CN103020935B - The image super-resolution method of the online dictionary learning of a kind of self-adaptation - Google Patents

Abstract

The invention discloses the image super-resolution method of the online dictionary learning of a kind of self-adaptation, first selected one group of high resolving power and low resolution training plan image set, then on high/low training plan image set, a kind of corresponding relation is set up, provide more prior imformation by high/low resolution dictionary to for reconstructed image, under high amplification factor, also can obtain good quality reconstruction; Present invention uses SP sparse coding algorithm simultaneously, overcome the shortcoming that conventional greedy algorithm reconstruct degree of accuracy is not high, maintain lower computation complexity simultaneously; Advantage has taken the slow shortcoming of (as MOD, K-SVD etc.) calculation of complex in main flow dictionary learning algorithm instantly, training speed, shorten image reconstruction time on the whole, with existing based on learning compared with image super-resolution technology, the method that the present invention proposes has higher reconstruction accuracy and shorter algorithm time.

Description

The image super-resolution method of the online dictionary learning of a kind of self-adaptation

Technical field

The present invention relates to the image super-resolution technology in signal transacting and multimedia-data procession field, especially relate to the image super-resolution method of the online dictionary learning of a kind of self-adaptation.

Background technology

Image super-resolution (super resolution, SR) refers to that single width or several low-resolution images revert to the process of high resolving power (high resolution, HR) image.Along with image is in the increasingly extensive application of all trades and professions, the requirement of people to image resolution ratio is also more and more higher, because HR image means that image has high pixel density, more details can be provided for people, and these details often play a key effect in image practical application.Current image super-resolution technology has all achieved in fields such as medical imaging, remote sensing detecting, public safeties and has applied widely, and even in some image applications field, the resolution of image has become the important indicator weighing picture quality.Therefore further investigate image super-resolution technology, there is very important practical significance.

Obtain the most direct method of high-definition picture and use high-resolution image sensors exactly, but the making of high-resolution image sensors is often subject to the restriction of technological level and cost, therefore, under the prerequisite not changing sensor, the method for software is used to go the resolution improving image to become the popular research direction in computer vision field.Image super-resolution technology can be divided into three main category: based on interpolation, based on rebuild and based on study method, wherein based on Model Reconstruction and based on study method be research direction main in recent years.The mapping model of a low-resolution image to high-definition picture is mainly built based on the method for rebuilding, reconstruct efficiency is higher, but be difficult to find the mapping model that is unified, and reconstructed image quality sharply can decline when the image super-resolution reconstruct carrying out high amplification factor.And reconstruct accurate, robustness advantages of higher based on the method for study because having, be current most popular image super-resolution technology.

Super-resolution algorithms thought based on study is proposed in 2002 by people such as Freeman the earliest, they utilize markov network to learn the relation between high and low frequency information, compared to before based on interpolation and based on rebuild method, this method of sample learning that utilizes can obtain more high-frequency information, solves because prior imformation providing capability is not enough and rebuilds the serious problem of image fault under causing high amplification factor.But the shortcoming of this method is also obvious, is exactly to require higher to the selection of training sample, and very responsive to the noise in image.The people such as Chang proposes the image super-resolution method embedded based on neighborhood subsequently, and the basic thought of this kind of method is that high-low resolution image block corresponding to hypothesis can form the stream shape with identical local geometry at their feature space.This algorithm needs less sample relatively, and has good noiseproof feature.But algorithm Problems existing is high-low resolution image block, and the more difficult neighborhood of setting up when neighborhood embeds keeps relation, in order to improve this problem, has occurred based on the training sample selection algorithm of Histogram Matching with based on methods such as local residual error embeddings.The people such as Karl propose to use support vector regression (SVR) to realize image super-resolution, and SVR, by the automatic selection to sample, employs less training set, but the contrast of image is declined relatively.2010, the people such as Yang are under compressed sensing (CS) framework, sparse representation theory is adopted to propose a kind of image super-resolution reconstructing method based on study, they learn one group of rarefaction representation base from the low resolution training image of one group of high-definition picture and correspondence thereof, this group set of bases forms a complete dictionary of mistake, make each image block in training set can cross complete dictionary rarefaction representation by this by linear programming, subsequently in super-resolution image reconstruction process, first obtain original low-resolution image and cross the rarefaction representation coefficient under complete dictionary, then high-definition picture is reconstructed with this group rarefaction representation coefficient weighting.This algorithm initiative CS theory is used for image super-resolution technology, overcome the select permeability for Size of Neighborhood in neighborhood embedding grammar, namely when solving rarefaction representation, without the need to specifying the number of the required base of reconstruct, it represents that coefficient and base number are obtained by linear programming for solution simultaneously.But this algorithm exists, and training sample is excessive, dictionary is too complicated to process of establishing, dictionary selects not have the defects such as adaptivity.In the same year, Pu sword etc. proposes again the algorithm employing BP sparse coding and K-SVD dictionary updating in dictionary learning, achieves than the former better super-resolution efect; But this algorithm still also exists the defects such as training sample time length.

