CN104036482B - Facial image super-resolution method based on dictionary asymptotic updating - Google Patents

Abstract

The invention discloses a facial image super-resolution method based on dictionary asymptotic updating. In the training stage, super-resolution reconstruction is carried out on low-resolution facial images of a low-resolution facial image training set with a one removing method to obtain a low-resolution intermediate dictionary; the low-resolution intermediate dictionary serves as a new low-resolution facial image training set for inputting, and reconstruction is carried out to obtain a new low-resolution intermediate dictionary; the process is repeated, and finally multiple low-resolution intermediate dictionaries are obtained. In the testing stage, according to the input low-resolution facial images, the prior low-resolution intermediate dictionary and a high-resolution facial image training set, super-resolution reconstruction is carried out on the input low-resolution facial images to obtain pre-estimated high-resolution facial images; the process is repeated, and finally the high-resolution facial images are reconstructed. By means of the facial image super-resolution method, the reconstruction effect which is high in quality and close to a true condition can be achieved.

Description

A kind of face image super-resolution method based on the asymptotic renewal of dictionary

Technical field

The present invention relates to image super-resolution field, be specifically related to a kind of facial image oversubscription based on the asymptotic renewal of dictionary Resolution method.

Background technology

Face image super-resolution technology refers to utilize low resolution face sample image and high-resolution human face sample graph As composition training storehouse, study low-resolution image and high-definition picture between relation, and utilize learn to pass tie up to The process of a high-resolution human face image is doped in the case of the low-resolution face image of a given input.It is in intelligence The fields such as energy video monitoring, digital entertainment, human face segmentation and identification have a wide range of applications background.

Image super-resolution technology was suggested so far from 1984, caused of computer vision and machine learning field The extensive concern of persons.Freeman et al. (document 1:W.Freeman, E.Pasztor, and O.Carmichael.Learning low-level vision[J].International Journal of Computer Vision, 2000,40 (1): 25 47.) a kind of image super-resolution method based on Markov network is proposed, this is also the earliest The super-resolution method based on study proposed.Baker and Kanade (document 2:S.Baker and in 2000 T.Kanade.Hallucinating faces.In FG, Grenoble, France, Mar.2000,83-88.) it is specifically designed for people Face, it is proposed that a kind of method of unreal structure of face (face hallucination), this is first face image super-resolution method. Subsequently, Liu et al. (document 3:C.Liu, H.Shum, and W.Freeman.Face Hallucination:Theory and Practice [J] .International Journal of Computer Vision, 2007,75 (1): 115-134.) propose The two-step method of face reconstruct, the face of the reconstruct overall situation respectively and local face.So far, face image super-resolution method based on study draws Having played the extensive concern of people, the most representational method is Chang et al. (document 4:H.Chang, D.Yeung, and Y.Xiong.Super-resolution through neighbor embedding[A].In Proc.IEEE CVPR’04 [C] .Washington, 2004.275 282.) propose is a kind of based on the image super-resolution being locally linear embedding into manifold learning Method, manifold learning thought is incorporated in image super-resolution reconstruct by first.2005, Wang et al. (document 5: X.Wang and X.Tang.Hallucinating face by eigentransformation[J].IEEE Trans.SMC (Part C), 2005,35 (3): 425 434.) the overall face face image super-resolution side that a kind of feature based is changed is proposed Method, noise inputs is compared robust by the method.

Facial image is the object of a class highly structural, and the positional information of facial image is non-in human face analysis with synthesis The most important.Inspired by this, 2010, Ma et al. (document 6:X.Ma, J.P Zhang, and C.Qi.Hallucinating Face by position-patch.Pattern Recognition, 43 (6): 3,178 3194,2010.) propose a kind of based on The face image super-resolution method of block of locations, utilizes training set people to the image block of given low-resolution face image position In face image, all image blocks of same position carry out least square linear synthesis.This method avoid manifold learning or feature The steps such as extraction, improve efficiency, also improve the quality of composograph simultaneously.Jung in 2011 et al. is at document 7 (C.Jung,L.Jiao,B.Liu,and M.Gong,“Position-Patch Based Face Hallucination Using Convex Optimization,”IEEE Signal Process.Lett.,vol.18,no.6,pp.367–370, 2011.) propose a kind of position based on convex optimization image block face super-resolution method in, sparse constraint is joined image block Solve in expression, utilize sparse regularization method to obtain the optimal reconstruction weight of human face super-resolution.2012, Hu Ruimin et al. At patent 1 (Hu Ruimin, Jiang Junjun, Wang Bing, Han Zhen, Huang Kebin, Lu Tao, Wang Yimin, a kind of face based on local constraint representation Super resolution ratio reconstruction method, number of patent application: 201110421452.3) in further improve face oversubscription based on block of locations Resolution method, retrains, with the local geometric of manifold, the sparse constraint that substituted in document 7 in process of reconstruction carrying out image block, Make reconstructed results have openness and locality simultaneously.Recently, Hu Ruimin et al. (patent 2: Hu Ruimin, Jiang Junjun, Dong little Hui, Han Zhen, Chen Jun, a kind of face super-resolution method embedded based on local restriction iteration neighborhood, number of patent application: 201310147620.3) on the basis of above-mentioned patent 1, introduce iteration neighborhood embed thought, it is further proposed that one based on The face super-resolution method that local restriction iteration neighborhood embeds.Up to the present, this face embedded based on iteration neighborhood Super-resolution method is effect the best way.

Either use least square method for expressing, sparse representation method, local constraint representation method or iteration neighborhood Embedding grammar, they seek to the high resolution space after the manifold structure of low resolution remains to reconstruct, the most fully dig Pick is not by the geometry information in original high resolution manifold space of the process influence that degrades, and it is reliable that this makes reconstructed results lack Property.

Summary of the invention

Present invention aim at providing a kind of based on the asymptotic renewal of dictionary " by slightly to essence " face image super-resolution side Method.During reconstructing human face super resolution, the high-resolution human face image result reconstructed not only according to previous step updates defeated Enter low resolution test facial image, and low resolution face training sample is updated, reduce high-low resolution training The dimension in space is poor such that it is able to more accurately carries out neighborhood and embeds holding study and prediction.

