x_{i^{\&prime;}j}^m\right\}}_{i^{\&prime;}=1}^n;$

C3, weight coefficient calculate: the dimensionality reduction proper vector set obtaining at step C2 in find out and dimensionality reduction proper vector

between k dimensionality reduction proper vector of Euclidean distance minimum, k=5～10, according to step C1 neutron proper vector x _{i ' j}with dimensionality reduction proper vector in step C2

between mapping relations one by one, and the call number of the k searching out a dimensionality reduction proper vector, the training that obtains in steps A is successively low, high-resolution features matrix X ^sand Y ^smiddlely find out that corresponding k is low to training, high-resolution features is vectorial, and, high-resolution features low to training by this k is vectorial forms respectively that j neighbour is low, high-resolution features matrix

with

according to j neighbour's low resolution eigenmatrix

with j low resolution proper vector to be reconstructed

calculate j similarity group

with j scale factor group

and associating

with

calculate j normalization and embed weight coefficient group

C4, reconstruction high-definition picture piece: embed weight coefficient group according to j normalization

with j neighbour's high-resolution features matrix

linear weighted function form, estimate j rebuild after high-resolution features vector

again with the brightness average of j low-resolution image piece to be reconstructed be added, and be converted to image block form, can show that j is rebuild rear high-definition picture piece;

Repeat above step C1～step C4, obtain altogether N ₂individual size is high-definition picture piece after the reconstruction of z*z, obtains the preliminary image H of super-resolution rebuilding after lap splice ₀;

D, aftertreatment:

Adopt the preliminary image H of iteration back-projection algorithms to super-resolution rebuilding ₀carry out Q iterative computation processing, Q=10～30, obtain the final image H of super-resolution rebuilding ^*.

Compared with prior art, the invention has the beneficial effects as follows:

One, the present invention adopts I and II subspace projection method by subcharacter matrix projection to lower dimensional space, obtain corresponding dimensionality reduction eigenmatrix, reduce to greatest extent the dimension of original low resolution proper vector, and more effectively represent the feature of low-resolution image piece.Therefore, the Time & Space Complexity of the inventive method reduces, and arithmetic speed improves.

Two, the directly Euclidean distance between dimensionality reduction proper vector relatively at lower dimensional space but not on original higher dimensional space of the present invention, due to the overall situation that has comprised raw data in dimensionality reduction eigenmatrix and local structural information, can find out the neighborhood piece mating the most with low-resolution image piece to be reconstructed more efficiently according to dimensionality reduction proper vector.Visible, the present invention has higher matching precision to finding neighborhood piece.

Three, the present invention utilizes the similarity between weight coefficient and two proper vectors to have approximate proportional relation, construct similarity between low resolution proper vector to be reconstructed and neighbour's low resolution proper vector and corresponding scale factor, calculate more accurate weight coefficient, be conducive to estimate high-definition picture piece.Visible, the present invention has higher estimated accuracy and stronger adaptability.

In a word, the inventive method adopts I and II subspace projection method that original high dimensional data is projected on a lower dimensional space, make the character representation of low-resolution image piece become more succinct, efficient, can search out the more neighborhood piece of coupling, and construct more accurate weight coefficient by the similarity between proper vector and scale factor, rebuild rear high-definition picture piece thereby estimate more accurately, super-resolution rebuilding better effects if, the similarity of rebuilding image and real-world object is higher, is conducive to later stage real-world object identifying processing.

In above-mentioned step C2, adopt I and II subspace projection method, by j sub-eigenmatrix

carry out obtaining j dimensionality reduction eigenmatrix after Feature Dimension Reduction specific practice be:

One-level subspace projection:

Calculate j sub-eigenmatrix j corresponding radial basis kernel matrix $K_j={\left\{K_{i^{\&prime;}{j}^{\&prime;}j}\right\}}_{i^{\&prime;}{,j}^{\&prime;}=1}^n={\left\{\exp (-{\left|\right|x_{i^{\&prime;}j}-x_{j^{\&prime;}j}\left|\right|}^2/{\mathrm{\&beta;}}_j)\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n,$ Wherein the parameter of j radial basis kernel function is

then to j radial basis kernel matrix K _jcarry out obtaining j centralization kernel matrix after centralization processing

g=I-1/n in formula, I is a unit matrix that size is n*n, 1 is that a size is n*n, and all values is 1 matrix; Solve j centralization kernel matrix descending Eigenvalues Decomposition equation

i '=1,2,3 ..., n, j=1,2,3 ..., N ₂, λ in formula _{i ' j}for the individual eigenwert of i ' by after descending sort, α _{i ' j}it is the individual eigenvalue λ of i ' _{i ' j}the corresponding individual proper vector of i '; Again to the individual proper vector α of i ' _{i ' j}carry out obtaining orthogonalization proper vector after orthogonalization process

choose front r eigenvalue of maximum λ _{i ' j}corresponding orthogonalization proper vector r=50～n, the r selecting an orthogonalization proper vector

form j one-level subspace projection matrix

front r described eigenvalue of maximum

sum accounts for all eigenwerts

the more than 99% of sum; By formula draw j one-level mapping matrix

t is matrix transpose computing, all one-level mapping vectors

(1≤i '≤dimension n) is r;