Summary of the invention

It is short that technical matters to be solved by this invention is to provide a kind of training sample time, the image super-resolution method of the online dictionary learning of the self-adaptation that picture quality is high.

The present invention solves the problems of the technologies described above adopted technical scheme: the image super-resolution method of the online dictionary learning of a kind of self-adaptation, comprises the following steps:

1. one group of low-resolution image of one group of high-definition picture and correspondence thereof is chosen as training sample;

2. the high-frequency characteristic of training sample is extracted, obtain one group of low resolution sample characteristics image of one group of high resolving power sample characteristics image and its correspondence, Q the high resolving power sample characteristics image fritter randomly drawed in high resolving power sample characteristics image forms matrix M, extract low resolution characteristic image fritter corresponding with the high resolving power sample characteristics image fritter extracted in low resolution sample characteristics image form matrix M ', wherein Q is more than or equal to 30,000 and is less than or equal to 100,000, by matrix M and matrix M ' be divided into k class, wherein k>=2, obtain matrix M ' k cluster centre m ₁, m ₂, m ₃..., m _kand initial sub-dictionary set { (D _l1, D _h1), (D _l2, D _h2), (D _l3, D _h3) ..., (D _lk, D _hk), wherein D _l1, D _l2, D _l3..., D _lkrepresent k the sub-dictionary of initial low resolution, D _h1, D _h2, D _h3..., D _hkrepresent k the sub-dictionary of initial high resolution,

3. utilize on-line Algorithm to be optimized initial sub-dictionary set, obtain sub-the dictionary set { (D of optimal objective _l1-best, D _h1-best), (D _l2-best, D _h2-best), (D _l3-best, D _h3-best) ..., (D _lk-best, D _hk-best), wherein D _l1-best, D _l2-best, D _l3-best..., D _lk-bestrepresent k the sub-dictionary of optimum low resolution target, D _h1-best, D _h2-best, D _h3-best..., D _hk-bestrepresent k the sub-dictionary of optimum high resolving power target;

4. input needs the low-resolution image X carrying out super-resolution amplification, extracts the high-frequency characteristic of low-resolution image X, obtains the low resolution characteristic image X' that low-resolution image X is corresponding, then choose q the image fritter X of low resolution characteristic image X' _q, q>=1, image fritter X _qcorresponding matrix is designated as x _q, compute matrix x respectively _qwith cluster centre m ₁, m ₂, m ₃..., m _keuclidean distance, compare x _qwith the size of the Euclidean distance of each cluster centre, obtain the cluster centre m that Euclidean distance is minimum _n, 1≤n≤k, selects with m _nthe sub-dictionary of optimum low resolution target that the sub-dictionary of initial low resolution for cluster centre is corresponding, is denoted as D _lq-best;

5. SP algorithm compute matrix x is utilized _qat D _lq-bestunder rarefaction representation factor alpha _q, α _q=argmin||x _q-D _lq-bestα _q|| ₂+ λ || α _q|| ₁, α _q=SP (D _lq-best, x _q), λ represents regularization coefficient and 0< λ <1, and concrete steps are as follows:

5.-1 by D _lq-bestin with matrix x _qthe row index of the K row atom that correlativity is maximum is designated as represent D _lp-bestin row number be former molecular matrix, representing matrix x _q? on projection, ${\hat{x}}_q=D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{\&prime;}{x}_q,$ Wherein $D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{\&prime;}={\left(D_{\mathrm{lq}-\mathrm{best}-{\tilde{T}}_0}^{*}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}\right)}^{-1}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{*},$ * the transposition of representing matrix;

5.-2 initialization: definition original state projection initial residual vector be r ₀, x' under original state _qthe row index of K sequence atom corresponding to middle element maximal value is designated as I ₀, $r_0=\mathrm{resid}(x_q,D_{\mathrm{lq}-\mathrm{best}-I_0})=x_q-{\hat{x}}_q,$ represent D _lp-bestin row number be I ₀former molecular matrix;

5.-3 set current iteration number of times as ω, ω>=1, project in current iteration residual vector be r _ω, order $x_q^{\&prime;}=D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{\&prime;}{x}_q,$ $D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{\&prime;}={\left(D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{*}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}\right)}^{-1}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{*},$ X ' in current iteration _pthe row index of K sequence atom corresponding to middle element maximal value is I _ω, in conjunction with formula { D _lq-bestin with r _ω-1the row index of the K row atom that correlativity is maximum } and upgrade r _ω, and I _ω, r _ω-1represent projection residual vector in ω-1 iteration, represent in row number be I _ωformer molecular matrix, represent D _lp-bestin row number be former molecular matrix;

