CN103871041A - Image super-resolution reconstruction method based on cognitive regularization parameters - Google Patents

Abstract

The invention discloses an image super-resolution reconstruction method based on cognitive regularization parameters. A human eye cognition theory is used for calculating appropriate regularization parameters for all image blocks, and the regularization parameters are called as the cognitive regularization parameters and introduced into the process of solving sparse representation, then in combination with the super-resolution reconstruction method based on sparse representation, all the blocks are reconstructed, and finally all the reconstructed blocks are recombined to obtain a high-resolution image. The image super-resolution reconstruction method is used for testing in a facial image, and the result shows that the method has a better image reconstruction effect than that of a method using fixed regularization parameters.

Description

The image super-resolution reconstructing method building based on cognitive regularization parameter

Technical field

What the present invention relates to is a kind of technical field of image processing, specifically a kind of image super-resolution reconstructing method building based on cognitive regularization parameter.

Background technology

Along with the development of information age, information obtain and be treated as more and more important problem.For image, the resolution of image has represented the quantity of information that image comprises.Image resolution ratio is higher, and the detailed information that can provide is just abundanter, also just more accurate, careful to the description of objective scene.Because sensor manufacturing technology has run into bottleneck, traditional pass through to improve hardware configuration to improve the method for image resolution ratio no longer applicable.Under such background, super-resolution reconstruction (Super-Resolution Reconstruction, SRR) provide a new solution by Digital Signal Processing for this difficult problem, its target is the frequency component of having lost by recovering some, realize digital picture from low resolution (Low-Resolution, LR) image is to the conversion of high resolving power (High-Resolution, HR) image.

Image super-resolution reconstructing method mainly can be divided into the algorithm based on frequency domain and the algorithm based on spatial domain.Super-resolution reconstruction based on frequency domain is mainly to solve interpolation problem on the frequency change territory of image, by eliminating the spectral aliasing of low-resolution image, carry out realize target, it be a kind of intuitively, go distortion method, but be subject to the restriction of Fourier transform theory, and do not comprise the prior-constrained information of image, thereby its development is greatly limited, and reconstruct poor effect.In view of the above-mentioned limitation of frequency domain method, current research is all carried out substantially in spatial domain.Super-resolution reconstruction based on spatial domain need to consider to affect the spatial domain factor of imaging effect, comprise optical dimming and motion blur etc., and it is set up to observation model flexibly, it can comprise abundant prior-constrained information, thereby can obtain better reconstruct effect.Algorithm based on spatial domain can be divided into again based on interpolation, based on reconstruction and the method based on study.

In recent years, the ultra-resolution ratio reconstructing method based on study becomes the study hotspot in field for this reason, and aspect single-frame images reconstruct, is showing outstanding effect.Method based on study is to collect to contain and the high low-resolution image pair of low-resolution image with category information, composing training set, and analyze its corresponding statistical relationship, retrain super-resolution reconstruction process as priori.Its thought is still obtains priori, but source is not limited only to low-resolution image itself, also comprises the statistics of some approximate images.Its advantage is to take full advantage of the prior imformation of image, in the situation that not increasing input picture sample size, still can produce new high frequency details, obtains than the better reconstruct effect of other ultra-resolution ratio reconstructing methods.

Through the literature search of prior art is found, along with the theoretical development of compressed sensing (Compressive Sensing, CS), the people such as Jianchao Yang have proposed the super-resolution reconstruction algorithm based on rarefaction representation.This algorithm projects to high low-resolution image piece on identical rarefaction representation through different super complete dictionaries, and breakthrough point using this as study and reconstruct, has obtained good reconstruct effect.In this algorithm, the regularization parameter λ that solves rarefaction representation use is mainly for the sparse property of the required solution vector α of balance and the approximate evaluation fidelity of reconstruction result.Can find by emulation experiment, for different images, optimum regularization parameter λ value is not identical, and this is relevant to the textural characteristics of image.Therefore, using fixing regularization parameter is not optimum solution.And human eye cognitive theory shows the response difference of human eye to image different texture feature, for this reason, image can be divided into three kinds of dissimilar regions: (1) strong edge regions, in this region, brightness of image changes greatly and is obvious, and this type of region comes across the profile place of picture material more; (2) texture region, in this region, brightness of image exists and changes by a small margin and constantly repeatedly change; (3) smooth region, in this region, brightness of image changes littlely and not obvious, is common in the background area of image, as large stretch of sky etc.Strong edge regions can provide more image outline information; On the other hand, if smooth region goes wrong or comprises noise, can produce larger impact to observer's visual experience.Therefore, introducing human eye cognitive theory can effectively solve the optimization problem of regularization parameter λ in sparse vector solution procedure.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art, a kind of image super-resolution reconstructing method building based on cognitive regularization parameter is provided.

Technical solution of the present invention is as follows:

A kind of image super-resolution reconstructing method building based on cognitive regularization parameter, its feature is, first, pending low-resolution image is carried out to piecemeal, utilize human eye cognitive theory, according to the textural characteristics of each image block, calculate respectively suitable regularization parameter, i.e. described cognitive regularization parameter; Then, the cognitive regularization parameter building is incorporated in the solution procedure of rarefaction representation, then in conjunction with the reconstructing method based on rarefaction representation, all piecemeals is carried out to super-resolution reconstruction; Finally, all piecemeals of recombinating obtain high-definition picture.

The detailed process of the inventive method comprises the following steps:

1) the single width low-resolution image Y of input N × M size ₀, adopt bicubic interpolation method to be amplified doubly (establishing a is the enlargement factor of expecting, a is positive integer and a>1) of a, obtain matrix Y ∈ R ^{aN × aM};

2) matrix Y piecemeal is extracted to feature, obtain set of eigenvectors U{t ₁, t ₂..., t _q, wherein Q=a (N-4) * a (M-4);

3) the cognitive regularization parameter λ of the each piecemeal of compute matrix Y _i, wherein i=1,2 ..., Q;

4) traversal set of eigenvectors U{t ₁, t ₂..., t _q, to each vectorial t _i(1≤i≤Q) arranges the cognitive regularization parameter λ of its correspondence _i, solve rarefaction representation, then carry out super-resolution reconstruction, obtain the proper vector z of corresponding high-definition picture _i.When having traveled through all proper vector t _iafter, just obtain the blocking characteristic vector set V{z of reconstruct high-definition picture ₁, z ₂..., z _q;

5) according to high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _qand matrix Y, restructuring obtains high-definition picture Z ';

6) adopt iterative backprojection method to carry out overall reconstruct to Z ', further remove fuzzy and noise, finally obtain high-definition picture Z;

7) output high-definition picture Z.

The single width low-resolution image Y of described step 1) input N × M size ₀, and adopt bicubic interpolation method to carry out super-resolution pre-service, and amplified a doubly, obtain matrix Y ∈ R ^{aN × aM}, be specially:

1.1) the single width low-resolution image of input N × M size,

1.2) judge that low-resolution image is gray level image or coloured image, judge the dimension d in image array space,

In the time of d=2, low-resolution image is gray level image, is amplified to a doubly by bicubic interpolation method, obtains matrix Y ∈ R ^{aN × aM};

In the time of d=3, low-resolution image is coloured image, first it is carried out to color space conversion, and it is transformed into YCbCr space from rgb space, and conversion formula is:

I _Y=0.299*I _R+0.587*I _G+0.114*I _B

I _Cb=0.564*(I _B-Y)

I _Cr=0.713*(I _R-Y)

Wherein I _r, I _gand I _brepresent respectively low-resolution image Y ₀at 3 components of rgb space, I _y, I _cband I _crrepresent respectively low-resolution image Y ₀at 3 components in YCbCr space, then to I _y, I _cband I _crthese 3 components adopt respectively bicubic interpolation method to amplify a doubly, obtain matrix I _y∈ R ^{aN × aM}, I _cb∈ R ^{aN × aM}and I _cr∈ R ^{aN × aM}.Make Y=I _y, obtain matrix Y ∈ R ^{aN × aM}.