Secondary subspace projection:

Calculate j one-level mapping matrix j corresponding core distance function matrix $D_j^r={\left\{D_{i^{\&prime;}{j}^{\&prime;}j}^r\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n={\left\{\sqrt{2-2*\exp (-||x_{i^{\&prime;}j}^r-x_{j^{\&prime;}j}^r{\left|\right|}^2/{\mathrm{\&gamma;}}_j)}\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n,$ Wherein the parameter of j core distance function is then construct j adjacency matrix

as i ' ∈ Λ _{j ' j}or j ' ∈ Λ _{i ' j}time, otherwise, S _{i ' j ' j}=0, wherein Λ _{j ' j}and Λ _{i ' j}be expressed as

neighborhood tally set, the element number of neighborhood tally set is b=5～10; Calculate j adjacency matrix S _jj corresponding Laplacian Matrix F _j=diag (S _j* 1 _n)-S _j, wherein 1 _nbeing expressed as a size is n*1, and all values is 1 column vector, and diag () is expressed as diagonalization of matrix computing; Then calculate respectively j symmetric matrix $U_j=X_j^r*F_j*F_j*{\left(X_j^r\right)}^T$ With j diagonal matrix $V_j=X_j^r*\left\{\mathrm{diag}(S_j*1_n)\right\}*{\left(X_j^r\right)}^T,$ J symmetric matrix U _jwith j diagonal matrix V _jare all size matrixes for r*r, combine and solve U _jand V _jbroad sense ascending order Eigenvalues Decomposition equation

in formula for the individual eigenwert of i ' after arranging by ascending order, p _{i ' j}it is the individual eigenwert of i '

the corresponding individual proper vector of i '; Choose a front m minimal eigenvalue

characteristic of correspondence vector p _{i ' j}, m=10～r, the m a selecting proper vector

form j secondary subspace projection matrix P _j=[p _1j, p _2j..., p _mj], by formula

can draw j dimensionality reduction eigenmatrix

all dimensionality reduction proper vectors

(1≤i '≤dimension n) is m.

Adopt after above one-level subspace projection method, the global structure information that has comprised original high dimensional data in one-level mapping matrix, has retained more partial structurtes information after above secondary subspace projection in the dimensionality reduction eigenmatrix obtaining.Adopt I and II subspace projection method, dimensionality reduction eigenmatrix has not only retained the global structure information of raw data but also has retained partial structurtes information, realization character dimensionality reduction, can more effectively express the feature of low-resolution image piece, thereby makes super-resolution rebuilding become succinct and efficient.

In above-mentioned step C3, combine j similarity group

with j scale factor group calculate j normalization and embed weight coefficient group

specific practice be:

Calculate respectively j neighbour's low resolution eigenmatrix that step C3 obtains

in k training low resolution proper vector (1≤i "≤k) with j low resolution proper vector to be reconstructed

between similarity

with corresponding scale factor

wherein

with

be expressed as training low resolution proper vector

with j low resolution proper vector to be reconstructed in u brightness value, ε is 1*10 ^-4～1*10 ^-2positive number; The k calculating is to similarity

with scale factor c _{i " j}form respectively j similarity group

with j scale factor group combine j similarity group

with j scale factor group

calculate j and embed weight coefficient group

and embed weight coefficient group to j

after doing normalized, obtain j normalization embedding weight coefficient group ${\left\{{\hat{w}}_{i^{\&prime;\&prime;}j}\right\}}_{i^{\&prime;\&prime;}=1}^k={\{w_{i^{\&prime;\&prime;}j}/{\mathrm{\&Sigma;}}_{i^{\&prime;\&prime;}j}^k{w}_{i^{\&prime;\&prime;}j}\}}_{i^{\&prime;\&prime;}=1}^k.$

Construct similarity and the scale factor between low resolution proper vector to be reconstructed and the training low resolution proper vector of mating the most by above method, with they calculate more accurate weight coefficient, meet the requirement that weight coefficient and similarity become to be similar to direct ratio, can from training storehouse, get more high-frequency information, be conducive to improve the estimated accuracy of high-definition picture piece after rebuilding, thereby obtain better super-resolution rebuilding effect.

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

Accompanying drawing explanation

Training image and the test pattern of Fig. 1 (a)～Fig. 1 (f) for using in the embodiment of the present invention.

Fig. 2 (A)～Fig. 2 (E) is for adopting algorithms of different to realize the simulation experiment result of image super-resolution rebuilding.

In Fig. 2 (A)～Fig. 2 (E), intermediate rectangular block diagram is the regional area of rebuilding on image, corner block diagram is that this regional area amplifies the design sketch of 2 times, and Fig. 2 (A) is for adopting the result figure of NESR algorithm (document 1); Fig. 2 (B) is for adopting the result figure of NeedFS algorithm (document 2); Fig. 2 (C) is for adopting the result figure of CSNE algorithm (document 3); Fig. 2 (D) is for adopting the result figure of JLNE algorithm (document 4); The result figure that Fig. 2 (E) is the inventive method.