5.-4 compare r _ωwith r _ω-1if, || r _ω|| ₂>||r _ω-1|| ₂, then iteration terminates, otherwise, 5. carry out iteration renewal in-3 using returning step as current iteration number of times after ω adds 1;

5., after-5 iteration complete, least square method is used to try to achieve x _qat dictionary D _lq-bestoptimum rarefaction representation factor alpha _q;

6. select and D _lq-bestthe corresponding sub-dictionary D of high resolving power target _hq-best, utilize rarefaction representation factor alpha _qand D _hq-bestsolve x _qat D _hq-besthigh-definition picture reconstruct fritter y under corresponding _q=D _hq-bestα _q;

7. according to step 4. ~ method 6., process by all image fritters of " it " font to low resolution characteristic image X', obtain initial high-resolution reconstruction image

8. to high-resolution reconstruction image carry out block process and obtain final high-resolution reconstruction image Y.

The concrete steps that 3. described step is optimized initial sub-dictionary set are as follows:

3.-1 couple of sub-dictionary D of low resolution _l1be optimized, concrete steps are:

A, suppose that the total iterations optimized is T, in the t time iteration, input any one the characteristic image block f in low resolution sample characteristics image _l, 1≤t≤T;

B, fix the sub-dictionary of target that t-1 iteration obtains subspace back tracking method is used to solve λ represents regularization coefficient and 0< λ <1, and wherein, argmin represents the minimum value solving functional, || || represent and solve norm, obtain characteristic image block f in the t time iteration _lat the sub-dictionary of target under sparse decomposition coefficients Λ _t;

C, fixing sparse decomposition coefficients Λ _tif, the sub-dictionary D of low resolution _l1there is p atom, order $A_t=[a_1,a_2,...,a_j,...,a_p]=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&Lambda;}}_i{\mathrm{\&Lambda;}}_i^T,B_t=[b_1,b_2,...,b_j,...,b_p]=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{f}_l{\mathrm{\&Lambda;}}_i^T,$ I=1,2 ... t, a _jrepresent A _tmiddle jth row, b _jrepresent B _tmiddle jth row, a _jand b _jbe the matrix of p × 1,1≤j≤p;

D, establish the sub-dictionary D of low resolution _l1a jth atom of the corresponding sub-dictionary of target is d _j, to d _jbe optimized, then $d_j=\frac{1}{\max ({\left|\right|u_j\left|\right|}_2,1)}{u}_j,u_j=\frac{1}{A_{\mathrm{jj}}}(b_j-D_{{l1}_{t-j}}^{\&prime;}{a}_j)+d_j,$ represent the sub-dictionary D of low resolution _l1the sub-dictionary of the target upgraded, A _jjrepresent a _jthe value of middle jth row, max represents the maximal value of solved function;

E, upgrade low resolution sub-dictionary D according to steps d _l1p atom, complete the t time iteration, obtain the sub-dictionary D of low resolution _l1the sub-dictionary of target after the t time iteration

F, general substitute into formula $D_{{l1}_t}=\arg \min \frac{1}{t}\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}(\frac{1}{2}{\left|\right|f_l-D_{{l1}_t}^{\text{\&prime;}}{\mathrm{\&Lambda;}}_i\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|{\mathrm{\&Lambda;}}_i\left|\right|}_1),$ 0< λ <1, obtains the sub-dictionary of target that the t time circulation upgrades

G, the rest may be inferred, and completing input picture is characteristic image block f _ltime, the sub-dictionary D of low resolution _l1t iteration, obtain characteristic image block f _lthe sub-dictionary of target of corresponding optimization

Except f in h, successively input low resolution sample characteristics image _lother all characteristic image blocks in addition, the principle identical according to step a ~ g is trained, and completes the sub-dictionary D of initial low resolution _l1training, last is taken turns the sub-dictionary of updated target as the sub-dictionary D of initial low resolution _l1the sub-dictionary D of optimal objective _l1-best;

3.-2 use the sub-dictionary D of low resolution _l1the same principle be optimized is respectively to D _l2, D _l3..., D _lk, D _h1, D _h2, D _h3..., D _hkbe optimized, obtain D _l2, D _l3..., D _lk, D _h1, D _h2, D _h3..., D _hkthe corresponding sub-dictionary of optimal objective, finally obtains sub-the dictionary set { (D of optimal objective _l1-best, D _h1-best), (D _l2-best, D _h2-best), (D _l3-best, D _h3-best) ..., (D _lk-best, D _hk-best).