For reaching above-mentioned purpose, the technical solution used in the present invention is that a kind of facial image based on the asymptotic renewal of dictionary surpasses Resolution method, comprises the steps:

Step 1, making b=0, b is the number of plies of current low-resolution dictionary, the low-resolution face image that input builds in advance Training set I^LWith high-resolution human face training set of images I^H,

If comprising N in low-resolution face image training set to open low resolution face sample image, any of which opens low point Resolution face sample image is designated asIndex i=1,2 ..., N,High-resolution human face image is trained Concentration comprises N and opens high-resolution human face sample image, and any of which is opened high-resolution human face sample image and is designated asIndex i= 1,2 ..., N,All low resolution face sample images and high-resolution human face sample image are adopted It is respectively divided overlapped image block by consistent mode；

Step 2, uses and goes a method to b layer low-resolution face image training set I^L(b)In every low resolution face Sample image carries out super-resolution reconstruction respectively, obtains b+1 layer low-resolution face image training set I^L(b+1), as b+1 Dictionary in the middle of layer low resolution；During b=0, the 0th layer of low-resolution face image training set uses the low resolution people built in advance Face training set of images I^L；

Including to b layer low-resolution face image training setIn every low resolution Rate facial image performs to include following sub-step respectively,

Step 2.1, if taking b layer low-resolution face image training setIn i-th Open low resolution face sample imageAs input low-resolution face image, b layer low-resolution face image training set In remaining all low resolution face sample images as new low-resolution face image training set,High-resolution human face training set of imagesMiddle phase Answer remaining all high-resolution human face sample images as new high-resolution human face training set of images

Step 2.2, with the b layer low-resolution face image training set that gained in step 2.1 is newNew b layer High-resolution human face training set of imagesAs input, the input low-resolution face image that step 2.1 is takenCarry out Super-resolution reconstruction, estimates to obtain inputting low-resolution face imageCorresponding high-resolution human face imageWillAs B+1 layer low-resolution face image training set I^L(b+1)In i-th low resolution face sample image

Step 3, it may be judged whether b=B-1, if otherwise making b=b+1, the b+1 layer obtained in step 2 with current iteration Low-resolution face image training set I^L(b+1)As input, return step 2 carries out next iteration and obtains the low resolution of next layer Dictionary in the middle of rate；If then obtaining dictionary I in the middle of multilamellar low resolution^L(1),I^L(2),…,I^L(B), enter step 4；

Step 4, according to low-resolution face image to be tested, low-resolution dictionary I of all levels^L(0),I^L(1),I^{L (2)},…,I^L(B)High-resolution human face training set of images I with step 1 input^H, by slightly reconstructing input low resolution face to smart The high-resolution human face image that image is corresponding, including following sub-step,

Step 4.1, if b=0, inputs low-resolution face image to be testedThe low-resolution dictionary of all levels I^L(0),I^L(1),I^L(2),…,I^L(B)With high-resolution human face training set of images I^H,

Step 4.2, according to b layer low-resolution dictionary I^L(b), to estimating high-resolution human face imageCarry out super-resolution Rate reconstructs, and obtains estimating high-resolution human face imagePerform step 4.2 for the first time and use low resolution people to be tested Face imageHigh-resolution human face image is estimated as initial

Step 4.3, it may be judged whether b=B-1, if otherwise making b=b+1, returning step 4.2, utilizing and performing step 4.2 at this The high-resolution human face image that middle reconstruct obtainsAs estimating high-resolution human face image when performing step 4.2 next time, Optimizing further and estimate high-resolution human face image, if then stopping iteration, finally reconstructing high-resolution human face image

And, the implementation of step 2.2 is as follows,

If the low-resolution face image to inputThe image block collection dividing overlapped image block composition isTo high-resolution human face training set of imagesWith low-resolution face image training setPoint High-definition picture block training set { y is obtained after not dividing overlapped image block_j(p, q) | 1≤p≤U, 1≤q≤V, j=1,2 ..., I-1, i+1 ..., N} and low-resolution image block training setIts In, (p, q) represents facial image position coordinates, and U represents the image block number of every string on a facial image, and V represents a people The image block number of every a line on face image；

Low-resolution face image for inputIn each face image blockTake low resolution face Training set of imagesIn the image block of each low resolution face sample image relevant position as sample point, set up low resolution Rate face sample block spaceTake high-resolution human face training set of imagesIn every The image block of individual high-resolution human face sample image relevant position, as sample point, sets up high-resolution human face sample block space {y_j(p, q) | j=1,2 ..., i-1, i+1 ..., N}, as high-definition picture block dictionary；Then, for the low resolution of input Rate facial imageIn each face image blockPerform below scheme respectively,

Step 2.2a, making s=0, s is current iteration number of times；

Step 2.2b, based on to facial image blockObtain estimates high-definition picture block accordinglyCalculate itself and each image block y in the high-definition picture block dictionary of relevant position_j(p, distance q), and find it The index of K the image block that middle distance is minimum, it is achieved as follows,

${\mathrm{dist}}^{b\left(s\right)}(p,q)=\left[\begin{array}{c}\left|\right|y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_1(p,q)|{|}_2,||y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_2(p,q)|{|}_2,\mathrm{...},\\ \left|\right|y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_{i-1}(p,q)|{|}_2,||y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_{i+1}(p,q)|{|}_2,\mathrm{...},\left|\right|y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_N(p,q)|{|}_2\end{array}\right]$

$N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)=\sup port\left({\mathrm{dist}}^{b\left(s\right)}\right(p,q\left){|}_K\right),$

Wherein, dist^b(s)(p,q)∈R^N-1RepresentWith N-1 image block { y in high-definition picture block dictionary_j (p, q) | j=1,2 ..., i-1, i+1 ..., the N-1 dimensional vector that the distance of N} is arranged in, R is vector space, dist^b(s)(p,q) |_KRepresent dist^b(s)(p, q) in minimum K value, | | | |₂Represent two norms,It is to estimate high-resolution Image blockK the image block minimum with the distance in high-definition picture block dictionary is instructed at high-resolution human face image Practice the constituted set of index concentrated；

When performing step 2.2b for the first time, estimate high-definition picture blockLow resolution face by input ImageAfter Bicubic is upsampled to high-definition picture size, fetch bit put (p, q) on image block obtained by；

Step 2.2c, K the image block utilizing the distance in step 2.2b gained high-definition picture block dictionary minimum exists The image block of low resolution corresponding in low resolution face sample block space, to estimating high-definition picture blockEnter Line linearity reconstructs, and the weight coefficient obtaining linear reconstruction is as follows,

$\begin{array}{cc}s.t.& {\mathrm{\Σ}}_{k\∈N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)}{w}_k^{b\left(s\right)}(p,q)=1,\end{array}$