Fig. 3 is that existing four kinds of methods and the inventive method are carried out image block root-mean-square error value E after super-resolution rebuilding to (a)～(f) the six width image in Fig. 1 respectively _phistogram.

Fig. 4 is that existing four kinds of methods and the inventive method are carried out image block structural similarity value S after super-resolution rebuilding to (a)～(f) the six width image in Fig. 1 respectively _phistogram.

Embodiment

Embodiment

Based on an image super-resolution rebuilding method for subspace projection and neighborhood embedding, comprise the following steps:

A, training:

Using high-definition picture identical L width resolution, that size is identical as training high-definition picture l=1,2 ..., L, L=3～80; To every width training high-definition picture

carry out obtaining N after overlap partition ₁individual size is the training high-definition picture piece of z*z, N ₁=1000～7000, z=6,9,12,15, obtain altogether N=L*N ₁individual training high-definition picture piece, extract after the standardization brightness of each training high-definition picture piece as a training high resolving power standardization brightness image block, i training high resolving power standardization brightness image block is converted to i by an order being listed as and trains high-resolution features vector

i=1,2 ..., N, each training high-resolution features vector

dimension be d ₁=z ², all training high-resolution features vectors

(1≤i≤n) training high-resolution features matrix of composition

To l (1≤l≤L) width training high-definition picture

do a times of down-sampling processing, a=2,3,4,5, obtain corresponding l width training low-resolution image again to every width training low-resolution image do after a times of up-sampling processed and obtain corresponding training interpolation image

extract every width training interpolation image

the vertical and second order level of single order level, single order, second order VG (vertical gradient) feature, this four width Gradient Features image is carried out to overlap partition, every width training interpolation image simultaneously

after overlap partition, obtain 4*N ₁individual size is the training low resolution Gradient Features image block of z*z, obtain altogether 4*N training low resolution Gradient Features image block, every four training low resolution Gradient Features image blocks, as a training low resolution Gradient Features image block group, are converted to i training low resolution proper vector by i training low resolution Gradient Features image block group by an order being listed as

each training low resolution proper vector dimension be d ₂=4*z ², all training low resolution proper vectors

training low resolution eigenmatrix of (1≤i≤N) composition $X^s=[x_1^s,x_2^s,\&CenterDot;\&CenterDot;\&CenterDot;,x_N^s];$

B, pre-service:

Input low-resolution image R to be reconstructed ^d, its resolution and all training low-resolution images

the resolution of (1≤l≤L) is identical, by low-resolution image R to be reconstructed ^dcarry out after a times of up-sampling processed obtaining interpolation image R to be reconstructed ^c, extract interpolation image R to be reconstructed ^cthe vertical and second order level of single order level, single order, second order VG (vertical gradient) feature, this four width Gradient Features image is carried out obtaining altogether 4*N after overlap partition simultaneously ₂individual size is the low resolution Gradient Features image block to be reconstructed of z*z, N ₂=1000～7000, every four low resolution Gradient Features image blocks to be reconstructed, as a low resolution Gradient Features image block group to be reconstructed, are converted to j low resolution proper vector to be reconstructed by j low resolution Gradient Features image block group to be reconstructed by an order being listed as

j=1,2 ..., N ₂, each low resolution proper vector to be reconstructed

dimension and all training low resolution proper vectors

the dimension of (1≤i≤N) is identical, is d ₂=4*z ², all low resolution proper vectors to be reconstructed

(1≤j≤N ₂) a low resolution eigenmatrix to be reconstructed of composition $X^t=[x_1^t,x_2^t,\&CenterDot;\&CenterDot;\&CenterDot;,x_{N_2}^t];$

C, super-resolution rebuilding:

C1, subcharacter matrix generate: to the low resolution proper vector each to be reconstructed obtaining in step B (1≤j≤N ₂), the training low resolution eigenmatrix obtaining in steps A successively

in find out and j low resolution proper vector to be reconstructed

between n-1=100～300 the training low resolution proper vector of Euclidean distance minimum, by j low resolution proper vector to be reconstructed

as subcharacter vector x _1j, and by the n-1 searching out a training low resolution proper vector by with j low resolution proper vector to be reconstructed

between Euclidean distance from small to large successively as subcharacter vector x _2j, x _3j..., x _nj, form thus j sub-eigenmatrix

C2, dimensionality reduction eigenmatrix generate: adopt I and II subspace projection method, by j sub-eigenmatrix

carry out Feature Dimension Reduction, each subcharacter vector x _{i ' j}(1≤i '≤n) project on a low n-dimensional subspace n, obtain altogether n dimensionality reduction proper vector

each dimensionality reduction proper vector

dimension be m < d ₂; Each subcharacter vector x _{i ' j}with corresponding dimensionality reduction proper vector

form mapping relations one by one, after I and II subspace projection, dimension is d ₂subcharacter vector x _{i ' j}converting dimension to is the dimensionality reduction proper vector of m

realization character dimensionality reduction, all dimensionality reduction proper vectors