Described bicubic interpolation method, its concrete steps are as follows:

(a) establishing input matrix is Y=[g ₁, g ₂..., g _m], Y ∈ R ^{n × M}, wherein g _i∈ R ⁿthe i column vector of representing matrix Y (i=1,2 ..., M).Expand matrix Y, concrete steps are: first make Y ₁=[g ₁, g ₁, Y, g _m, g _m]=[h ₁, h ₂..., h _n] ^t, wherein h _j∈ R ^m+4representing matrix Y ₁j row vector (j=1,2 ..., N); Then make Y ₂=[h ₁, h ₁, Y ₁, h _n, h _n] ^t; Finally make Y=Y ₂.

(b) establishing enlargement factor is a, output matrix X ∈ R ^{aN × aM}in each element be calculated as follows:

X(i,j)=A*B*C

Wherein: i=1,2 ..., aN, j=1,2 ..., aM

A=[S(1+u)S(u)S(1-u)S(2-u)]

$B=\left[\begin{array}{cccc}Y(p-1,q-1)& Y(p-1,q)& Y(p-1,q+1)& Y(p-1,q+2)\\ Y(p,q-1)& Y(p,q)& Y(p,q+1)& Y(p,q+2)\\ Y(p+1,q+1)& Y(p+1,q)& Y(p+1,q+1)& Y(p+1,q+2)\\ Y(p+2,q-1)& Y(p+2,q)& Y(p+2,q+1)& Y(p+2,q+2)\end{array}\right]$

C=[S(1+v)S(v)S(1-v)S(2-v)]

$S\left(x\right)=\left\{\begin{array}{c}1-2{\left|x\right|}^2+{\left|x\right|}^3,\left|x\right|<1\\ 4-8\left|x\right|+5{\left|x\right|}^2-{\left|x\right|}^3,1\&le;\left|x\right|<2\\ 0,\left|x\right|\&GreaterEqual;2\end{array}\right.$

U=(i%a)/a(% represents modulo operation)

v=(j%a)/a

P=[i/a]+2([] represent downward rounding operation)

q=[j/a]+2

Described step 2) obtain the set of eigenvectors U of matrix Y, be specially:

2.1) 1 rank of horizontal direction and 1 rank of 2 ladder degree eigenmatrixes and vertical direction and the 2 ladder degree eigenmatrixes of difference compute matrix Y, obtain 4 eigenmatrixes and be respectively T _h1, T _h2, T _v1and T _v2, its dimension is identical with Y, and its process is:

2.1.1) 1 ladder degree matrix T of the horizontal direction of described compute matrix Y _h1method as follows:

If filter operator is f ₁=[1,0,1], calculate convolution:

T ₁=Y*f ₁

Obtain T ₁∈ R ^{aN × (aM+2)}, delete the 1st row and (aM+2) row, obtain T _h1∈ R ^{aN × aM};

2.1.2) 1 ladder degree matrix T of the vertical direction of described compute matrix Y _v1method as follows:

If filter operator is

, calculate convolution:

T ₂=Y*f ₂

Obtain T ₂∈ R ^{(aN+2) × aM}, delete the 1st row and (aN+2) OK, obtain T _v1∈ R ^{aN × aM};

2.1.3) 2 ladder degree matrix T of the horizontal direction of described compute matrix Y _h2method as follows:

If filter operator is f ₃=[1,0 ,-2,0,1], calculate convolution:

T ₃=Y*f ₃

Obtain T ₃∈ R ^{aN × (aM+4)}, delete the 1st row, the 2nd row, (aM+3) row and (aM+4) row, obtain T _h2∈ R ^{aN × aM};

2.1.4) 2 ladder degree matrix T of the vertical direction of described compute matrix Y _v2method as follows:

If filter operator is

calculate convolution:

T ₄=Y*f ₄

Obtain T ₄∈ R ^{(aN+4) × aM}, delete the 1st row, the 2nd row, (aN+3) row and (aM+4) OK, obtain T _v2∈ R ^{aN × aM};

2.2) to matrix T _h1proceed as follows: the T that filter width is a _h1edge, obtain matrix T ｀ _h1∈ R ^{a (N-2) × a (M-2)}; Ergodic Matrices T ' according to the order of sequence _h1in element, get piecemeal

and be converted into vector

(wherein i=1,2 ..., Q, and Q=a (N-4) * a (M-4)), obtain vector set

being implemented as follows of aforesaid operations:

2.2.1) T that described filter width is a _h1edge, refer to puncture table T _h11st～a capable, the aN-a+1～aN is capable, 1st～a row and the aM-a+1～aM row, obtains T ' _h1∈ R ^{a (N-2) × a (M-2)};

2.2.2) described traversal according to the order of sequence refers to: by order from left to right, from top to bottom, Ergodic Matrices T ' successively _h1element;

Described piecemeal is chosen and is referred to: if this pixel coordinate (p, q) that traversal arrives meets:

1≤p≤a* (N-2)-b+1 and 1≤q≤a* (M-2)-b+1

P and q are integer, and establishing point block size is b × b, and the left upper apex take this pixel as piecemeal, cuts apart and obtain piecemeal

then merge in order

b row vector, obtain vector

so just obtain vector set

2.3) similar, to T _h2, T _v1and T _v2carry out identical operation, obtain respectively vector set

with

2.4) travel through U simultaneously _h1, U _h2, U _v1and U _v2four set, merge vector

with

obtain vector

(wherein i=1,2 ..., Q),

So just obtain the set of eigenvectors U{t of matrix Y ₁, t ₂..., t _q.

The cognitive regularization parameter λ of the described each piecemeal of step 3) compute matrix Y _i, detailed process is as follows:

3.1), according to human eye cognitive theory, calculate the texture cognitive model coefficient of each pixel in Y:

3.1.1) Y is carried out to wavelet transformation, every one-level wavelet transformation can form 4

the subgraph of size, is respectively low-frequency approximation component L, vertical high frequency details component H _v, horizontal high frequency details component H _h, diagonal angle high frequency details component H _d.