Wherein, k represents call number, and its span is in setIn, y_k(p q) represents high-resolution In rate facial image training set kth open high-resolution human face sample image position (p, q) on image block,Represent Image block y in high-resolution human face training set of images_k(p, q) corresponding to reconstruction weights coefficient,Return about variable w^b(s)(p, the w when obtaining minima of function q)^b(s)(p, value q),Represent optimal reconstruction weight,Represent To two norms | | | |₂Result squared, " ο " represents the inner product operation between two vectors, and τ is Equilibrium fitting error drawn game The regularization parameter of portion's constraint,Represent the summation of bracket interior element；

Step 2.2d, according to optimal reconstruction weightNew high-definition picture block is rebuild by following formula

$y_i^{b(s+1)}(p,q)=\underset{k\∈N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)}{\Σ}{\hat{w}}_k^{b\left(s\right)}(p,q)y_k(p,q)$

Step 2.2e, it may be judged whether s=S-1, if then stopping iterative process, last iteration obtains If otherwise making s=s+1, returning step 2.2b and carrying out next iteration, and using current iteration to perform step 2.2d gainedUsed when performing step 2.2b as next iteration estimate high-definition picture block

Low-resolution face image for inputIn each face image blockReconstruct by above flow process After, the high-definition picture block that all weightings are reconstructedAccording to position superposition, the most each pixel is respectively divided by The number of times that relevant position is overlapping, reconstructs high-resolution human face image

And, the implementation of step 4.2 is as follows,

If to estimating high-resolution human face imageDivide overlapped image block, obtainTo high-resolution human face training set of images I^HWith low-resolution face image training set I^{L (b)}High-definition picture block training set { y is obtained after being respectively divided overlapped image block_j(p,q)|1≤p≤U,1≤q≤V, J=1,2 ..., N} and low-resolution image block training set

To estimating high-resolution human face imageIn each face image blockTake low-resolution face image instruction Practice collection I^L(b)In the image block of each low resolution face sample image relevant position as sample point, set up low resolution face Sample block spaceTake high-resolution human face training set of images I^HIn each high-resolution human face sample The image block of this image relevant position, as sample point, sets up high-resolution human face sample block space { y_j(p, q) | j=1, 2 ..., N}, as high-definition picture block dictionary；

For each face image blockPerform below scheme respectively:

Step 4.2a, making s=0, s is current iteration number of times；

Step 4.2b, based on to facial image blockObtain estimates high-definition picture blockCalculate The distance of each image block in its high-definition picture block dictionary with relevant position, and find K the image that wherein distance is minimum The index of block, method is as follows,

${\mathrm{dist}}_t^{b\left(s\right)}(p,q)=\[\left|\right|y_t^{b\left(s\right)}(p,q)-y_1(p,q)|{|}_2,||y_t^{b\left(s\right)}(p,q)-y_2(p,q)|{|}_2,...,\left|\right|y_t^{b\left(s\right)}(p,q)-y_N(p,q)|{|}_2\],$

$N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)=\sup port\left({\mathrm{dist}}_t^{b\left(s\right)}\right(p,q\left){|}_K\right),$

Wherein,RepresentWith image block { y N number of in high-definition picture block dictionary_j(p, Q) | j=1,2 ..., the N-dimensional vector that the distance of N} is arranged in, R is vector space,RepresentIn K minimum value, | | | |₂Represent two norms,It is in high-definition picture block dictionary and to estimate high score Resolution image blockK the image block of distance minimum the constituted collection of index in high-resolution human face training set of images Close；

When performing step 4.2b for the first time, estimate high-definition picture blockBy estimating high-resolution human face figure PictureAfter Bicubic is upsampled to high-definition picture size, fetch bit put (p, q) on image block obtained by；

Step 4.2c, K the image block utilizing the distance in step 4.2b gained high-definition picture block dictionary minimum exists The image block of low resolution corresponding in low resolution face sample block space, to facial image blockLinearly weigh Structure, the weight coefficient obtaining linear reconstruction is as follows,

$\begin{array}{cc}s.t.& {\mathrm{\Σ}}_{k\∈N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)}{w}_{t,k}^{b\left(s\right)}(p,q)=1,\end{array}$

Wherein, k represents call number, and its span is in setIn, y_k(p q) represents high-resolution In rate facial image training set kth open high-resolution human face sample image position (p, q) on image block,Represent height Image block y in resolution facial image training set_k(p, q) corresponding to reconstruction weights coefficient,Return about variableFunction when obtaining minimaValue,Represent optimal reconstruction weight,Represent To two norms | | | |₂Result squared, " ο " represents the inner product operation between two vectors, and τ is Equilibrium fitting error drawn game The regularization parameter of portion's constraint,Represent the summation of bracket interior element；

Step 4.2d, is obtaining optimal reconstruction weightAfter, rebuild new high-definition picture by following formula Block

$y_t^{b(s+1)}(p,q)=\underset{k\∈N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)}{\Σ}{\hat{w}}_{t,k}^{b\left(s\right)}(p,q)y_k(p,q)$

Step 4.2e, it may be judged whether s=S-1, the most then stop iterative process, and last iteration obtains If it is not, then make s=s+1, and return step 4.2b and carry out next iteration, and use current iteration to perform step 4.2d gainedUsed when performing step 4.2b as next iteration estimate high-definition picture block

Will be to estimating high-resolution human face imageMiddle face images blockWeight the height reconstructed respectively Image in different resolution blockAccording to position superposition, then divided by the number of times that each location of pixels is overlapping, reconstruct high-resolution Rate facial image

The thought of low-resolution face image dictionary updating is incorporated in reconstructing human face super resolution by the present invention first, The relation between low-resolution spatial and high resolution space study high-low resolution image after asymptotic renewal, it is thus achieved that obtain More high-quality and truth closer to reconstruction effect.The facial image based on the asymptotic renewal of dictionary that the present invention proposes Super-resolution method uses " by thick to essence " thought, is mainly reflected in two aspects: first, reconstruct high-resolution human face image Constantly iteration optimization.I.e. for each layer of middle low resolution face training set and high-resolution human face training set, estimate and obtain High-resolution human face image and high-resolution training sample between distance as constraint, retrain next time in super-resolution Reconstruction weights, continues to optimize reconstruction result；Second, the renewal learning of low resolution face training set.I.e. original for input Low resolution face training set and original high resolution face training set, low resolution face training set in the middle of study multilamellar, by The least low resolution training space is poor with the dimension in original high resolution training space such that it is able to more accurately carry out neighbour Territory embeds and keeps study and prediction.