Described step 8. in go block disposal route to be get average to the pixel of lap after each iteration.

Compared with prior art, the invention has the advantages that and overcome traditional images super-resolution problem such as reconstruction quality decline and algorithm time length under high amplification factor well:

1) compare with the image super-resolution technology based on model based on interpolation with existing, the method that the present invention proposes overcomes the former can not provide the defect that maybe can not provide enough prior imformations, first selected one group of high resolving power and low resolution training plan image set, then on high/low training plan image set, a kind of corresponding relation is set up, provide more prior imformation by high/low resolution dictionary to for reconstructed image, under high amplification factor, also can obtain good quality reconstruction;

2) with existing based on learning compared with image super-resolution technology, the method that the present invention proposes has higher reconstruction accuracy and shorter algorithm time, present invention uses SP sparse coding algorithm, overcome the shortcoming that conventional greedy algorithm reconstruct degree of accuracy is not high, maintain lower computation complexity simultaneously; And online dictionary learning algorithm, overcome the shortcoming that (as MOD, K-SVD etc.) calculation of complex in main flow dictionary learning algorithm instantly, training speed are slow, therefore further shorten image reconstruction time on the whole.

Accompanying drawing explanation

The process flow diagram of Fig. 1 the inventive method;

Fig. 2 (a) original high resolution cloud atlas image;

The cloud atlas image that Fig. 2 (b) adopts bilinear interpolation method to reconstruct;

The cloud atlas image that Fig. 2 (c) adopts Yang method to reconstruct;

The cloud atlas image that Fig. 2 (d) adopts the inventive method to reconstruct;

Fig. 3 (a) original high resolution Cat image;

The Cat image that Fig. 3 (b) adopts bilinear interpolation method to reconstruct;

The Cat image that Fig. 3 (c) adopts Yang method to reconstruct;

The Cat image that Fig. 3 (d) adopts the inventive method to reconstruct;

Fig. 4 (a) original high resolution Building image;

The Building image that Fig. 4 (b) adopts bilinear interpolation method to reconstruct;

The Building image that Fig. 4 (c) adopts Yang method to reconstruct;

The Building image that Fig. 4 (d) adopts the inventive method to reconstruct.

Embodiment

Below in conjunction with accompanying drawing embodiment, the present invention is described in further detail.

As shown in Figure 1, the image super-resolution method of the online dictionary learning of a kind of self-adaptation, is characterized in that comprising the following steps:

1. one group of low-resolution image of one group of high-definition picture and correspondence thereof is chosen as training sample;

2. the high-frequency characteristic of training sample is extracted, obtain one group of low resolution sample characteristics image of one group of high resolving power sample characteristics image and its correspondence, Q the high resolving power sample characteristics image fritter randomly drawed in high resolving power sample characteristics image forms matrix M, extract low resolution characteristic image fritter corresponding with the high resolving power sample characteristics image fritter extracted in low resolution sample characteristics image form matrix M ', wherein Q is more than or equal to 30,000 and is less than or equal to 100,000, by matrix M and matrix M ' be divided into k class, wherein k>=2, obtain matrix M ' k cluster centre m ₁, m ₂, m ₃..., m _kand initial sub-dictionary set { (D _l1, D _h1), (D _l2, D _h2), (D _l3, D _h3) ..., (D _lk, D _hk), wherein D _l1, D _l2, D _l3..., D _lkrepresent k the sub-dictionary of initial low resolution, D _h1, D _h2, D _h3..., D _hkrepresent k the sub-dictionary of initial high resolution,

3. utilize on-line Algorithm to be optimized initial sub-dictionary set, obtain sub-the dictionary set { (D of optimal objective _l1-best, D _h1-best), (D _l2-best, D _h2-best), (D _l3-best, D _h3-best) ..., (D _lk-best, D _hk-best), wherein D _l1-best, D _l2-best, D _l3-best..., D _lk-bestrepresent k the sub-dictionary of optimum low resolution target, D _h1-best, D _h2-best, D _h3-best..., D _hk-bestrepresent k the sub-dictionary of optimum high resolving power target; Concrete steps are as follows:

3.-1 couple of sub-dictionary D of low resolution _l1be optimized, concrete steps are:

A, suppose that the total iterations optimized is T, in the t time iteration, input any one the characteristic image block f in low resolution sample characteristics image _l, 1≤t≤T;

B, fix the sub-dictionary of target that t-1 iteration obtains subspace back tracking method is used to solve λ represents regularization coefficient and 0< λ <1, and wherein, argmin represents the minimum value solving functional, || || represent and solve norm, obtain characteristic image block f in the t time iteration _lat the sub-dictionary of target under sparse decomposition coefficients Λ _t;