3.1.2) calculating contrast image

$C=\frac{C_v+C_h+C_d}{3}$

Wherein,

for vertical contrast,

for horizontal contrast,

for diagonal angle contrast.From definition, the Wavelet Contrast C on different directions _v, C _hand C _dembody respectively the contrast of its corresponding low frequency component of high frequency (background luminance) of image different directions, considered the contrast situation of prospect and background simultaneously, thereby reflected each pixel difference visually in image.Then adopt the bicubic differential technique described in step 1) to amplify 2 times to C, obtain the contrast image C ∈ R of Y ^{aN × aM}

3.1.3) for the different texture region of image, super-resolution reconstruction operates the emphasis difference of paying close attention to.For strong edge regions, in super-resolution reconstruction, want refinement details, corresponding regularization parameter will be got smaller value; And for smooth region, requiring the result after super-resolution reconstruction more level and smooth, regularization parameter will be got larger value.For this reason, the cognitive texture model coefficient Q that structure location of pixels (k, s) is located _k,sfor:

$Q_{k,s}=\mathrm{\&rho;}\underset{(\mathrm{\&mu;},\mathrm{\&eta;})\&Element;\mathrm{neighborhood\; of}(k,s)}{\mathrm{\&Sigma;}}\frac{\left|C_{\mathrm{\&mu;},\mathrm{\&eta;}}\right|}{\left|n_{k,s}\right|}{F}_{\mathrm{\&mu;},\mathrm{\&eta;}}$

Wherein, ρ is normalized parameter, the span of texture model matrix of coefficients Q is approximately fixed between [0,1], neighborhood of (k, s) represent (k, s) neighborhood, it is defined as point centered by pixel (k, s), size is the rectangular area of (2 δ+1) × (2 θ+1), and δ, θ are positive integer; | n _k,s| be the number of wavelet coefficient in (k, s) neighborhood; C _{μ, η}represent the luminance contrast that position (μ, η) is located, by 3.1.2) calculate F _{μ, η}represent the coefficient fluctuation degree in neighborhood (2 δ+1) × (2 θ+1), it is defined as:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}=0.5F_{\mathrm{\&mu;},\mathrm{\&eta;}}^h+0.5F_{\mathrm{\&mu;},\mathrm{\&eta;}}^v$

Wherein,

for level fluctuation degree, be defined as:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}^h=\frac{1}{2\mathrm{\&delta;}+1}\underset{m=\mathrm{\&mu;}-\mathrm{\&delta;}}{\overset{\mathrm{\&mu;}+\mathrm{\&delta;}}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Sigma;}}_{n=\mathrm{\&eta;}-\mathrm{\&theta;}}^{\mathrm{\&eta;}+\mathrm{\&theta;}-1}|C_{m,n}-C_{m,n+1}|}{{\mathrm{\&Sigma;}}_{n=\mathrm{\&eta;}-\mathrm{\&theta;}}^{\mathrm{\&eta;}+\mathrm{\&theta;}}\left|C_{m,n}\right|}$

for vertical fluctuation degree, be defined as:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}^v=\frac{1}{2\mathrm{\&theta;}+1}\underset{n=\mathrm{\&eta;}-\mathrm{\&theta;}}{\overset{\mathrm{\&eta;}+\mathrm{\&theta;}}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Sigma;}}_{m=\mathrm{\&mu;}-\mathrm{\&delta;}}^{\mathrm{\&mu;}+\mathrm{\&delta;}-1}|C_{m,n}-C_{m+1,n}|}{{\mathrm{\&Sigma;}}_{m=\mathrm{\&mu;}-\mathrm{\&delta;}}^{\mathrm{\&mu;}+\mathrm{\&delta;}}\left|C_{m,n}\right|}$

Wherein, the wavelet coefficient of texture region generally speaking undulatory property is larger, and smooth region wavelet coefficient is less and it is milder to change, and the wavelet coefficient of strong edge regions exists a peak value, at the two ends of peak value, is monotone variation substantially.Therefore the fluctuation degree of wavelet coefficient can become a whether important indicator in texture region of this position of process decision chart picture.In addition, the model coefficient of borderline region is set to 0.

3.2) calculate the cognitive regularization parameter λ of each image block _i;

In the technical program, obtained the cognitive regularization parameter λ of this piecemeal by the mean value calculation of the texture model coefficient of each pixel of each image block _i:

${\mathrm{\&lambda;}}_i=\frac{\text{1}}{\text{\&gamma;}}(1-\frac{1}{b^2}\underset{(k,s)\&Element;\mathrm{patch}}{\mathrm{\&Sigma;}}{Q}_{k,s})$

Wherein, b ²what represent is a point block size, and γ adjusts the factor.Because Q _{k, s ∈}[0,1], so

γ is mainly used to adjust λ _imaximal value.For the less picture of noise, γ can be set to higher value, guarantees Image Reconstruction quality; For the larger picture of noise, γ can be set to smaller value, effectively to remove the noise in image.The method of the cognitive regularization parameter of above-mentioned calculating, only need once calculate, and has avoided each piecemeal to complete the problem that will re-start iteration after super-resolution reconstruction, and computation complexity reduces greatly.

{ the λ obtaining as stated above ₁, λ ₂..., λ _qand U{t ₁, t ₂..., t _qcorresponding one by one.

Described step 4) is obtained high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _q, be specially traversal set of eigenvectors U{t ₁, t ₂..., t _q, to vectorial t _iproceed as follows:

4.1) make y=t _i, utilize low-resolution image dictionary D _ly is carried out to rarefaction representation, can be written as:

min:‖α‖ ₀

$s.t.:{\left|\right|{\mathrm{FD}}_{\text{l}}\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\&le;\&Element;$

Wherein, F is that linear feature extracts operator, and it can the sparse factor alpha of exact constrain and the distance of y.Because α is enough sparse, and D _lmeet limited equidistant character (Restricted Isometry Property, RIP), so above formula can be converted into minimum 1-norm problem:

min:‖α‖ ₁

$s.t:{\left|\right|{\mathrm{FD}}_l\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\&le;\&Element;$

Recycling lagrange's method of multipliers is converted into formula:

Wherein, cognitive regularization parameter λ _icalculated the sparse property that its balance is understood and the approximate evaluation fidelity of y by step 3).On the other hand, due to the overlapping problem of piecemeal, need to consider to make D _hα, with reconstruct high resolving power piecemeal overlapping region is out as far as possible approaching, so improve constraint condition is:

min: ‖α‖ ₁

$s.t.:\begin{array}{c}{\left|\right|{\mathrm{FD}}_l\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\&le;\&Element;1\\ {\left|\right|{\mathrm{PD}}_l\mathrm{\&alpha;}-w\left|\right|}_2^2\&le;\&Element;2\end{array}$

Wherein, matrix P is for extracting current piecemeal and overlapping between reconstruct high-definition picture, and w has comprised the overlapping value of reconstruct high-definition picture.And then can be optimized for:

$\underset{\mathrm{\&alpha;}}{\min }{\text{||}\tilde{D}\text{\&alpha;-}\tilde{y}\text{||}}_2^2+{\mathrm{\&lambda;}}_i{\left|\right|\mathrm{\&alpha;}\left|\right|}_1$

Wherein

low-resolution image input can be controlled by parameter beta, a high-definition picture piece mating with the adjacent piecemeal that reconstruct is good can be found.

According to the method described above, can try to achieve the solution α of rarefaction representation ^*.

4.2) according to x=D _hα ^*try to achieve x, make z _i=x, can obtain the estimation z of high-definition picture blocking characteristic vector _i.

After having traveled through, just obtain high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _q.