Accompanying drawing explanation

Fig. 1 is the flow chart of the embodiment of the present invention.

Detailed description of the invention

Technical solution of the present invention can use software engineering to realize automatic flow and run.Below in conjunction with the accompanying drawings with embodiment to this Inventive technique scheme further describes.

Seeing Fig. 1, the embodiment of the present invention concretely comprises the following steps:

Step 1, making b=0, b is the number of plies of current low-resolution dictionary, and those skilled in the art can preset in the number of plies voluntarily Limit B, in the present embodiment, number of plies upper limit B of low-resolution dictionary takes 4；The low-resolution face image training that input builds in advance Collection I^LWith high-resolution human face training set of images I^H,

If comprising N in low-resolution face image training set to open low resolution face sample image, any of which opens low point Resolution face sample image is designated asIndex i=1,2 ..., N, i.e.High-resolution human face image is instructed White silk concentration comprises N and opens high-resolution human face sample image, and any of which is opened high-resolution human face sample image and is designated asIndex i =1,2 ..., N, i.e.The present invention is to the low-resolution face image of input, all low resolution people Face sample image uses consistent mode to be respectively divided overlapped image block with high-resolution human face sample image, specifically draws Point mode can be found in patent 1.

In embodiment, all high-resolution human face sample images are the facial image through manual alignment registration, and pixel is big Little is 128 × 112.In low-resolution face image training set, every low resolution face sample image is by high-resolution training set The high-resolution human face sample image of middle correspondence is obtained by 4 × 4 smothing filterings 4 times of down-samplings, low-resolution image pixel Size is 32 × 28, and high-definition picture block size is set to 12 × 12, and adjacent image block overlaid pixel value is set to 4, low resolution Tile size is 3 × 3, and adjacent image block overlaid pixel value is 1.

After can carrying out based on the low-resolution face image training set built in advance and high-resolution human face training set of images Continuous step.

Step 2, uses " going a method " to every low resolution face sample in b layer low-resolution face image training set This image carries out super-resolution reconstruction respectively, obtains b+1 layer low-resolution face image training set, as one layer of low resolution Middle dictionary is (as shown in Fig. 1 (iii), by I^L(0)Progressive updating obtains I^L(1)、I^L(2)…)。

B=0 when entering step 2 for the first time, represents original low-resolution layer, the 0th layer of low-resolution face image training set (i.e. the 0th layer low-resolution dictionary) uses low-resolution face image training set I built in advance^L, i.e. I^L(0)=I^L.Laggard B=1 when entering step 2,2 ..., b layer low-resolution face image training set uses last iteration to perform gained knot during step 2 Really.

Embodiment is to b layer low-resolution face image training setIn every low point Resolution facial image performs to include following sub-step respectively:

Step 2.1, if taking b layer low-resolution face image training setIn i-th (i value is 1,2 ..., one of N) a low resolution face sample imageAs input low-resolution face image, b layer Remaining (removing i-th low resolution training sample of b layer) all low resolution people in low-resolution face image training set Face sample image as new low-resolution face image training set,High Resolution facial image training setIn the most remaining (remove i-th high-resolution human face image instruction Practice sample) all high-resolution human face sample images are as new high-resolution human face training set of images

Step 2.2, with the new b layer low-resolution face image training set obtained in step 2.1, high-resolution human face Training set of imagesWithAs input, to the input low-resolution face image in step 2.1Carry out super-resolution Reconstruct, estimates to obtain inputting low-resolution face imageCorresponding high-resolution human face image；

In embodiment, to input low-resolution face imageWhen carrying out super-resolution reconstruction, newly constructed low resolution Facial image training setWith high-resolution human face training set of imagesTraining sample pair set in advance is provided.For the sake of ease of implementation, it is provided that The detail of high-resolution human face image reconstruction is as follows:

If the low-resolution face image to input(b layer low-resolution face image training set I^L(b)I-th image) The image block collection dividing overlapped image block composition is(" t " in subscript bracket be For the ease of distinguishing the test image in this stageAnd training imageRight High-resolution human face training set of imagesWith low-resolution face image training setIt is respectively divided overlapped image block After obtain high-definition picture block training set { y_j(p, q) | 1≤p≤U, 1≤q≤V, j=1,2 ..., i-1, i+1 ..., N} and Low-resolution image block training setWherein, (p, q) Representing facial image position coordinates, U represents the image block number of every string on a facial image, and V represents on a facial image The image block number of every a line.

Low-resolution face image for inputIn each face image blockTake low resolution face Training set of imagesIn the image block of each low resolution face sample image relevant position as sample point, set up low resolution Rate face sample block spaceTake high-resolution human face training set of imagesIn every The image block of individual high-resolution human face sample image relevant position, as sample point, sets up high-resolution human face sample block space {y_j(p, q) | j=1,2 ..., i-1, i+1 ..., N}, as high-definition picture block dictionary.Then, for the low resolution of input Rate facial imageIn each face image blockPerform below scheme respectively:

Step a, making s=0, s is current iteration number of times, and those skilled in the art can preset maximum iteration time S voluntarily, this In embodiment, maximum iteration time S takes 5.

Step b, based on to facial image blockObtain estimates high-definition picture block accordingly( During s=0, when performing step b first, estimate high-definition picture blockIt it is exactly the low-resolution face image of inputAfter Bicubic is upsampled to high-definition picture size, fetch bit put (p, q) on image block obtained by), calculate Each image block y in its high-definition picture block dictionary with relevant position_j(p, distance q), and find the K that wherein distance is minimum The index of individual image block, method is as follows,

${\mathrm{dist}}^{b\left(s\right)}(p,q)=\left[\begin{array}{c}\left|\right|y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_1(p,q)|{|}_2,||y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_2(p,q)|{|}_2,\mathrm{...},\\ \left|\right|y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_{i-1}(p,q)|{|}_2,||y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_{i+1}(p,q)|{|}_2,\mathrm{...},\left|\right|y_{i\left(t\right)}^{b\left(s\right)}(p,q)-y_N(p,q)|{|}_2\end{array}\right]$

$N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)=\sup port\left({\mathrm{dist}}^{b\left(s\right)}\right(p,q\left){|}_K\right),$

Wherein, dist^b(s)(p,q)∈R^N-1RepresentWith N-1 image block { y in high-definition picture block dictionary_j (p, q) | j=1,2 ..., i-1, i+1 ..., the N-1 dimensional vector that the distance of N} is arranged in, R is vector space, dist^b(s)(p,q) |_KRepresent dist^b(s)(p, q) in minimum K value, | | | |₂Represent two norms,It is to estimate high-resolution Image blockK the image block minimum with the distance in high-definition picture block dictionary is instructed at high-resolution human face image Practice the index (i.e. the index of high-resolution human face sample image belonging to image block) concentrated and constituted set (i.e. dist^b(s)(p,q) |_KSupport collection), those skilled in the art can preset the value of K voluntarily, and in the present embodiment, K is set to 150.