C, fixing sparse decomposition coefficients Λ _tif, the sub-dictionary D of low resolution _l1there is p atom, order $A_t=[a_1,a_2,...,a_j,...,a_p]=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&Lambda;}}_i{\mathrm{\&Lambda;}}_i^T,B_t=[b_1,b_2,...,b_j,...,b_p]=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{f}_l{\mathrm{\&Lambda;}}_i^T,$ I=1,2 ... t, a _jrepresent A _tmiddle jth row, b _jrepresent B _tmiddle jth row, a _jand b _jbe the matrix of p × 1,1≤j≤p;

D, establish the sub-dictionary D of low resolution _l1a jth atom of the corresponding sub-dictionary of target is d _j, to d _jbe optimized, then $d_j=\frac{1}{\max ({\left|\right|u_j\left|\right|}_2,1)}{u}_j,u_j=\frac{1}{A_{\mathrm{jj}}}(b_j-D_{{l1}_{t-j}}^{\&prime;}{a}_j)+d_j,$ represent the sub-dictionary D of low resolution _l1the sub-dictionary of the target upgraded, A _jjrepresent a _jthe value of middle jth row, max represents the maximal value of solved function;

E, upgrade low resolution sub-dictionary D according to steps d _l1p atom, complete the t time iteration, obtain the sub-dictionary D of low resolution _l1the sub-dictionary of target after the t time iteration

F, general substitute into formula $D_{{l1}_t}=\arg \min \frac{1}{t}\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}(\frac{1}{2}{\left|\right|f_l-D_{{l1}_t}^{\text{\&prime;}}{\mathrm{\&Lambda;}}_i\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|{\mathrm{\&Lambda;}}_i\left|\right|}_1),$ 0< λ <1, obtains the sub-dictionary of target that the t time circulation upgrades

G, the rest may be inferred, and completing input picture is characteristic image block f _ltime, the sub-dictionary D of low resolution _l1t iteration, obtain characteristic image block f _lthe sub-dictionary of target of corresponding optimization

Except f in h, successively input low resolution sample characteristics image _lother all characteristic image blocks in addition, the principle identical according to step a ~ g is trained, and completes the sub-dictionary D of initial low resolution _l1training, last is taken turns the sub-dictionary of updated target as the sub-dictionary D of initial low resolution _l1the sub-dictionary D of optimal objective _l1-best;

3.-2 use the sub-dictionary D of low resolution _l1the same principle be optimized is respectively to D _l2, D _l3..., D _lk, D _h1, D _h2, D _h3..., D _hkbe optimized, obtain D _l2, D _l3..., D _lk, D _h1, D _h2, D _h3..., D _hkthe corresponding sub-dictionary of optimal objective, finally obtains sub-the dictionary set { (D of optimal objective _l1-best, D _h1-best), (D _l2-best, D _h2-best), (D _l3-best, D _h3-best) ..., (D _lk-best, D _hk-best);

4. input needs the low-resolution image X carrying out super-resolution amplification, extracts the high-frequency characteristic of low-resolution image X, obtains the low resolution characteristic image X' that low-resolution image X is corresponding, then choose q the image fritter X of low resolution characteristic image X' _q, q>=1, image fritter X _qcorresponding matrix is designated as x _q, compute matrix x respectively _qwith cluster centre m ₁, m ₂, m ₃..., m _keuclidean distance, compare x _qwith the size of the Euclidean distance of each cluster centre, obtain the cluster centre m that Euclidean distance is minimum _n, 1≤n≤k, selects with m _nthe sub-dictionary of optimum low resolution target that the sub-dictionary of initial low resolution for cluster centre is corresponding, is denoted as D _lq-best;

5. SP algorithm compute matrix x is utilized _qat D _lq-bestunder rarefaction representation factor alpha _q, α _q=argmin||x _q-D _lq-bestα _q|| ₂+ λ || α _q|| ₁, α _q=SP (D _lq-best, x _q), λ represents regularization coefficient and 0< λ <1, and concrete steps are as follows:

5.-1 by D _lq-bestin with matrix x _qthe row index of the K row atom that correlativity is maximum is designated as represent D _lp-bestin row number be former molecular matrix, representing matrix x _q? on projection, ${\hat{x}}_q=D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{\&prime;}{x}_q,$ Wherein $D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{\&prime;}={\left(D_{\mathrm{lq}-\mathrm{best}-{\tilde{T}}_0}^{*}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}\right)}^{-1}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{*},$ * the transposition of representing matrix;