Above-mentioned used dictionary is to D _hand D _lobtained by precondition, the method for training is as follows:

(a) first collect image that the resolution close with picture material to be tested of some is higher as high resolving power training plan image set.Down-sampled by high-definition picture being carried out to bicubic, dwindle a doubly, thereby obtain corresponding low resolution training plan image set;

Described bicubic is down-sampled, be enlargement factor be 1/a described 1.2) in bicubic interpolation method;

(b) obtain the set of eigenvectors of all low resolution training images, concrete grammar and step 2) consistent; Be provided with n and open low resolution training image, obtain n vector set

this n vector set is merged into a set Y in order ^l;

(c) obtain the set of eigenvectors of all high resolving power training images, concrete grammar is: first adopt described bicubic interpolation method, by low-resolution image L _i(i=1,2 ..., n) interpolation amplification a doubly, obtains M _i(i=1,2 ..., n); Then calculate high-definition picture H _iwith M _idifference, obtain Dif _i=H _i-M _i; Afterwards according to step 2.2) in to T _h1processing mode to Dif _icarry out identical processing, obtain vector set (i=1,2 ..., n), obtain so altogether n vector set then this n vector set is merged in order to a set X ^h;

(d) in order to train two super complete dictionary D of high low resolution _hand D _l, and these two dictionaries will guarantee that the rarefaction representation of corresponding high low-resolution image piece is identical, list system of equations:

$\left\{\begin{array}{c}{D}_h=\arg \underset{D_h,\mathrm{\&Phi;}}{\min }{\left|\right|X^h{-D}_h\mathrm{\&Phi;}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1\\ D_1=\arg \underset{D_{l,}\mathrm{\&Phi;}}{\min }{\left|\right|Y^l-D_l\mathrm{\&Phi;}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1\end{array}\right.$

And to be combined be a formula:

$\underset{\{D_h,D_l,\mathrm{\&Phi;}\}}{\min }\frac{1}{b^2}{\left|\right|X^h-D_h\mathrm{\&Phi;}\left|\right|}_2^2+\frac{1}{{4b}^2}{\left|\right|Y^1-D_1\mathrm{\&Phi;}\left|\right|}_2^2+\mathrm{\&lambda;}(\frac{1}{b^2}+\frac{1}{{4b}^2}){\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

Wherein, tile size is b × b, and Φ is rarefaction representation matrix.Merge D _hand D _l, can obtain

$\underset{\{D_h,D_l,z\}}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2+\widehat{\mathrm{\&lambda;}}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

Wherein, $X_C=\left[\begin{array}{c}\frac{1}{b}{X}^h\\ \frac{1}{2b}{Y}^l\end{array}\right],D_C=\left[\begin{array}{c}\frac{1}{b}{D}_h\\ \frac{1}{2b}{D}_l\end{array}\right],\widehat{\mathrm{\&lambda;}}=\mathrm{\&lambda;}(\frac{1}{b^2}+\frac{1}{{4b}^2}),$ As fixing D _cduring with in Φ one, solve another and can be converted into the optimum solution problem that solves, so can be to D _creplace iteration optimization with Φ, concrete grammar is as follows:

(i) by D _cbe initialized as gaussian random matrix, and each row is standardized;

(ii) fix D _c, upgrade Φ by following formula:

$\mathrm{\&Phi;}=\underset{z}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2+\widehat{\mathrm{\&lambda;}}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

(iii) fix Φ, upgrade D by following formula _c:

$\begin{array}{c}{D}_C=\arg \underset{D_C}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2\\ s.t.{\left|\right|D_i\left|\right|}_2^2\&le;l,i=\mathrm{1,2},...,K\end{array}$

Wherein D _irepresent D _ci row vector, K represents D _crow vector number;

(iv) iterate (ii) and (iii) until convergence;

(v) obtain D _cbe the super complete dictionary of requirement, decompose and obtain D _hand D _i.

Described step 5) is according to high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _qand matrix Y, restructuring obtains high-definition picture Z ', is specially:

5.1) the proper vector z to all high-definition picture piecemeals _i∈ V, is divided into b isometric vector, then, using this b vector as row vector, is merged in order the piecemeal Z of b × b size _i, wherein i=1,2 ..., Q.Obtain like this partitioned matrix set { Z ₁, Z ₂..., Z _q;

5.2) by all partitioned matrix set Z _ibe merged into a matrix Z ' ∈ R ^{a (N-2) × a (M-2)}, concrete grammar is as follows:

Make Z '=0, E=0, Z ' ∈ R ^{a (N-2) × a (M-2)}, E ∈ R ^{a (N-2) × a (M-2)}, i=1, by order from left to right, from top to bottom, the element of Ergodic Matrices Z ' successively, if this pixel coordinate (p, q) traversing meets:

1≤p≤a* (N-2)-b+1 and 1≤q≤a* (M-2)-b+1

Wherein p and q are integer, order:

Z‘(p:(p+b-1),q:(q+b-1))=Z‘(p:(p+b-1),q:(q+b-1))+Z _i

i=i+1

Each element of matrix E is used for the accumulative frequency of the pixel of the correspondence position that records matrix Z ', after traversal finishes, superposition image vegetarian refreshments between piecemeal is got to average, and each element value of order matrix Z ', divided by the element value of the correspondence position of matrix E, finally obtains Z ';

5.3) Z ' is added to middle a (N-2) × a (M-2) region of Y, gained new images assignment is Z ', obtains Z ' ∈ R ^{aN × aM}.

Described step 6) adopts iterative backprojection method to carry out overall reconstruct to Z ', further removes fuzzy and noise, finally obtains high-definition picture Z.Described iterative backprojection method, is specially and solves following formula optimization problem:

$Z=\underset{\text{Z}}{\min }{\left|\right|\mathrm{\&Theta;\&Psi;Z}-Y_0\left|\right|}_2^2+c{\left|\right|Z-Z^{\&prime;}\left|\right|}_2^2$

Wherein Ψ represents fuzzy matrix, and Θ represents down-sampled matrix, Y ₀for the low-resolution image of N × M size of input.

Described step 7) output high-definition picture Z, specific as follows:

If input picture is black white image, the Z obtaining in step 6) is the image obtaining after super-resolution reconstruction;

If input picture is coloured image, make I _y=Z, by (I _y, I _cb, I _cr) be transformed into rgb color space, that is:

I _R=I _Y+1.402I _Cr

I _G=Z-0.344I _Cb-0.714I _Cr

I _B=I _Y+1.772I _Cb

Then make Z=(I _r, I _g, I _b) ∈ R ^{aN × aM × 3}, be the high-definition picture finally obtaining.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is the test result contrast of the present invention and other algorithms, and wherein (a) is low-resolution image, (b) is true high-definition picture, (c), for using the result of fixing regularization parameter value (λ=0.2) method, (d) is the inventive method result.

Embodiment

Below describe by reference to the accompanying drawings the present invention in detail and be applied to the specific embodiment of the super-resolution reconstruction of facial image.

The present embodiment uses face picture as training atlas and test pattern.The training atlas using comes from Georgia Institute of Technology's face database (Georgia Tech Face Database), the face picture that this face database has comprised 50 people, everyone comprises again 15 images of different angles, expression, picture format is JPG, and in image, the size of face is about 150 × 150 pixels.

The present embodiment has been chosen first two in the picture of front 40 people in this face database, totally 80 images are as training atlas, test pattern is chosen at random from remaining 10 people's image, and the present embodiment selects Fig. 2 (b) as test pattern, and size is 136 × 190.The expectation enlargement factor of the present embodiment is made as 2, and detailed process is as follows:

1) Fig. 2 (b) is carried out to bicubic down-sampled, dwindle 2 times, obtain Fig. 2 (a) of 68 × 95 sizes.Fig. 2 (a) is as the input low-resolution image of ultra-resolution ratio reconstructing method; And Fig. 2 (b) is as real high-definition picture, compare for the high-definition picture obtaining with reconstruct.40 training images selecting are as high resolving power training plan image set.Down-sampled by high-definition picture being carried out to bicubic interpolation, dwindle 2 times, thereby obtain corresponding low resolution training plan image set.