(1≤i '≤n) j dimensionality reduction eigenmatrix of composition $X_j^m={\left\{x_{i^{\&prime;}j}^m\right\}}_{i^{\&prime;}=1}^n;$

More than adopt I and II subspace projection method, by j sub-eigenmatrix

carry out obtaining j dimensionality reduction eigenmatrix after Feature Dimension Reduction specific practice be:

One-level subspace projection:

Calculate j sub-eigenmatrix

j corresponding radial basis kernel matrix $K_j={\left\{K_{i^{\&prime;}{j}^{\&prime;}j}\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n={\left\{\exp ({-\left|\right|x_{i^{\&prime;}j}-x_{j^{\&prime;}j}\left|\right|}^2/{\mathrm{\&beta;}}_j)\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n,$ Wherein the parameter of j radial basis kernel function is then to j radial basis kernel matrix K _jcarry out obtaining j centralization kernel matrix after centralization processing

g=I-1/n in formula, I is a unit matrix that size is n*n, 1 is that a size is n*n, and all values is 1 matrix; Solve j centralization kernel matrix

descending Eigenvalues Decomposition equation

i '=1,2,3 ..., n, j=1,2,3 ..., N ₂, λ in formula _{i ' j}for the individual eigenwert of i ' by after descending sort, α _{i ' j}it is the individual eigenvalue λ of i ' _{i ' j}the corresponding individual proper vector of i '; Again to the individual proper vector α of i ' _{i ' j}carry out obtaining orthogonalization proper vector after orthogonalization process

choose front r eigenvalue of maximum λ _{i ' j}corresponding orthogonalization proper vector

r=50～n, the r selecting an orthogonalization proper vector

form j one-level subspace projection matrix front r described eigenvalue of maximum sum accounts for all eigenwerts

the more than 99% of sum; By formula draw j one-level mapping matrix

t is matrix transpose computing, all one-level mapping vectors

(1≤i '≤dimension n) is r;

Secondary subspace projection:

Calculate j one-level mapping matrix j corresponding core distance function matrix $D_j^r={\left\{D_{i^{\&prime;}{j}^{\&prime;}j}^r\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n={\left\{\sqrt{2-2*\exp ({-\left|\right|x_{i^{\&prime;}j}^r-x_{j^{\&prime;}j}^r\left|\right|}^2/{\mathrm{\&gamma;}}_j)}\right\}}_{i^{\&prime;},j^{\&prime;}=1}^n,$ Wherein the parameter of j core distance function is

then construct j adjacency matrix

as i ' ∈ Λ _{j ' j}or j ' ∈ Λ _{i ' j}time,

otherwise, S _{i ' j ' j}=0, wherein Λ _{j ' j}and Λ _{i ' j}be expressed as

neighborhood tally set, the element number of neighborhood tally set is b=5～10; Calculate j adjacency matrix S _jj corresponding Laplacian Matrix F _j=diag (S _j* 1 _n)-S _j, wherein 1 _nbeing expressed as a size is n*1, and all values is 1 column vector, and diag () is expressed as diagonalization of matrix computing; Then calculate respectively j symmetric matrix $U_j=X_j^r*F_j*{\left(X_j^r\right)}^T$ With j diagonal matrix $V_j=X_j^r*\left\{\mathrm{diag}(S_j*1_n)\right\}*{\left(X_j^r\right)}^T,$ J symmetric matrix U _jwith j diagonal matrix V _jare all size matrixes for r*r, combine and solve U _jand V _jbroad sense ascending order Eigenvalues Decomposition equation

in formula

for the individual eigenwert of i ' after arranging by ascending order, p _{i ' j}it is the individual eigenwert of i '

the corresponding individual proper vector of i '; Choose a front m minimal eigenvalue

characteristic of correspondence vector p _{i ' j}, m=10～r, the m a selecting proper vector

form j secondary subspace projection matrix P _j=[p _1j, p _2j..., p _mj], by formula

can draw j dimensionality reduction eigenmatrix

all dimensionality reduction proper vectors

(1≤i '≤dimension n) is m;

C3, weight coefficient calculate: the dimensionality reduction proper vector set obtaining at step C2 in find out and dimensionality reduction proper vector

between k dimensionality reduction proper vector of Euclidean distance minimum, k=5～10, according to step C1 neutron proper vector x _{i ' j}with dimensionality reduction proper vector in step C2 between mapping relations one by one, and the call number of the k searching out a dimensionality reduction proper vector, the training that obtains in steps A is successively low, high-resolution features matrix X ^sand Y ^smiddlely find out that corresponding k is low to training, high-resolution features is vectorial, and, high-resolution features low to training by this k is vectorial forms respectively that j neighbour is low, high-resolution features matrix

with

according to j neighbour's low resolution eigenmatrix

with j low resolution proper vector to be reconstructed calculate j similarity group

with j scale factor group

and associating

with

calculate j normalization and embed weight coefficient group

More than combine j similarity group

with j scale factor group

calculate j normalization and embed weight coefficient group specific practice be:

Calculate respectively j neighbour's low resolution eigenmatrix that step C3 obtains

in k training low resolution proper vector

(1≤i "≤k and j low resolution proper vector to be reconstructed

between similarity

with corresponding scale factor wherein

with be expressed as training low resolution proper vector

with j low resolution proper vector to be reconstructed

in u brightness value, ε is 1*10 ^-4～1*10 ^-2positive number; The k calculating is to similarity with scale factor c _{i " j}form respectively j similarity group

with j scale factor group

combine j similarity group

with j scale factor group calculate j and embed weight coefficient group

and embed weight coefficient group to j

after doing normalized, obtain j normalization embedding weight coefficient group ${\left\{{\hat{w}}_{i^{\&prime;\&prime;}j}\right\}}_{i^{\&prime;\&prime;}=1}^k={\{w_{i^{\&prime;\&prime;}j}/{\mathrm{\&Sigma;}}_{i^{\&prime;\&prime;}=1}^k{w}_{i^{\&prime;\&prime;}j}\}}_{i^{\&prime;\&prime;}=1}^k;$

C4, reconstruction high-definition picture piece: embed weight coefficient group according to j normalization

with j neighbour's high-resolution features matrix

linear weighted function form, estimate j rebuild after high-resolution features vector

again with the brightness average of j low-resolution image piece to be reconstructed be added, and be converted to image block form, can show that j is rebuild rear high-definition picture piece;

Repeat above step C1～step C4, obtain altogether N ₂individual size is high-definition picture piece after the reconstruction of z*z, obtains the preliminary image H of super-resolution rebuilding after lap splice ₀;

D, aftertreatment:

Adopt the preliminary image H of iteration back-projection algorithms to super-resolution rebuilding ₀carry out Q iterative computation processing, Q=10～30, obtain the final image H* of super-resolution rebuilding.

Emulation experiment:

The condition of emulation experiment and design parameter are:

In Fig. 1, choose the big or small natural image for 384*510 of L=5 width as training high-definition picture, a remaining width is as test reference image, and emulation experiment has been done in rotation altogether 6 times successively.

The sampling multiple a=3 of training high-definition picture, tile size is z*z=9*9, obtains altogether N=L*N after doubling of the image piecemeal ₁=5*5440=27200 image block, the dimension of training high-resolution features vector is d ₁=z ²=9 ²=81, the dimension of training low resolution proper vector is d ₂=4*z ²=4*9 ²=324.

Image using test reference image after 3 times of down-samplings is as low-resolution image to be reconstructed, and size is 128 × 170.The interpolation image that low-resolution image to be reconstructed is carried out to obtain after 3 times of up-samplings carries out obtaining N after overlap partition ₂=5440 low-resolution image pieces to be reconstructed, the dimension of low resolution proper vector to be reconstructed is d ₂=324.All subcharacter matrix X _jvectorial number in (1≤j≤5440) is n=101, it is r=100 that one-level is shone upon vectorial dimension, in secondary subspace projection process, the element number of neighborhood tally set is b=5, the dimension of dimensionality reduction proper vector is m=22, the number of the dimensionality reduction proper vector of finding is k=9, ε=1*10 ^-3, the iterations that aftertreatment is used is Q=20.

Adopt existing four kinds of methods simultaneously, be respectively NESR algorithm (document 1), NeedFS algorithm (document 2), CSNE algorithm (document 3) and JLNE algorithm (document 4), and the inventive method is similarly being carried out super-resolution emulation reconstruction under emulation experiment condition to (a)～(f) the six width image in Fig. 1.

Subjective vision Contrast on effect result as shown in Figure 2, Fig. 2 only provide (b) in Fig. 1, (c) and (d) three width images carry out the result of emulation experiment.Fig. 2 (A)～Fig. 2 (D) is respectively the simulation experiment result of document 1～4, the simulation experiment result that Fig. 2 (E) is the inventive method.In Fig. 2 (A)～Fig. 2 (E), intermediate rectangular block diagram is the regional area of rebuilding on image, and corner block diagram is that this regional area amplifies the design sketch of 2 times.Relatively partial enlarged drawing can be found out: the reconstruction image of NESR, NeedFS and CSNE algorithm there will be fuzzy and texture aliasing, in the reconstruction image of JLNE algorithm, texture edge is level and smooth not, detailed information in the reconstruction image of the inventive method is more clear, and edge is more level and smooth.Visible, the inventive method is better than existing four kinds of methods in subjective vision effect.

In order more accurately the whole bag of tricks to be carried out to objective evaluation, below with image block root-mean-square error value E _pwith image block structural similarity value S _pas the objective indicator of evaluating the whole bag of tricks quality, wherein E _pand S _pcomputing formula as follows:

$E_p=\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}\underset{j=1}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}{\mathrm{\&Sigma;}}}\sqrt{\frac{1}{d_1}\underset{v=1}{\overset{d_1}{\mathrm{\&Sigma;}}}{(y_{\mathrm{jv}}-y_{\mathrm{jv}}^t)}^2}$

$S_p=\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}\underset{j=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\frac{({2\mathrm{\&mu;}}_{1j}{\mathrm{\&mu;}}_{2j}+{\mathrm{\&epsiv;}}_1)({2\mathrm{\&sigma;}}_{12j}+{\mathrm{\&epsiv;}}_2)}{({\mathrm{\&mu;}}_{1\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{\&mu;}}_{2\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{\&epsiv;}}_1)({\mathrm{\&sigma;}}_{1\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{\&sigma;}}_{2\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000139605970000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{\&epsiv;}}_2)}$

In the same form, y _jvfor v brightness value of j image block on original high resolution image,

for v brightness value of j image block on super-resolution rebuilding image, d ₁for the number of the contained brightness value of each image block, identical with the dimension of training high-resolution features vector, be d ₁=81, N ₂for rebuilding rear high-definition picture piece number.