Step c, as shown in Fig. 1 (ii), using calculated distance as the Reconstruction Constraints of image block, and utilizes step b The K obtained a high-resolution image block (K the image block that the distance in high-definition picture block dictionary is minimum) is in low resolution The image block of low resolution corresponding in rate face sample block space is to estimating high-definition picture blockCarry out linear Reconstruct (as shown in Fig. 1 (i)), obtains the weight coefficient of linear reconstruction, and method is as follows:

$\begin{array}{cc}s.t.& {\mathrm{\Σ}}_{k\∈N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)}{w}_k^{b\left(s\right)}(p,q)=1,\end{array}$

Wherein, k represents call number, and its span is in setIn, y_k(p q) represents high-resolution In rate facial image training set kth open high-resolution human face sample image position (p, q) on image block,Represent Image block y in high-resolution human face training set of images_k(p, q) corresponding to reconstruction weights coefficient,Return about variable w^b(s)(p, the w when obtaining minima of function q)^b(s)(p, value q),Represent optimal reconstruction weight,Represent To two norms | | | |₂Result squared, " ο " represents the inner product operation between two vectors, and τ is Equilibrium fitting error drawn game The regularization parameter of portion's constraint,Represent the summation of bracket interior element.

Step d, is obtaining optimal reconstruction weightAfter, new high-definition picture can be rebuild by following formula Block

$y_i^{b(s+1)}(p,q)=\underset{k\∈N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)}{\Σ}{\hat{w}}_k^{b\left(s\right)}(p,q)y_k(p,q)$

Step e, it may be judged whether s=S-1？If then stopping iterative process, last iteration obtainsIf not Then make s=s+1, return step b and carry out next iteration, and use current iteration to perform step d gainedUnder as An iteration is used when performing step b estimates high-definition picture block

Low-resolution face image for inputIn each face image blockReconstruct by above flow process After, the high-definition picture block that all weightings are reconstructedAccording to position superposition, the most each pixel is respectively divided by The number of times that relevant position is overlapping, reconstructs high-resolution human face image

To b layer low-resolution face image training setIn every low resolution people After face image performs step 2.1 respectively, 2.2 super-resolution reconstructions complete, obtain corresponding high-resolution human face imageI=1, 2 ..., N, willAs b+1 layer low-resolution face image training set I^L(b+1)In i-th low resolution face sample imageI.e. can get dictionary in the middle of b+1 layer low resolution.

Step 3, it may be judged whether b=B-1, if otherwise making b=b+1, the low resolution obtained in step 2 with current iteration Middle dictionary I^L(b+1)(b+1 layer low-resolution face image training set), as input, returns step 2 and carries out next iteration Obtain dictionary in the middle of the low resolution of next layer；If the dictionary number of plies reaches to pre-set in the middle of the low resolution then asked for Value B, last iteration obtains dictionary I in the middle of B layer low resolution^L(B), finally give dictionary I in the middle of multilamellar low resolution^{L (1)},I^L(2),…,I^L(B), enter step 4.

Step 4, (includes original low according to the low-resolution dictionary of low-resolution face image to be tested, all levels Layers of resolution I^L(0)=I^L, dictionary I in the middle of multilamellar low resolution^L(1),I^L(2),…,I^L(B)) and the original high resolution dictionary of correspondence (the i.e. high-resolution human face training set of images I of step 1 input^H), " by thick to smart " reconstruct input low-resolution face image Corresponding high-resolution human face image.

Embodiment includes following sub-step:

Step 4.1, if b=0, inputs low-resolution face image to be testedThe low-resolution dictionary of all levels I^L(0),I^L(1),I^L(2),…,I^L(B)With high-resolution human face training set of images I^H,

Step 4.2, according to b layer low-resolution dictionary I^L(b), to estimating high-resolution human face image(b=0, i.e. Once perform step 4.2 and use low-resolution face image to be testedHigh-resolution human face image is estimated as initial) carry out super-resolution reconstruction, obtain estimating high-resolution human face image

When performing step 4.2 for the first time, b=0, the 0th layer of low-resolution dictionary uses the low resolution face built in advance Training set of images I^L, i.e. I^L(0)=I^L.During subsequent execution step 4.2, use dictionary I in the middle of corresponding low resolution according to b value^{L (1)},I^L(2),…,I^L(B)。

The detail of high-resolution human face image reconstruction is as follows:

To estimating high-resolution human face imageDivide overlapped image block, dividing mode still with to all low resolutions Rate face sample image keeps consistent with the dividing mode of high-resolution human face sample image, obtains It is exactly to low-resolution face image to be tested during execution step 4.2 for the first timeDivide what overlapped image block was constituted Image block collection is { x_t(p, q) | 1≤p≤U, 1≤q≤V}, i.e.To high-resolution human face training set of images I^HWith low-resolution face image training set I^L(b)The training of high-definition picture block is obtained after being respectively divided overlapped image block Collection { y_j(p, q) | 1≤p≤U, 1≤q≤V, j=1,2 ..., N} and low-resolution image block training set

To estimating high-resolution human face imageIn each face image blockTake low-resolution face image Training set I^L(b)In the image block of each low resolution face sample image relevant position as sample point, set up low resolution people Face sample block spaceTake high-resolution human face training set of images I^HIn each high-resolution human face The image block of sample image relevant position, as sample point, sets up high-resolution human face sample block space { y_j(p, q) | j=1, 2 ..., N}, as high-definition picture block dictionary.

For each face image blockPerform below scheme respectively:

Step a, making s=0, s is current iteration number of times.Those skilled in the art can preset corresponding maximum iteration time voluntarily S, value is the most identical with the value in step 2.2 herein.In the present embodiment, maximum iteration time S takes 5.