Because Fig. 2 (a) is coloured image, first it is carried out to color space conversion, it is transformed into YCbCr space from rgb space, adopt respectively bicubic interpolation algorithm to amplify 2 times to Y, Cb and these 3 components of Cr, obtain matrix Y ∈ R ^{136 × 190}, Cb ∈ R ^{136 × 190}with Cr ∈ R ^{136 × 190}, temporarily preserve Cb and Cr.

2) establishing point block size is 5 × 5, and overlapping size is 4, obtains the set of eigenvectors U{t of Y ₁, t ₂..., t ₂₃₂₉₆, specific as follows:

2.1) 1 rank of horizontal direction and 1 rank of 2 ladder degree eigenmatrixes and vertical direction and the 2 ladder degree eigenmatrixes of difference compute matrix Y, obtain 4 eigenmatrixes and be respectively T _h1, T _h2, T _v1and T _v2;

2.2) to matrix T _h1proceed as follows:

2.2.1) puncture table T _h11st～2 row, 189～190 row, 1st～2 row and 189th～190 row, obtain T ' _h1∈ R ^{132 × 186};

2.2.2) press order from left to right, from top to bottom, Ergodic Matrices T ' successively _h1element, if this pixel coordinate (p, q) traversing meet:

1≤p≤128 and 1≤q≤182

Wherein p and q are integer, and the left upper apex take this pixel as piecemeal, cuts apart and obtain piecemeal

then merge in order

5 row vectors, obtain vector

so just obtain vector set $U_{h1}=\{t_{h1}^1,t_{h1}^2,...,t_{h1}^{23296}\};$

2.3) to T _h2, T _v1and T _v2carry out above-mentioned 2.2) identical operation, obtain respectively vector set

with

2.4) travel through U simultaneously _h1, U _h2, U _v1and U _v2four set, merge vector with

obtain vectorial t _i∈ R ¹⁰⁰(wherein i=1,2 ..., 23296),

so just obtain the set of eigenvectors U{t of matrix Y ₁, t ₂..., t ₂₃₂₉₆.

3) the cognitive regularization parameter λ of the each piecemeal of compute matrix Y _i, detailed process is as follows:

3.1) according to human eye cognitive theory, the texture cognitive model coefficient of each pixel in compute matrix Y, concrete steps are as follows:

3.1.1) matrix Y is carried out to wavelet transformation, every one-level wavelet transformation forms the subgraph of 4 68 × 95 sizes, is respectively low-frequency approximation component L, vertical high frequency details component H _v, horizontal high frequency details component H _h, diagonal angle high frequency details component H _d;

3.1.2) calculate contrast image C ∈ R ^{68 × 95}:

$C=\frac{C_v+C_h+C_d}{3}$

Wherein, for vertical contrast,

for horizontal contrast,

for diagonal angle contrast;

Adopt bicubic differential technique to amplify 2 times to C, obtain the contrast image C ∈ R of matrix Y ^{136 × 190};

3.1.3) the cognitive texture model coefficient Q that calculating pixel point (k, s) is located _k,s, formula is as follows:

$Q_{k,s}=\mathrm{\&rho;}\underset{(\mathrm{\&mu;},\mathrm{\&eta;})\&Element;\mathrm{neighborhood\; of}(k,s)}{\mathrm{\&Sigma;}}\frac{\left|C_{\mathrm{\&mu;},\mathrm{\&eta;}}\right|}{9}{F}_{\mathrm{\&mu;},\mathrm{\&eta;}}$

Wherein, ρ is normalized parameter, make the span of texture model matrix of coefficients Q approximately fix on [0,1], between, neighborhood of (k, s) represents (k, s) neighborhood, it is defined as centered by pixel (k, s) point, the size rectangular area as 3 × 3, C _{μ, η}the contrast size that position (μ, η) is located, F _{μ, η}it is the coefficient fluctuation degree in neighborhood 3 × 3.F _{μ, η}computing formula be:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}=0.5F_{\mathrm{\&mu;},\mathrm{\&eta;}}^h+0.5F_{\mathrm{\&mu;},\mathrm{\&eta;}}^v$

Wherein, level fluctuation degree

computing formula be:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}^h=\frac{1}{3}\underset{m=\mathrm{\&mu;}-1}{\overset{\mathrm{\&mu;}+1}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Sigma;}}_{n=\mathrm{\&eta;}-1}^{\mathrm{\&eta;}}|C_{m,n}-C_{m,n+1}|}{{\mathrm{\&Sigma;}}_{n=\mathrm{\&eta;}-1}^{\mathrm{\&eta;}+1}\left|C_{m,n}\right|}$

Vertical fluctuation degree

computing formula be:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}^v=\frac{1}{3}\underset{n=\mathrm{\&eta;}-1}{\overset{\mathrm{\&eta;}+1}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Sigma;}}_{m=\mathrm{\&mu;}-1}^{\mathrm{\&mu;}}|C_{m,n}-C_{m+1,n}|}{{\mathrm{\&Sigma;}}_{m=\mathrm{\&mu;}-1}^{\mathrm{\&mu;}+1}\left|C_{m,n}\right|}$

3.2) obtained the cognitive regularization parameter λ of this piecemeal by the mean value calculation of each 5 × 5 image block texture model coefficient _i:

${\mathrm{\&lambda;}}_i=\frac{1}{\mathrm{\&gamma;}}(1-\frac{1}{5^2}\underset{(k,s)\&Element;\mathrm{patch}}{\mathrm{\&Sigma;}}{Q}_{k,s})$

Wherein establish γ=5, so just can be in the hope of λ _i∈ [0,0.2].

4) traversal U{t ₁, t ₂..., t ₂₃₂₉₆, to t _i(i=1,2 ..., 23296) proceed as follows:

First solve following formula:

$\underset{\mathrm{\&alpha;}}{\min }{\text{||}\tilde{D}\text{\&alpha;-}\tilde{y}\text{||}}_2^2+{\mathrm{\&lambda;}}_i{\left|\right|\mathrm{\&alpha;}\left|\right|}_1$

Wherein

f is that linear feature extracts operator, and matrix P is for extracting current piecemeal and overlapping between reconstruct high-definition picture piece, and w has comprised the overlapping value of reconstruct high-definition picture piece, setting parameter β=1.Can obtain the solution α of rarefaction representation ^*.

Then according to x=D _hα ^*try to achieve x, make z _i=x, can obtain the estimation z of high-definition picture blocking characteristic vector _i.

After having traveled through, just obtain high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _q.