5.-2 initialization: definition original state projection initial residual vector be r ₀, x' under original state _qthe row index of K sequence atom corresponding to middle element maximal value is designated as I ₀, $r_0=\mathrm{resid}(x_q,D_{\mathrm{lq}-\mathrm{best}-I_0})=x_q-{\hat{x}}_q,$ represent D _lp-bestin row number be I ₀former molecular matrix;

5.-3 set current iteration number of times as ω, ω>=1, project in current iteration residual vector be r _ω, order $x_q^{\&prime;}=D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{\&prime;}{x}_q,$ $D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{\&prime;}={\left(D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{*}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}\right)}^{-1}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{*},$ X ' in current iteration _pthe row index of K sequence atom corresponding to middle element maximal value is I _ω, in conjunction with formula { D _lq-bestin with r _ω-1the row index of the K row atom that correlativity is maximum } and upgrade r _ω, and I _ω, r _ω-1represent projection residual vector in ω-1 iteration, represent in row number be I _ωformer molecular matrix, represent D _lp-bestin row number be former molecular matrix;

5.-4 compare r _ωwith r _ω-1if, || r _ω|| ₂>||r _ω-1|| ₂, then iteration terminates, otherwise, 5. carry out iteration renewal in-3 using returning step as current iteration number of times after ω adds 1;

5., after-5 iteration complete, least square method is used to try to achieve x _qat dictionary D _lq-bestoptimum rarefaction representation factor alpha _q;

6. select and D _lq-bestthe corresponding sub-dictionary D of high resolving power target _hq-best, utilize rarefaction representation factor alpha _qand D _hq-bestsolve x _qat D _hq-besthigh-definition picture reconstruct fritter y under corresponding _q=D _hq-bestα _q;

7. according to step 4. ~ method 6., process by all image fritters of " it " font to low resolution characteristic image X', obtain initial high-resolution reconstruction image ;

8. to high-resolution reconstruction image carry out block process and obtain final high-resolution reconstruction image Y, wherein go block disposal route to be get average to the pixel of lap after each iteration.

The validity of simulating, verifying method of the present invention by experiment.Experiment simulation carries out on Matlab7.0 platform.Select three 512 × 512 high resolution gray images as original image in experiment altogether, be respectively the original high resolution remote sensing satellite cloud atlas shown in Fig. 2 (a), the original high resolution Cat image shown in Fig. 3 (a) and the original high resolution Building image shown in Fig. 4 (a).First to three width original images by four times of down-samplings, fuzzy and add process of making an uproar and obtain corresponding low-resolution image, then four times of super-resolution amplifying and reconfigurations are made respectively by the low-resolution image that bilinear interpolation method, Yang method and the inventive method are corresponding to three width original images, image reconstruction quality and algorithm time are compared, draws simulation result.Extract 50,000 characteristic image fritters respectively in high resolving power sample characteristics image and low resolution sample characteristics image and form initial dictionary, namely Q equals 50,000, and Image Reconstruction chooses 3 × 3 image blocks, and lap is 1 pixel.Wherein, adopt the cloud atlas image of bilinear interpolation method reconstruct as shown in Fig. 2 (b); Adopt the cloud atlas image of Yang method reconstruct as shown in Fig. 2 (c); Adopt the cloud atlas image of the inventive method reconstruct as shown in Fig. 2 (d); Adopt the Cat image of bilinear interpolation method reconstruct as shown in Fig. 3 (b); Adopt the Cat image of Yang method reconstruct as shown in Fig. 3 (c); Adopt the Cat image of the inventive method reconstruct as shown in Fig. 3 (d); Adopt the Building image of bilinear interpolation method reconstruct as shown in Fig. 4 (b); Adopt the Building image of Yang method reconstruct as shown in Fig. 4 (c); Shown in Building image graph Fig. 4 (d) adopting the inventive method to reconstruct.Reconstructed image quality adopts to be passed judgment on the Y-PSNR (PSNR) of former full resolution pricture:

$\mathrm{PSNR}=-10\&times;\log 10\left(\frac{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(f(i,j)-f^{\&prime;}(i,j))}^2}{M\&times;N\&times;f_{\max }^2}\right)---\left(1\right)$

In formula (1), f (i, j) represents the i-th row and the j row pixel of original high-resolution image, f'(i, j) represent degrade after the i-th row of super-resolution reconstruction image and j row pixel, f _maxrepresent image max pixel value, M × N is image size.Institute the methodical time with second (s) for unit.Three width image simulation data results are as shown in Table 1 and Table 2:

The lower three width reconstructed image PSNR (dB) of table 1 distinct methods

Table 2 Yang method and the inventive method required time (sample training time+reconstitution time (s))

Claims (3)