Step b, based on to facial image blockObtain estimates high-definition picture block(at s=0 Time, when performing step b first, estimate high-definition picture blockIt is exactly to estimate high-resolution human face imageWarp Cross after Bicubic is upsampled to high-definition picture size, fetch bit put (p, q) on image block obtained by), calculate itself and phase Answer the distance of each image block in the high-definition picture block dictionary of position, and find the rope of wherein K the image block that distance is minimum Drawing, method is as follows,

${\mathrm{dist}}_t^{b\left(s\right)}(p,q)=\[\left|\right|y_t^{b\left(s\right)}(p,q)-y_1(p,q)|{|}_2,||y_t^{b\left(s\right)}(p,q)-y_2(p,q)|{|}_2,...,\left|\right|y_t^{b\left(s\right)}(p,q)-y_N(p,q)|{|}_2\],$

$N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)=\sup port\left({\mathrm{dist}}_t^{b\left(s\right)}\right(p,q\left){|}_K\right),$

Wherein,RepresentWith image block { y N number of in high-definition picture block dictionary_j(p, Q) | j=1,2 ..., the N-dimensional vector that the distance of N} is arranged in, R is vector space,RepresentIn K minimum value, | | | |₂Represent two norms,It is in high-definition picture block dictionary and to estimate high score Resolution image blockK the image block of distance minimum index (i.e. image in high-resolution human face training set of images The index of high-resolution human face sample image belonging to block) constituted set (i.e.Support collection).

Step c, K the high-definition picture block utilizing step b to obtain is corresponding in low resolution face sample block space Low-resolution image block to facial image blockCarrying out linear reconstruction, obtain the weight coefficient of linear reconstruction, method is such as Under:

$\begin{array}{cc}s.t.& {\mathrm{\Σ}}_{k\∈N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)}{w}_{t,k}^{b\left(s\right)}(p,q)=1,\end{array}$

Wherein, k represents call number, and its span is in setIn, y_k(p q) represents high-resolution In rate facial image training set kth open high-resolution human face sample image position (p, q) on image block,Represent height Image block y in resolution facial image training set_k(p, q) corresponding to reconstruction weights coefficient,Return about variableFunction when obtaining minimaValue,Represent optimal reconstruction weight.Represent To two norms | | | |₂Result squared, " ο " represents the inner product operation between two vectors, and τ is Equilibrium fitting error drawn game The regularization parameter of portion's constraint,Represent the summation of bracket interior element.

Step d, is obtaining optimal reconstruction weightAfter, new high-definition picture can be rebuild by following formula Block

$y_t^{b(s+1)}(p,q)=\underset{k\∈N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)}{\Σ}{\hat{w}}_{t,k}^{b\left(s\right)}(p,q)y_k(p,q)$

Step e, it may be judged whether s=S-1？The most then stop iterative process；If it is not, then make s=s+1, and return step b Carry out next iteration, and use current iteration to perform step d gainedWhen performing step b as next iteration Used estimates high-definition picture blockCurrent iteration is i.e. used to estimate the high-resolution human face obtained in step d ImageAnd the distance between high-resolution training sample is as constraint, retrain the reconstruct power in super-resolution next time Weight, continues to optimize reconstruction result；Until iterations reaches value S pre-set, export final high-definition picture block

Will be to estimating high-resolution human face imageMiddle face images blockWeight the height reconstructed respectively Image in different resolution blockAccording to position superposition, then divided by the number of times that each location of pixels is overlapping, reconstruct high-resolution Rate facial image

Step 4.3, it may be judged whether b=B-1, if otherwise making b=b+1, returning step 4.2, utilizing and performing step at this The high-resolution human face image obtained is reconstructed in 4.2As estimating high-resolution human face when performing step 4.2 next time Image, optimizing further and estimates high-resolution human face image, if then stopping iteration, finally reconstructing high-resolution human face image

In order to verify effectiveness of the invention, employing CAS-PEAL-R1 China's face database on a large scale (document 8: W.Gao,B.Cao,S.Shan,X.Chen,et al.The CAS-PEAL Large-Scale Chinese Face Database and Baseline Evaluations[J].IEEE Trans.SMC(Part A),2008,38(1):149- 161) test, select the front face image under all 1040 individual neutral expression, normal illuminations.Take face district Territory is also cut into 128 × 112 pixels, carries out automatic aligning further according to position of human eye, obtains original high-resolution human face Image.Low-resolution face image by after 4 times of Bicubic down-samplings of high-resolution human face image again 4 times of Bicubic up-sample Arrive.Randomly choose 1000 as training sample, 40 conduct test images of general's residue.The reconstruct effect that the present invention is obtained by we Overall face method and some methods based on block position that fruit proposes in document 5 with Wang et al. contrast, such as neighborhood Embedding grammar (document 4), rarefaction representation method (document 6) and iteration imbedding method (patent 2) etc..

Step 1,2,3 being the training stage, step 4 is test phase.

The embodiment of the present invention relates generally to dictionary number of plies B and survey in the middle of the low resolution of two parameters, i.e. training stage Low resolution test image maximum iteration time S in examination stage.Experiment shows, when middle dictionary number of plies B reaches 4, and the present invention Method just can reach a reasonable reconstruction result, and subjective and objective result all tends towards stability.Greatest iteration when test image When number of times S reaches 5, the subjective and objective result of the inventive method all tends towards stability.Therefore B=4, S=5 in embodiment, be embodied as Time those skilled in the art can preset adjustment the most voluntarily.

Experiment uses Y-PSNR (Peak Signal to Noise Ratio, PSNR) to weigh the excellent of contrast algorithm Bad, SSIM is then the index weighing two width figure similarities, and its value is closer to 1, illustrates that the effect of image reconstruction is the best.Relatively with Average PSNR and the SSIM value that whole 40 test image procossing are obtained by upper method, overall situation face, neighborhood embeds, rarefaction representation, The average PSNR value of the methods such as local constraint representation and the inventive method is followed successively by 26.04,27.76,28.56,29.48, 30.22；Overall situation face, the average SSIM value of the methods such as neighborhood embeds, rarefaction representation, iteration imbedding method and the inventive method is followed successively by 0.7989,0.8841,0.8962,0.9138,0.9256.The inventive method algorithm (patent 2) more best than in control methods exists 0.74 dB and 0.0127 it is respectively increased in PSNR and SSIM value.As can be seen here, the inventive method is compared with other existing method phases Ratio, effect has had significant raising.