In two formulas, μ _1jand μ _2jbe respectively the brightness average of j image block on original high resolution image and super-resolution rebuilding image, σ _1jand σ _2jbe respectively the standard deviation of j image block on original high resolution image and super-resolution rebuilding image, σ _12jfor the standard covariance of j image block on j image block on original high resolution image and super-resolution rebuilding image, ε ₁=6.5, ε ₂=58.5.

Fig. 3 is that existing four kinds of methods and the inventive method are carried out image block root-mean-square error value E after super-resolution rebuilding to (a)～(f) the six width image in Fig. 1 respectively _phistogram, as can be seen from this figure, 6 width of the inventive method are rebuild the image block root-mean-square error value E of images _pall, lower than existing four kinds of methods, the difference minimum of reconstruction image and the original high resolution image of the inventive method is described, reconstruction effect is best.

Fig. 4 is that existing four kinds of methods and the inventive method are carried out image block structural similarity value S after super-resolution rebuilding to (a)～(f) the six width image in Fig. 1 respectively _phistogram, as can be seen from this figure, 6 width of the inventive method are rebuild the image block structural similarity value S of images _pall, higher than existing four kinds of methods, also illustrate that the inventive method can reconstruct more high-frequency information, closer to original high resolution image.

Above the simulation experiment result shows, subjective vision effect and objective evaluation index this aspect two on, the inventive method is all better than existing four kinds of methods, has feasibility and applicability in the application of image super-resolution rebuilding.

Claims (3)

1. the image super-resolution rebuilding method based on subspace projection and neighborhood embedding, comprises the following steps:

A, training:

Using high-definition picture identical L width resolution, that size is identical as training high-definition picture

l=1,2 ..., L, L=3～80; To every width training high-definition picture

carry out obtaining N after overlap partition ₁individual size is the training high-definition picture piece of z*z, N ₁=1000～7000, z=6,9,12,15, obtain altogether N=L*N ₁individual training high-definition picture piece, extract the standardization brightness of each training high-definition picture piece as a training high resolving power standardization brightness image block, i training high resolving power standardization brightness image block is converted to i training high-resolution features vector by an order being listed as

i=1,2 ..., N, each training high-resolution features vector

dimension be d ₁=z ², all training high-resolution features vectors

form a training high-resolution features matrix

To l (1≤l≤L) width training high-definition picture

do a times of down-sampling processing, a=2,3,4,5, obtain corresponding l width training low-resolution image again to every width training low-resolution image

do after a times of up-sampling processed and obtain corresponding training interpolation image

extract every width training interpolation image the vertical and second order level of single order level, single order, second order VG (vertical gradient) feature, this four width Gradient Features image is carried out to overlap partition, every width training interpolation image simultaneously

after overlap partition, obtain 4*N ₁individual size is the training low resolution Gradient Features image block of z*z, obtain altogether 4*N training low resolution Gradient Features image block, four dissimilar Gradient Features image blocks of each training low-resolution image piece, as a training low resolution Gradient Features image block group, are converted to i training low resolution proper vector by i training low resolution Gradient Features image block group by an order being listed as

each training low resolution proper vector

dimension be d ₂=4*z ², all training low resolution proper vectors

form a training low resolution eigenmatrix $X^s=[x_1^s,x_2^s,...,x_N^s];$

B, pre-service:

Input low-resolution image R to be reconstructed ^d, its resolution and all training low-resolution images

resolution identical, by low-resolution image R to be reconstructed ^dcarry out after a times of up-sampling processed obtaining interpolation image R to be reconstructed ^c, extract interpolation image R to be reconstructed ^cthe vertical and second order level of single order level, single order, second order VG (vertical gradient) feature, this four width Gradient Features image is carried out obtaining altogether 4*N after overlap partition simultaneously ₂individual size is the low resolution Gradient Features image block to be reconstructed of z*z, N ₂=1000～7000, four dissimilar Gradient Features image blocks of each low-resolution image piece to be reconstructed, as a low resolution Gradient Features image block group to be reconstructed, are converted to j low resolution proper vector to be reconstructed by j low resolution Gradient Features image block group to be reconstructed by an order being listed as j=1,2 ..., N ₂, each low resolution proper vector to be reconstructed

dimension and all training low resolution proper vectors

dimension identical, be d ₂=4*z ², all low resolution proper vectors to be reconstructed

form a low resolution eigenmatrix to be reconstructed $X^t=[x_1^t,x_2^t,...,x_{N_2}^t];$