1. an image super-resolution method for the online dictionary learning of self-adaptation, is characterized in that comprising the following steps:

1. one group of low-resolution image of one group of high-definition picture and correspondence thereof is chosen as training sample;

2. the high-frequency characteristic of training sample is extracted, obtain one group of low resolution sample characteristics image of one group of high resolving power sample characteristics image and its correspondence, Q the high resolving power sample characteristics image fritter randomly drawed in high resolving power sample characteristics image forms matrix M, extract low resolution characteristic image fritter corresponding with the high resolving power sample characteristics image fritter extracted in low resolution sample characteristics image form matrix M ', wherein Q is more than or equal to 30,000 and is less than or equal to 100,000, by matrix M and matrix M ' be divided into k class, wherein k>=2, obtain matrix M ' k cluster centre m ₁, m ₂, m ₃..., m _kand initial sub-dictionary set { (D _l1, D _h1), (D _l2, D _h2), (D _l3, D _h3) ..., (D _lk, D _hk), wherein D _l1, D _l2, D _l3..., D _lkrepresent k the sub-dictionary of initial low resolution, D _h1, D _h2, D _h3..., D _hkrepresent k the sub-dictionary of initial high resolution,

3. utilize on-line Algorithm to be optimized initial sub-dictionary set, obtain sub-the dictionary set { (D of optimal objective _l1-best, D _h1-best), (D _l2-best, D _h2-best), (D _l3-best, D _h3-best) ..., (D _lk-best, D _hk-best), wherein D _l1-best, D _l2-best, D _l3-best..., D _lk-bestrepresent k the sub-dictionary of optimum low resolution target, D _h1-best, D _h2-best, D _h3-best..., D _hk-bestrepresent k the sub-dictionary of optimum high resolving power target;

4. input needs the low-resolution image X carrying out super-resolution amplification, extracts the high-frequency characteristic of low-resolution image X, obtains the low resolution characteristic image X' that low-resolution image X is corresponding, then choose q the image fritter X of low resolution characteristic image X' _q, q>=1, image fritter X _qcorresponding matrix is designated as x _q, compute matrix x respectively _qwith cluster centre m ₁, m ₂, m ₃..., m _keuclidean distance, compare x _qwith the size of the Euclidean distance of each cluster centre, obtain the cluster centre m that Euclidean distance is minimum _n, 1≤n≤k, selects with m _nthe sub-dictionary of optimum low resolution target that the sub-dictionary of initial low resolution for cluster centre is corresponding, is denoted as D _lq-best;

5. SP algorithm compute matrix x is utilized _qat D _lq-bestunder rarefaction representation factor alpha _q, α _q=argmin||x _q-D _lq-bestα _q|| ₂+ λ || α _q|| ₁, α _q=SP (D _lq-best, x _q), λ represents regularization coefficient and 0< λ <1, and concrete steps are as follows:

5.-1 by D _lq-bestin with matrix x _qthe row index of the K row atom that correlativity is maximum is designated as represent D _lp-bestin row number be former molecular matrix, representing matrix x _q? on projection, ${\hat{x}}_q=D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{\&prime;}{x}_q,$ Wherein $D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{\&prime;}={\left(D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{*}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}\right)}^{-1}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_0}^{*},$ * the transposition of representing matrix;

5.-2 initialization: definition original state projection initial residual vector be r ₀, x' under original state _qthe row index of K sequence atom corresponding to middle element maximal value is designated as I ₀, $r_0=\mathrm{resid}(x_q,D_{\mathrm{lq}-\mathrm{best}-I_0})=x_q-{\hat{x}}_q,$ represent D _lp-bestin row number be I ₀former molecular matrix;

5.-3 set current iteration number of times as ω, ω>=1, project in current iteration residual vector be r _ω, order $x_q^{\&prime;}=D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{\&prime;}{x}_q,$ $D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{\&prime;}={\left(D_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{*}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}\right)}^{-1}{D}_{\mathrm{lq}-\mathrm{best}-{\tilde{I}}_{\mathrm{\&omega;}}}^{*},$ X ' in current iteration _pthe row index of K sequence atom corresponding to middle element maximal value is I _ω, in conjunction with formula with $r_{\mathrm{\&omega;}}=\mathrm{resid}(x_q,D_{\mathrm{lq}-\mathrm{best}-I_{\mathrm{\&omega;}}})$ Upgrade r _ω, and I _ω, r _ω-1represent projection residual vector in ω-1 iteration, represent D _lp-bestin row number be I _ωformer molecular matrix, represent D _lp-bestin row number be former molecular matrix;

5.-4 compare r _ωwith r _ω-1if, || r _ω|| ₂>||r _ω-1|| ₂, then iteration terminates, otherwise, 5. carry out iteration renewal in-3 using returning step as current iteration number of times after ω adds 1;