Claims (3)

1. a face image super-resolution method based on the asymptotic renewal of dictionary, it is characterised in that comprise the steps:

Step 1, making b=0, b is the number of plies of current low-resolution dictionary, the low-resolution face image training that input builds in advance Collection I^LWith high-resolution human face training set of images I^H,

If comprising N in low-resolution face image training set to open low resolution face sample image, any of which opens low resolution Face sample image is designated asIndex i=1,2 ..., N,In high-resolution human face training set of images Comprising N and open high-resolution human face sample image, any of which is opened high-resolution human face sample image and is designated asIndex i=1, 2 ..., N,All low resolution face sample images and high-resolution human face sample image are used Consistent mode is respectively divided overlapped image block；

Step 2, uses and goes a method to b layer low-resolution face image training set I^L(b)In every low resolution face sample Image carries out super-resolution reconstruction respectively, obtains b+1 layer low-resolution face image training set I^L(b+1), low as b+1 layer Dictionary in the middle of resolution；During b=0, the 0th layer of low-resolution face image training set uses the low resolution face figure built in advance As training set I^L；

Including to b layer low-resolution face image training setIn every low resolution people Face image performs a method respectively, including following sub-step,

Step 2.1, if taking b layer low-resolution face image training setIn i-th low point Resolution face sample imageAs input low-resolution face image, surplus in b layer low-resolution face image training set Remaining all low resolution face sample images as new low-resolution face image training set,High-resolution human face training set of imagesMiddle phase Answer remaining all high-resolution human face sample images as new high-resolution human face training set of images

Step 2.2, with the b layer low-resolution face image training set that gained in step 2.1 is newNew b floor height is differentiated Rate facial image training setAs input, the input low-resolution face image that step 2.1 is takenCarry out super-resolution Rate reconstructs, and estimates to obtain inputting low-resolution face imageCorresponding high-resolution human face imageWillAs b+1 Layer low-resolution face image training set I^L(b+1)In i-th low resolution face sample image

Step 3, it may be judged whether b=B-1, B are the default number of plies upper limit, if otherwise making b=b+1, with current iteration in step 2 B+1 layer low-resolution face image training set I obtained^L(b+1)As input, return step 2 carries out next iteration and obtains Dictionary in the middle of the low resolution of next layer；If then obtaining dictionary I in the middle of multilamellar low resolution^L(1),I^L(2),…,I^L(B), enter Step 4；

Step 4, according to low-resolution face image to be tested, low-resolution dictionary I of all levels^L(0),I^L(1),I^{L (2)},…,I^L(B)High-resolution human face training set of images I with step 1 input^H, by slightly reconstructing input low resolution face to smart The high-resolution human face image that image is corresponding, including following sub-step,

Step 4.1, if b=0, inputs low-resolution face image to be testedLow-resolution dictionary I of all levels^L(0), I^L(1),I^L(2),…,I^L(B)With high-resolution human face training set of images I^H,

Step 4.2, according to b layer low-resolution dictionary I^L(b), to estimating high-resolution human face imageCarry out Super-resolution reconstruction Structure, obtains estimating high-resolution human face imagePerform step 4.2 for the first time and use low resolution face figure to be tested PictureHigh-resolution human face image is estimated as initial

Step 4.3, it may be judged whether b=B-1, if otherwise making b=b+1, returning step 4.2, utilizing in this performs step 4.2 The high-resolution human face image that reconstruct obtainsAs estimating high-resolution human face image when performing step 4.2 next time, Optimizing further and estimate high-resolution human face image, if then stopping iteration, finally reconstructing high-resolution human face image

Face image super-resolution method based on the asymptotic renewal of dictionary the most according to claim 1, it is characterised in that: step The implementation of 2.2 is as follows,

If the low-resolution face image to inputThe image block collection dividing overlapped image block composition isTo high-resolution human face training set of imagesWith low-resolution face image training set High-definition picture block training set { y is obtained after being respectively divided overlapped image block_j(p, q) | 1≤p≤U, 1≤q≤V, j=1, 2 ..., i-1, i+1 ..., N} and low-resolution image block training set Wherein, (p, q) represents facial image position coordinates, and U represents the image block number of every string on a facial image, and V represents one The image block number of every a line on facial image；

Low-resolution face image for inputIn each face image blockTake low-resolution face image Training setIn the image block of each low resolution face sample image relevant position as sample point, set up low resolution people Face sample block spaceTake high-resolution human face training set of imagesIn each high The image block of resolution face sample image relevant position, as sample point, sets up high-resolution human face sample block space { y_j(p, Q) | j=1,2 ..., i-1, i+1 ..., N}, as high-definition picture block dictionary；Then, for the low resolution face of input ImageIn each face image blockPerform below scheme respectively,

Step 2.2a, making s=0, s is current iteration number of times；

Step 2.2b, based on to facial image blockObtain estimates high-definition picture block accordinglyMeter Calculate itself and each image block y in the high-definition picture block dictionary of relevant position_j(p, distance q), and it is minimum to find wherein distance The index of K image block, it is achieved as follows,

${\mathrm{dist}}^{b\left(s\right)}\left(p,q\right)=\left[\begin{array}{c}\left|\right|y_{i\left(t\right)}^{b\left(s\right)}\left(p,q\right)-y_1\left(p,q\right)|{|}_2,||y_{i\left(t\right)}^{b\left(s\right)}\left(p,q\right)-y_2\left(p,q\right)|{|}_2,...,\\ \left|\right|y_{i\left(t\right)}^{b\left(s\right)}\left(p,q\right)-y_{i-1}\left(p,q\right)|{|}_2,||y_{i\left(t\right)}^{b\left(s\right)}\left(p,q\right)-y_{i+1}\left(p,q\right)|{|}_2,...,\left|\right|y_{i\left(t\right)}^{b\left(s\right)}\left(p,q\right)-y_N\left(p,q\right)|{|}_2\end{array}\right]$

$N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)=\sup port\left({\mathrm{dist}}^{b\left(s\right)}\right(p,q\left){|}_K\right),$

Wherein, dist^b(s)(p,q)∈R^N-1RepresentWith N-1 image block { y in high-definition picture block dictionary_j(p, Q) | j=1,2 ..., i-1, i+1 ..., the N-1 dimensional vector that the distance of N} is arranged in, R is vector space, dist^b(s)(p,q)|_KTable Show dist^b(s)(p, q) in minimum K value, | | | |₂Represent two norms,It is to estimate high-definition picture BlockK the image block minimum with the distance in high-definition picture block dictionary is at high-resolution human face training set of images In the constituted set of index, support (dist^b(s)(p,q)|_K) represent dist^b(s)(p,q)|_KSupport collection；