C, super-resolution rebuilding:

C1, subcharacter matrix generate: to the low resolution proper vector each to be reconstructed obtaining in step B

the training low resolution eigenmatrix obtaining in steps A successively

in find out and j low resolution proper vector to be reconstructed

between n-1=100～300 the training low resolution proper vector of Euclidean distance minimum, by j low resolution proper vector to be reconstructed

as subcharacter vector x _1j, and by the n-1 searching out a training low resolution proper vector by with j low resolution proper vector to be reconstructed

between Euclidean distance from small to large successively as subcharacter vector x _2j, x _3j..., x _nj, form thus j sub-eigenmatrix $X_j={\left\{x_{i\&prime;j}\right\}}_{i\&prime;=1}^n;$

C2, dimensionality reduction eigenmatrix generate: adopt I and II subspace projection method, by j sub-eigenmatrix

carry out Feature Dimension Reduction, each subcharacter vector x _{i ' j}(1≤i '≤n) project on a low n-dimensional subspace n, obtain altogether n dimensionality reduction proper vector

each dimensionality reduction proper vector dimension be m<d ₂; Each subcharacter vector x _{i ' j}with corresponding dimensionality reduction proper vector

form mapping relations one by one, after I and II subspace projection, dimension is d ₂subcharacter vector x _{i ' j}converting dimension to is the dimensionality reduction proper vector of m

realization character dimensionality reduction, all dimensionality reduction proper vectors

form j dimensionality reduction eigenmatrix $X_j^m={\left\{x_{i\&prime;j}^m\right\}}_{i\&prime;=1}^n;$

C3, weight coefficient calculate: the dimensionality reduction proper vector set obtaining at step C2

in find out and dimensionality reduction proper vector

between k dimensionality reduction proper vector of Euclidean distance minimum, k=5～10, according to step C1 neutron proper vector x _{i ' j}with dimensionality reduction proper vector in step C2

between mapping relations one by one, and the call number of the k searching out a dimensionality reduction proper vector, the training that obtains in steps A is successively low, high-resolution features matrix X ^sand Y ^smiddlely find out that corresponding k is low to training, high-resolution features is vectorial, and, high-resolution features low to training by this k is vectorial forms respectively that j neighbour is low, high-resolution features matrix $X_j^f={\left\{x_{i\&Prime;j}^f\right\}}_{i\&Prime;=1}^k$ With $Y_j^f={\left\{y_{i\&Prime;j}^f\right\}}_{i\&Prime;=1}^k;$ According to j neighbour's low resolution eigenmatrix $X_j^f={\left\{x_{i\&Prime;j}^f\right\}}_{i\&Prime;=1}^k$ With j low resolution proper vector to be reconstructed

calculate j similarity group

with j scale factor group

and associating with

calculate j normalization and embed weight coefficient group

C4, reconstruction high-definition picture piece: embed weight coefficient group according to j normalization

with j neighbour's high-resolution features matrix

linear weighted function form, estimate j rebuild after high-resolution features vector

again with the brightness average of j low-resolution image piece to be reconstructed

be added, and be converted to image block form, can show that j is rebuild rear high-definition picture piece;

Repeat above step C1～step C4, obtain altogether N ₂individual size is high-definition picture piece after the reconstruction of z*z, obtains the preliminary image H of super-resolution rebuilding after lap splice ₀;

D, aftertreatment:

Adopt the preliminary image H of iteration back-projection algorithms to super-resolution rebuilding ₀carry out Q iterative computation processing, Q=10～30, obtain the final image H of super-resolution rebuilding ^*.

2. image super-resolution rebuilding method according to claim 1, is characterized in that, adopts I and II subspace projection method in described step C2, by j sub-eigenmatrix carry out obtaining j dimensionality reduction eigenmatrix after Feature Dimension Reduction

specific practice be:

One-level subspace projection:

Calculate j sub-eigenmatrix

j corresponding radial basis kernel matrix $K_j={\left\{K_{i\&prime;j\&prime;j}\right\}}_{i\&prime;,j\&prime;=1}^n={\left\{\exp (-{\left|\right|x_{i\&prime;j}-x_{j\&prime;j}\left|\right|}^2/{\mathrm{\&beta;}}_j)\right\}}_{i\&prime;,j\&prime;=1}^n,$ Wherein the parameter of j radial basis kernel function is ${\mathrm{\&beta;}}_j={\left({\mathrm{\&Sigma;}}_{i\&prime;,j\&prime;=1}^n\right||x_{i\&prime;j}-x_{j\&prime;j}||/n^2)}^2;$ Then to j radial basis kernel matrix K _jcarry out obtaining j centralization kernel matrix after centralization processing

g=I-1/n in formula, I is a unit matrix that size is n*n, 1 is that a size is n*n, and all values is 1 matrix; Solve j centralization kernel matrix descending Eigenvalues Decomposition equation