5., after-5 iteration complete, least square method is used to try to achieve x _qat dictionary D _lq-bestoptimum rarefaction representation factor alpha _q;

6. select and D _lq-bestthe corresponding sub-dictionary D of high resolving power target _hq-best, utilize rarefaction representation factor alpha _qand D _hq-bestsolve x _qat D _hq-besthigh-definition picture reconstruct fritter y under corresponding _q=D _hq-bestα _q;

7. according to step 4. ~ method 6., process by all image fritters of " it " font to low resolution characteristic image X', obtain initial high-resolution reconstruction image

8. to high-resolution reconstruction image carry out block process and obtain final high-resolution reconstruction image Y.

2. the image super-resolution method of the online dictionary learning of a kind of self-adaptation according to claim 1, is characterized in that the concrete steps that 3. described step is optimized initial sub-dictionary set are as follows:

3.-1 couple of sub-dictionary D of low resolution _l1be optimized, concrete steps are:

A, suppose that the total iterations optimized is T, in the t time iteration, input any one the characteristic image block f in low resolution sample characteristics image _l, 1≤t≤T;

B, fix the sub-dictionary of target that t-1 iteration obtains subspace back tracking method is used to solve λ represents regularization coefficient and 0< λ <1, and wherein, argmin represents the minimum value solving functional, || || represent and solve norm, obtain characteristic image block f in the t time iteration _lat the sub-dictionary of target under sparse decomposition coefficients Λ _t;

C, fixing sparse decomposition coefficients Λ _tif, the sub-dictionary D of low resolution _l1there is p atom, order $A_t=[a_1,a_2,...,a_j,...,a_p]=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&Lambda;}}_i{\mathrm{\&Lambda;}}_i^T,$ $B_t=[b_1,b_2,...,b_j,...,b_p]=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{f}_l{\mathrm{\&Lambda;}}_i^T,i=\mathrm{1,2},...t,$ A _jrepresent A _tmiddle jth row, b _jrepresent B _tmiddle jth row, a _jand b _jbe the matrix of p × 1,1≤j≤p;

D, establish the sub-dictionary D of low resolution _l1a jth atom of the corresponding sub-dictionary of target is d _j, to d _jbe optimized, then $d_j=\frac{1}{\max ({\left|\right|u_j\left|\right|}_2,1)}{u}_j,$ $u_j=\frac{1}{A_{\mathrm{ij}}}(b_j-D_{{l1}_{t-j}}^{\&prime;}{a}_j)+d_j,$ represent the sub-dictionary D of low resolution _l1the sub-dictionary of the target upgraded, A _jjrepresent a _jthe value of middle jth row, max represents the maximal value of solved function;

E, upgrade low resolution sub-dictionary D according to steps d _l1p atom, complete the t time iteration, obtain the sub-dictionary D of low resolution _l1the sub-dictionary of target after the t time iteration

F, general substitute into formula $D_{{l1}_t}=\arg \min \frac{1}{t}\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}(\frac{1}{2}{\left|\right|f_l-D_{{l1}_t}^{\&prime;}{\mathrm{\&Lambda;}}_i\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|{\mathrm{\&Lambda;}}_i\left|\right|}_1),0<\mathrm{\&lambda;}<1,$ Obtain the sub-dictionary of target that the t time circulation upgrades

G, the rest may be inferred, and completing input picture is characteristic image block f _ltime, the sub-dictionary D of low resolution _l1t iteration, obtain characteristic image block f _lthe sub-dictionary of target of corresponding optimization

Except f in h, successively input low resolution sample characteristics image _lother all characteristic image blocks in addition, the principle identical according to step a ~ g is trained, and completes the sub-dictionary D of initial low resolution _l1training, last is taken turns the sub-dictionary of updated target as the sub-dictionary D of initial low resolution _l1the sub-dictionary D of optimal objective _l1-best;

3.-2 use the sub-dictionary D of low resolution _l1the same principle be optimized is respectively to D _l2, D _l3..., D _lk, D _h1, D _h2, D _h3..., D _hkbe optimized, obtain D _l2, D _l3..., D _lk, D _h1, D _h2, D _h3..., D _hkthe corresponding sub-dictionary of optimal objective, finally obtains the sub-dictionary set of optimal objective

{(D _l1-best,D _h1-best),(D _l2-best,D _h2-best),(D _l3-best,D _h3-best),…,(D _lk-best,D _hk-best)}。

3. the image super-resolution method of the online dictionary learning of a kind of self-adaptation according to claim 1, is characterized in that going block disposal route to be get average to the pixel of lap after each iteration during described step 8..