When performing step 2.2b for the first time, estimate high-definition picture blockLow-resolution face image by inputAfter Bicubic is upsampled to high-definition picture size, fetch bit put (p, q) on image block obtained by；

Step 2.2c, utilizes minimum K the image block of distance in step 2.2b gained high-definition picture block dictionary at low point The image block of low resolution corresponding in resolution face sample block space, to estimating high-definition picture blockCarry out line Property reconstruct, the weight coefficient obtaining linear reconstruction is as follows,

$\begin{array}{cc}s.t.& {\mathrm{\Σ}}_{k\∈N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)}{w}_k^{b\left(s\right)}(p,q)=1\end{array},$

Wherein, k represents call number, and its span is in setIn, y_k(p q) represents high-resolution human In face training set of images kth open high-resolution human face sample image position (p, q) on image block,Represent high score Image block y in resolution facial image training set_k(p, q) corresponding to reconstruction weights coefficient,Return about variable w^b(s) (p, the w when obtaining minima of function q)^b(s)(p, value q),Represent optimal reconstruction weight,Represent two Norm | | | |₂Result squared, " ο " represents the inner product operation between two vectors, τ be Equilibrium fitting error and local the most about The regularization parameter of bundle,Represent the summation of bracket interior element；

Step 2.2d, according to optimal reconstruction weightNew high-definition picture block is rebuild by following formula

$y_i^{b(s+1)}(p,q)=\underset{k\∈N_K^{b\left(s\right)}\left(y_{i\left(t\right)}^{b\left(s\right)}\right(p,q\left)\right)}{\Σ}{\hat{w}}_k^{b\left(s\right)}(p,q)y_k(p,q)$

Step 2.2e, it may be judged whether s=S-1, S are default maximum iteration time, if then stopping iterative process, for the last time Iteration obtainsIf otherwise making s=s+1, returning step 2.2b and carrying out next iteration, and using current iteration to perform Step 2.2d gainedUsed when performing step 2.2b as next iteration estimate high-definition picture block

Low-resolution face image for inputIn each face image blockAfter reconstructing by above flow process, will The high-definition picture block that all weightings reconstructAccording to position superposition, the most each pixel is respectively divided by corresponding positions Put overlapping number of times, reconstruct high-resolution human face image

Face image super-resolution method based on the asymptotic renewal of dictionary the most according to claim 1, it is characterised in that: step The implementation of 4.2 is as follows,

If to estimating high-resolution human face imageDivide overlapped image block, obtain To high-resolution human face training set of images I^HWith low-resolution face image training set I^L(b)It is respectively divided overlapped image block After obtain high-definition picture block training set { y_j(p, q) | 1≤p≤U, 1≤q≤V, j=1,2 ..., N} and low-resolution image Block training set

To estimating high-resolution human face imageIn each face image blockTake low-resolution face image training set I^L(b)In the image block of each low resolution face sample image relevant position as sample point, set up low resolution face sample Block spaceTake high-resolution human face training set of images I^HIn each high-resolution human face sample graph As the image block of relevant position is as sample point, set up high-resolution human face sample block space { y_j(p, q) | j=1,2 ..., N}, As high-definition picture block dictionary；

For each face image blockPerform below scheme respectively:

Step 4.2a, making s=0, s is current iteration number of times；

Step 4.2b, based on to facial image blockObtain estimates high-definition picture blockCalculate its with The distance of each image block in the high-definition picture block dictionary of relevant position, and find K image block of wherein distance minimum Index, method is as follows,

${\mathrm{dist}}_t^{b\left(s\right)}(p,q)=\[\left|\right|y_t^{b\left(s\right)}(p,q)-y_1(p,q)|{|}_2,||y_t^{b\left(s\right)}(p,q)-y_2(p,q)|{|}_2,...,\left|\right|y_t^{b\left(s\right)}(p,q)-y_N(p,q)|{|}_2\],$

$N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)=\sup port\left({\mathrm{dist}}_t^{b\left(s\right)}\right(p,q\left){|}_K\right),$

Wherein,RepresentWith image block { y N number of in high-definition picture block dictionary_j(p,q)|j =1,2 ..., the N-dimensional vector that the distance of N} is arranged in, R is vector space,RepresentMiddle minimum K value, | | | |₂Represent two norms,It is in high-definition picture block dictionary and to estimate high-resolution Image blockThe constituted set of index in high-resolution human face training set of images of K the image block of distance minimum；

When performing step 4.2b for the first time, estimate high-definition picture blockBy estimating high-resolution human face imageAfter Bicubic is upsampled to high-definition picture size, fetch bit put (p, q) on image block obtained by；

Step 4.2c, utilizes minimum K the image block of distance in step 4.2b gained high-definition picture block dictionary at low point The image block of low resolution corresponding in resolution face sample block space, to facial image blockCarry out linear reconstruction, It is as follows to the weight coefficient of linear reconstruction,

$\begin{array}{cc}s.t.& {\mathrm{\Σ}}_{k\∈N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\left(p,q\right)\right)}{w}_{t,k}^{b\left(s\right)}(p,q)=1\end{array},$

Wherein, k represents call number, and its span is in setIn, y_k(p q) represents high-resolution human In face training set of images kth open high-resolution human face sample image position (p, q) on image block,Represent high score Image block y in resolution facial image training set_k(p, q) corresponding to reconstruction weights coefficient,Return about variableFunction when obtaining minimaValue,Represent optimal reconstruction weight,Represent To two norms | | | |₂Result squared, " ο " represents the inner product operation between two vectors, and τ is Equilibrium fitting error drawn game The regularization parameter of portion's constraint,Represent the summation of bracket interior element；

Step 4.2d, is obtaining optimal reconstruction weightAfter, rebuild new high-definition picture block by following formula

$y_t^{b(s+1)}(p,q)=\underset{k\∈N_{t,K}^{b\left(s\right)}\left(y_t^{b\left(s\right)}\right(p,q\left)\right)}{\Σ}{\hat{w}}_{t,k}^{b\left(s\right)}(p,q)y_k(p,q)$

Step 4.2e, it may be judged whether s=S-1, the most then stop iterative process, and last iteration obtainsIf No, then make s=s+1, and return step 4.2b and carry out next iteration, and use current iteration to perform step 4.2d gainedUsed when performing step 4.2b as next iteration estimate high-definition picture block

Will be to estimating high-resolution human face imageMiddle face images blockWeight the high-resolution reconstructed respectively Rate image blockAccording to position superposition, then divided by the number of times that each location of pixels is overlapping, reconstruct high-resolution human Face image