i '=1,2,3 ..., n, j=1,2,3 ..., N ₂, λ in formula _{i ' j}for the individual eigenwert of i ' by after descending sort, α _{i ' j}it is the individual eigenvalue λ of i ' _{i ' j}the corresponding individual proper vector of i '; Again to the individual proper vector α of i ' _{i ' j}carry out obtaining orthogonalization proper vector after orthogonalization process

choose front r eigenvalue of maximum λ _{i ' j}corresponding orthogonalization proper vector

r=50～n, the r selecting an orthogonalization proper vector

form j one-level subspace projection matrix $A_j=[{\widehat{\mathrm{\&alpha;}}}_{1j},{\widehat{\mathrm{\&alpha;}}}_{2j},...,{\widehat{\mathrm{\&alpha;}}}_{\mathrm{rj}}],$ Front r described eigenvalue of maximum

sum accounts for all eigenwerts the more than 99% of sum; By formula

draw j one-level mapping matrix

t is matrix transpose computing, all one-level mapping vectors

dimension be r;

Secondary subspace projection:

Calculate j one-level mapping matrix

j corresponding core distance function matrix $D_j^r={\left\{D_{i\&prime;j\&prime;j}^r\right\}}_{i\&prime;,j\&prime;=1}^n={\left\{\sqrt{2-2*\exp (-{\left|\right|x_{i\&prime;j}^r-x_{j\&prime;j}^r\left|\right|}^2/{\mathrm{\&gamma;}}_j)}\right\}}_{i\&prime;,j\&prime;=1}^n,$ Wherein the parameter of j core distance function is ${\mathrm{\&gamma;}}_j={\left({\mathrm{\&Sigma;}}_{i\&prime;,j\&prime;=1}^n\right||x_{i\&prime;j}^r-x_{j\&prime;j}^r||/n^2)}^2;$ Then construct j adjacency matrix $S_j={\left\{S_{i\&prime;j\&prime;j}\right\}}_{i\&prime;,j\&prime;=1}^n,$ As i ' ∈ Λ _{j ' j}or j ' ∈ Λ _{i ' j}time, $S_{i\&prime;j\&prime;j}=1-D_{i\&prime;j\&prime;j}^r;$ Otherwise, S _{i ' j ' j}=0, wherein Λ _{j ' j}and Λ _{i ' j}be expressed as

neighborhood tally set, the element number of neighborhood tally set is b=5～10; Calculate j adjacency matrix S _jj corresponding Laplacian Matrix F _j=diag (S _j* 1 _n)-S _j, wherein 1 _nbeing expressed as a size is n*1, and all values is 1 column vector, and diag () is expressed as diagonalization of matrix computing; Then calculate respectively j symmetric matrix $U_j=X_j^r*F_j*{\left(X_j^r\right)}^T$ With j diagonal matrix $V_j=X_j^r*\left\{\mathrm{diag}(S_j*1_n)\right\}*{\left(X_j^r\right)}^T,$ J symmetric matrix U _jwith j diagonal matrix V _jare all size matrixes for r*r, combine and solve U _jand V _jbroad sense ascending order Eigenvalues Decomposition equation

in formula

for the individual eigenwert of i ' after arranging by ascending order, p _{i ' j}it is the individual eigenwert of i '

the corresponding individual proper vector of i '; Choose a front m minimal eigenvalue

characteristic of correspondence vector p _{i ' j}, m=10～r, the m a selecting proper vector

form j secondary subspace projection matrix P _j=[p _1j, p _2j..., p _mj], by formula can draw j dimensionality reduction eigenmatrix

all dimensionality reduction proper vectors

dimension be m.

3. image super-resolution rebuilding method according to claim 1, is characterized in that, combines j similarity group in described step C3

with j scale factor group

calculate j normalization and embed weight coefficient group

specific practice be:

Calculate respectively j neighbour's low resolution eigenmatrix that step C3 obtains

in k training low resolution proper vector

with j low resolution proper vector to be reconstructed

between similarity $K_{i\&Prime;j}^f=\exp (-{\left|\right|x_{i\&Prime;j}^f-x_j^t\left|\right|}^2/{\mathrm{\&beta;}}_j)$ With corresponding scale factor $c_{i\&Prime;j}={\left({\mathrm{\&Sigma;}}_{u=1}^{d_2}\right|x_{i\&Prime;\mathrm{ju}}^f-x_{\mathrm{ju}}^t|+\mathrm{\&epsiv;})}^{-1},$ Wherein

with

be expressed as training low resolution proper vector

with j low resolution proper vector to be reconstructed

in u brightness value, ε is 1*10 ^-4～1*10 ^-2positive number; The k calculating is to similarity

with scale factor c _{i ' ' j}form respectively j similarity group with j scale factor group combine j similarity group

with j scale factor group calculate j and embed weight coefficient group

and embed weight coefficient group to j

after doing normalized, obtain j normalization embedding weight coefficient group ${\left\{{\hat{w}}_{i\&Prime;j}\right\}}_{i\&Prime;=1}^k={\{w_{i\&Prime;j}/{\mathrm{\&Sigma;}}_{i\&Prime;=1}^k{w}_{i\&Prime;j}\}}_{i\&Prime;=1}^k.$

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