Above-mentioned used dictionary is to D _hand D _lobtained by precondition, the process of training is as follows:

The first step, the training set of the present embodiment comprises 80 images altogether as mentioned above, sets it as high-definition picture training set, down-sampled by high-definition picture being carried out to bicubic, dwindles 2 times, thereby obtains corresponding low resolution training plan image set;

Second step, obtains the set of eigenvectors of all low resolution training images, concrete grammar and step 2) consistent; Obtain 80 vector sets

this n vector set is merged into a set Y in order ^l;

The 3rd step, obtains the set of eigenvectors of all high resolving power training images, and concrete grammar is: first adopt described bicubic interpolation method, by low-resolution image L _i(i=1,2 ..., 80) and 2 times of interpolation amplifications, obtain M _i(i=1,2 ..., 80); Then calculate high-definition picture H _iwith M _idifference, obtain Dif _i=H _i-M _i; Afterwards according to step 2.2) in to T _h1processing mode to Dif _icarry out identical processing, obtain vector set (wherein i=1,2 ..., 80), obtain so altogether n vector set

then these 80 vector sets are merged in order to a set X ^h;

Finally in order to train two super complete dictionary D of high low resolution _hand D _l, and these two dictionaries will guarantee that the rarefaction representation of corresponding high low-resolution image piece is identical, solve following formula:

$\underset{\{D_h,D_l,z\}}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2+\widehat{\mathrm{\&lambda;}}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

Wherein, $X_C=\left[\begin{array}{c}\frac{1}{5}{X}^h\\ \frac{1}{10}{Y}^l\end{array}\right]{,D}_C=\left[\begin{array}{c}\frac{1}{5}{D}_h\\ \frac{1}{10}{D}_l\end{array}\right],\widehat{\mathrm{\&lambda;}}=\mathrm{\&lambda;}(\frac{1}{25}+\frac{1}{100}),$ If λ=0.15, the dimension of rarefaction representation vector is made as 1024 in addition.Iteration optimization can obtain D after calculating _c, then decompose and can obtain D _h, D _l.

5) the proper vector z to all high-definition picture piecemeals _i, be divided into 5 isometric vectors, then, using these 5 vectors as row vector, be merged in order the piecemeal Z of 5 × 5 sizes _i, wherein i=1,2 ..., 23296.Obtain like this partitioned matrix set { Z ₁, Z ₂..., Z ₂₃₂₉₆.By all piecemeal Z _ibe merged into a matrix, concrete grammar is as follows:

Make Z '=0, F=0, Z ' ∈ R ^{132 × 186}, F ∈ R ^{132 × 186}, i=1, by order from left to right, from top to bottom, the element of Ergodic Matrices Z ' successively, if this pixel coordinate (p, q) traversing meets:

1≤p≤128 and 1≤q≤182

Wherein p and q are integer, order:

Z‘(p:(p+4),q:(q+4))=Z‘(p:(p+4),q:(q+4))+Z _i

i=i+1

Each element of matrix F is used for the accumulative frequency of the pixel of the correspondence position that records matrix Z ', after traversal finishes, superposition image vegetarian refreshments between piecemeal is got to average, and each element value of order matrix Z ', divided by the element value of the correspondence position of matrix E, obtains Z ' ∈ R ^{132 × 186}.By be added to 132 × 186 regions, centre of Y of Z ', result assignment, to Z ', is obtained to Z ' ∈ R ^{136 × 190}.

6) adopt iterative backprojection method to carry out overall reconstruct to Z ', further remove fuzzy and noise, obtain Z.

7) make I _y=Z, by (I _y, I _cb, I _cr) be transformed into rgb color space, that is:

I _R=I _Y+1.402I _Cr

I _G=Z-0.344I _Cb-0.714I _Cr

I _B=I _Y+1.772I _Cb

Then make Z=(I _r, I _g, I _b) ∈ R ^{136 × 190 × 3}, be the high-definition picture finally obtaining, i.e. Fig. 2 (d).

In Fig. 2, (c), (d) figure adopts diverse ways (a) figure to be carried out to the result of super-resolution reconstruction, (c) figure is the result of fixing regularization parameter (λ=0.2) method, and (d) figure is the inventive method result.Both are respectively with respect to the PSNR value of former figure (b): 38.1128 and 39.0157, and the reconstruct effect of visible the inventive method is better than fixing regularization parameter method.

Claims (8)

1. the image super-resolution reconstructing method building based on cognitive regularization parameter, its feature is, first, pending low-resolution image is carried out to piecemeal, utilize human eye cognitive theory, according to the textural characteristics of each image block, calculate respectively cognitive regularization parameter; Then, the cognitive regularization parameter building is incorporated in the solution procedure of rarefaction representation, then in conjunction with the reconstructing method based on rarefaction representation, all piecemeals is carried out to super-resolution reconstruction; Finally, all piecemeals of recombinating obtain high-definition picture.

2. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 1, is characterized in that, the method comprises the steps:

1) the single width low-resolution image Y of input N × M size ₀, adopt bicubic interpolation method to be amplified a doubly, establishing a is the enlargement factor of expecting, a is positive integer and a>1, obtains matrix Y ∈ R ^{aN × aM};

2) matrix Y piecemeal is extracted to feature, obtain the set of eigenvectors U{t of matrix Y ₁, t ₂..., t _q, wherein Q=a (N-4) * a (M-4);

3) the cognitive regularization parameter λ of the each piecemeal of compute matrix Y _i, wherein i=1,2 ..., Q;

Be specially:

3.1) according to human eye cognitive theory, the texture cognitive model coefficient of each pixel in compute matrix Y:

3.1.1) matrix Y is carried out to wavelet transformation, every one-level wavelet transformation can form 4 the subgraph of size, is respectively low-frequency approximation component L, vertical high frequency details component H _v, horizontal high frequency details component H _h, diagonal angle high frequency details component H _d;

3.1.2) calculating contrast image

$C=\frac{C_v+C_h+C_d}{3}$

Wherein, for vertical contrast,

for horizontal contrast,

for diagonal angle contrast;

Bicubic differential technique described in employing step 1) amplifies 2 times to C, obtains the contrast image C ∈ R of matrix Y ^{aN × aM};

3.1.3) calculate the cognitive texture model coefficient Q that structure location of pixels (k, s) is located _k,s, formula is as follows:

$Q_{k,s}=\mathrm{\&rho;}\underset{(\mathrm{\&mu;},\mathrm{\&eta;})\&Element;\mathrm{neighborhood\; of}(k,s)}{\mathrm{\&Sigma;}}\frac{\left|C_{\mathrm{\&mu;},\mathrm{\&eta;}}\right|}{\left|n_{k,s}\right|}{F}_{\mathrm{\&mu;},\mathrm{\&eta;}}$

Wherein, ρ is normalized parameter, the span of texture model matrix of coefficients Q is approximately fixed between [0,1], neighborhood of (k, s) represent (k, s) neighborhood, it is defined as point centered by pixel (k, s), size is the rectangular area of (2 δ+1) × (2 θ+1), and δ, θ are positive integer; | n _k,s| be the number of wavelet coefficient in (k, s) neighborhood; C _{μ, η}represent the luminance contrast that position (μ, η) is located, F _{μ, η}represent the coefficient fluctuation degree in neighborhood (2 δ+1) × (2 θ+1), it is defined as:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}=0.5F_{\mathrm{\&mu;},\mathrm{\&eta;}}^h+0.5F_{\mathrm{\&mu;},\mathrm{\&eta;}}^v$

Wherein,

for level fluctuation degree, be defined as:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}^h=\frac{1}{2\mathrm{\&delta;}+1}\underset{m=\mathrm{\&mu;}-\mathrm{\&delta;}}{\overset{\mathrm{\&mu;}+\mathrm{\&delta;}}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Sigma;}}_{n=\mathrm{\&eta;}-\mathrm{\&theta;}}^{\mathrm{\&eta;}+\mathrm{\&theta;}-1}|C_{m,n}-C_{m,n+1}|}{{\mathrm{\&Sigma;}}_{n=\mathrm{\&eta;}-\mathrm{\&theta;}}^{\mathrm{\&eta;}+\mathrm{\&theta;}}\left|C_{m,n}\right|}$

for vertical fluctuation degree, be defined as:

$F_{\mathrm{\&mu;},\mathrm{\&eta;}}^v=\frac{1}{2\mathrm{\&theta;}+1}\underset{n=\mathrm{\&eta;}-\mathrm{\&theta;}}{\overset{\mathrm{\&eta;}+\mathrm{\&theta;}}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Sigma;}}_{m=\mathrm{\&mu;}-\mathrm{\&delta;}}^{\mathrm{\&mu;}+\mathrm{\&delta;}-1}|C_{m,n}-C_{m+1,n}|}{{\mathrm{\&Sigma;}}_{m=\mathrm{\&mu;}-\mathrm{\&delta;}}^{\mathrm{\&mu;}+\mathrm{\&delta;}}\left|C_{m,n}\right|}$

3.2) calculate the cognitive regularization parameter λ of each piecemeal _i, formula is as follows:

${\mathrm{\&lambda;}}_i=\frac{\text{1}}{\text{\&gamma;}}(1-\frac{1}{b^2}\underset{(k,s)\&Element;\mathrm{patch}}{\mathrm{\&Sigma;}}{Q}_{k,s})$

Wherein, b ²what represent is a point block size, and γ adjusts the factor;

4) traversal set of eigenvectors U{t ₁, t ₂..., t _q, to each vectorial t _i(1≤i≤Q) arranges the cognitive regularization parameter λ of its correspondence _i, solve rarefaction representation, then carry out super-resolution reconstruction, obtain the proper vector z of corresponding high-definition picture _i, when having traveled through all proper vector t _iafter, just obtain the blocking characteristic vector set V{z of reconstruct high-definition picture ₁, z ₂..., z _q;

5) according to the blocking characteristic vector set V{z of high-definition picture ₁, z ₂..., z _qand matrix Y, restructuring obtains high-definition picture Z ';

6) adopt iterative backprojection method to carry out overall reconstruct to high-definition picture Z ', remove fuzzy and noise, the high-definition picture Z being optimized;

7) the high-definition picture Z that output is optimized.

3. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 2, is characterized in that, described step 1) is specially:

1.1) the single width low-resolution image of input N × M size,

1.2) judge that low-resolution image is gray level image or coloured image, judge the dimension d in image array space,

In the time of d=2, low-resolution image is gray level image, is amplified to a doubly by bicubic interpolation method, obtains matrix Y ∈ R ^{aN × aM};

In the time of d=3, low-resolution image is coloured image, first it is carried out to color space conversion, and it is transformed into YCbCr space from rgb space, and conversion formula is:

Y=0.299*R+0.587*G+0.114*B

Cb=0.564*(B-Y)

Cr=0.713*(R-Y)

Wherein, R, G and B represent respectively three components of rgb space, and Y, Cb and Cr represent respectively three components in YCbCr space, then adopt respectively bicubic interpolation algorithm to be amplified to a doubly to this Y, Cb and tri-components of Cr, obtain respectively matrix Y ∈ R ^{aN × aM}, Matrix C b ∈ R ^{aN × aM}with Matrix C r ∈ R ^{aN × aM}, preservation matrix Cb and Cr.

4. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 2, is characterized in that described step 2) be specially:

2.1) 1 rank of horizontal direction and 1 rank of 2 ladder degree eigenmatrixes and vertical direction and the 2 ladder degree eigenmatrixes of difference compute matrix Y, obtain 4 eigenmatrixes and be respectively T _h1, T _h2, T _v1and T _v2, its dimension is identical with Y, and its process is:

2.1.1) 1 ladder degree matrix T of the horizontal direction of described compute matrix Y _h1method as follows:

If filter operator is f ₁=[1,0,1], calculate convolution:

T ₁=Y*f ₁

Obtain T ₁∈ R ^{aN × (aM+2)}, delete the 1st row and (aM+2) row, obtain T _h1∈ R ^{aN × aM};

2.1.2) 1 ladder degree matrix T of the vertical direction of described compute matrix Y _v1method as follows:

If filter operator is

calculate convolution:

T ₂=Y*f ₂

Obtain T _{2 ∈}r ^{(aN+2) × aM}, delete the 1st row and (aN+2) OK, obtain T _v1∈ R ^{aN × aM};

2.1.3) 2 ladder degree matrix T of the horizontal direction of described compute matrix Y _h2method as follows:

If filter operator is f ₃=[1,0 ,-2,0,1], calculate convolution:

T ₃=Y*f ₃

Obtain T ₃∈ R ^{aN × (aM+4)}, delete the 1st row, the 2nd row, (aM+3) row and (aM+4) row, obtain T _h2∈ R ^{aN × aM};

2.1.4) 2 ladder degree matrix T of the vertical direction of described compute matrix Y _v2method as follows:

If filter operator is calculate convolution:

T ₄=Y*f ₄

Obtain T ₄∈ R ^{(aN+4) × aM}, delete the 1st row, the 2nd row, (aN+3) row and (aM+4) OK, obtain T _v2∈ R ^{aN × aM};

2.2) to matrix T _h1proceed as follows: the T that filter width is a _h1edge, obtain matrix T ｀ _h1∈ R ^{a (N-2) × a (M-2)}; Ergodic Matrices T ｀ according to the order of sequence _h1in element, get piecemeal

and be converted into vector

wherein i=1,2 ..., Q, and Q=a (N-4) * a (M-4), obtain vector set

being implemented as follows of aforesaid operations:

2.2.1) T that described filter width is a _h1edge, refer to puncture table T _h11st～a capable, the aN-a+1～aN is capable, 1st～a row and the aM-a+1～aM row, obtains T ｀ _h1∈ R ^{a (N-2) × a (M-2)};

2.2.2) described traversal according to the order of sequence refers to: by order from left to right, from top to bottom, Ergodic Matrices T ｀ successively _h1element;

Described piecemeal is chosen and is referred to: if this pixel coordinate (p, q) that traversal arrives meets:

1≤p≤a* (N-2)-bb1 and 1≤q≤a* (M-2)-b+1

P and q are integer, and establishing point block size is b × b, and the left upper apex take this pixel as piecemeal, cuts apart and obtain piecemeal

then merge in order

b row vector, obtain vector

so just obtain vector set

2.3) to T _h2, T _v1and T _v2carry out identical operation, cut apart and obtain respectively

with

after, then obtain vector set

with $U_{v2}\{t_{v2}^1,t_{v2}^2,...,t_{v2}^Q\};$

2.4) travel through U simultaneously _h1, U _h2, U _v1and U _v2four set, merge vector

with obtain vector wherein i=1,2 ..., Q,

Finally obtain the set of eigenvectors U{t of matrix Y ₁, t ₂..., t _q.

5. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 2, is characterized in that, described step 4) is specially:

Obtain high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _q, be specially traversal set of eigenvectors U{t ₁, t ₂..., t _q, to vectorial t _iproceed as follows:

4.1) make y=t _i, utilize low-resolution image dictionary D ₁y is carried out to rarefaction representation, is written as:

min:‖α‖ ₀

$s.t.:{\left|\right|{\mathrm{FD}}_{\text{l}}\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\&le;\&Element;$

Wherein, F is that linear feature extracts operator;

Above formula is converted into minimum 1-norm problem:

min:‖α‖ ₁

$s.t:{\left|\right|{\mathrm{FD}}_l\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\&le;\&Element;$

Recycling lagrange's method of multipliers is converted into following formula:

$\underset{\text{\&alpha;}}{\min }{\left|\right|{\mathrm{FD}}_l\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\text{+}{\mathrm{\&lambda;}}_i{\left|\right|\mathrm{\&alpha;}\left|\right|}_1$

Wherein, cognitive regularization parameter λ _icalculated by step 3);

Improvement constraint condition is:

min:‖α‖ ₁

$s.t.:\begin{array}{c}{\left|\right|{\mathrm{FD}}_l\mathrm{\&alpha;}-\mathrm{Fy}\left|\right|}_2^2\&le;\&Element;1\\ {\left|\right|{\mathrm{PD}}_l\mathrm{\&alpha;}-w\left|\right|}_2^2\&le;\&Element;2\end{array}$

Wherein, matrix P is for extracting current piecemeal and overlapping between reconstruct high-definition picture, and w has comprised the overlapping value of reconstruct high-definition picture;

Be optimized for:

$\underset{\mathrm{\&alpha;}}{\min }{\text{||}\tilde{D}\text{\&alpha;-}\tilde{y}\text{||}}_2^2+{\mathrm{\&lambda;}}_i{\left|\right|\mathrm{\&alpha;}\left|\right|}_1$

Wherein

parameter beta can be controlled low-resolution image input, makes it find a high-definition picture piece mating with the adjacent piecemeal that reconstruct is good;

According to the method described above, try to achieve the solution α of rarefaction representation ^*;

4.2) according to x=D _hα ^*try to achieve x, make z _i=x, obtains the estimation z of high-definition picture blocking characteristic vector _i.

After having traveled through, obtain high-definition picture blocking characteristic vector set V{z ₁, z ₂..., z _q;

Above-mentioned used dictionary is to D _hand D ₁obtained by precondition, the method for training is as follows:

(a) first collect image that the resolution close with picture material to be tested of some is higher as high resolving power training plan image set.Down-sampled by high-definition picture being carried out to bicubic, dwindle a doubly, thereby obtain corresponding low resolution training plan image set;

Described bicubic is down-sampled, be enlargement factor be 1/a described 1.2) in bicubic interpolation method;

(b) obtain the set of eigenvectors of all low resolution training images, concrete grammar and step 2) consistent; Be provided with n and open low resolution training image, obtain n vector set

, this n vector set is merged into a set Y in order ^l;

(c) obtain the set of eigenvectors of all high resolving power training images, concrete grammar is: first adopt described bicubic interpolation method, by low-resolution image L _i(i=1,2 ..., n) interpolation amplification a doubly, obtains M _i(i=1,2 ..., n); Then calculate high-definition picture H _iwith M _idifference, obtain Dif _i=H _i-M _i; Afterwards according to step 2.2) in to T _h1processing mode to Dif _icarry out identical processing, obtain vector set (i=1,2 ..., n), obtain so altogether n vector set

then this n vector set is merged in order to a set X ^h;

(d) in order to train two super complete dictionary D of high low resolution _hand D _l, and these two dictionaries will guarantee that the rarefaction representation of corresponding high low-resolution image piece is identical, list system of equations:

$\left\{\begin{array}{c}{D}_h=\arg \underset{D_h,\mathrm{\&Phi;}}{\min }{\left|\right|X^h{-D}_h\mathrm{\&Phi;}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1\\ D_1=\arg \underset{D_{l,}\mathrm{\&Phi;}}{\min }{\left|\right|Y^l-D_l\mathrm{\&Phi;}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1\end{array}\right.$

And to be combined be a formula:

$\underset{\{D_h,D_l,\mathrm{\&Phi;}\}}{\min }\frac{1}{b^2}{\left|\right|X^h-D_h\mathrm{\&Phi;}\left|\right|}_2^2+\frac{1}{{4b}^2}{\left|\right|Y^1-D_1\mathrm{\&Phi;}\left|\right|}_2^2+\mathrm{\&lambda;}(\frac{1}{b^2}+\frac{1}{{4b}^2}){\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

Wherein, image block is that size is b × b, and Φ is rarefaction representation matrix;

Merge D _hand D _l,

$\underset{\{D_h,D_l,z\}}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2+\widehat{\mathrm{\&lambda;}}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

Wherein, $X_C=\left[\begin{array}{c}\frac{1}{b}{X}^h\\ \frac{1}{2b}{Y}^l\end{array}\right],D_C=\left[\begin{array}{c}\frac{1}{b}{D}_h\\ \frac{1}{2b}{D}_l\end{array}\right],\widehat{\mathrm{\&lambda;}}=\mathrm{\&lambda;}(\frac{1}{b^2}+\frac{1}{{4b}^2}),$ As fixing D _cduring with in Φ one, solve another and be converted into the optimum solution problem that solves, to D _creplace iteration optimization with Φ, concrete grammar is as follows:

(i) by D _cbe initialized as gaussian random matrix, and each row is standardized;

(ii) fix D _c, upgrade Φ by following formula:

$\mathrm{\&Phi;}=\underset{z}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2+\widehat{\mathrm{\&lambda;}}{\left|\right|\mathrm{\&Phi;}\left|\right|}_1$

(iii) fix Φ, upgrade D by following formula _c:

$\begin{array}{c}{D}_C=\arg \underset{D_C}{\min }{\left|\right|X_C-D_C\mathrm{\&Phi;}\left|\right|}_2^2\\ s.t.{\left|\right|D_i\left|\right|}_2^2\&le;l,i=\mathrm{1,2},...,K\end{array}$

Wherein D _irepresent D _ci row vector, K represents D _crow vector number;

(iv) iterate (ii) and (iii) until convergence;

(v) obtain D _cbe the super complete dictionary of requirement, decompose and obtain D _hand D _l.

6. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 2, is characterized in that, described step 5) is specially:

5.1) the proper vector z to all high-definition picture piecemeals _i∈ V, is divided into b isometric vector, then, using this b vector as row vector, is merged in order the piecemeal Z of b × b size _i, wherein i=1,2 ..., Q, obtains partitioned matrix set { Z ₁, Z ₂..., Z _q;

5.2) by all partitioned matrix set Z _ibe merged into a matrix Z ' ∈ R ^{a (N-2) × a (M-2)}, concrete grammar is as follows:

Make Z '=0, E=0, Z ' ∈ R ^{a (N-2) × a (M-2)}, E ∈ R ^{a (N-2) × a (M-2)}, i=1, by order from left to right, from top to bottom, the element of Ergodic Matrices Z ' successively, if this pixel coordinate (p, q) traversing meets:

1≤p≤a* (N-2)-b+1 and 1≤q≤a* (M-2)-b+1

Wherein p and q are integer, order:

Z‘(p:(p+b-1),q:(q+b-1))=Z‘(p:(p+b-1),q:(q+b-1))+Z _i

i=i+1

Each element of matrix E is used for the accumulative frequency of the pixel of the correspondence position that records matrix Z ', after traversal finishes, superposition image vegetarian refreshments between piecemeal is got to average, and each element value of order matrix Z ', divided by the element value of the correspondence position of matrix F, finally obtains Z ';

5.3) Z ' is added to middle a (N-2) × a (M-2) region of Y, gained new images assignment is given to obtain Z ', obtains Z ' ∈ R ^{aN × aM}.

7. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 2, is characterized in that the iterative backprojection method in described step 6) is specially and solves following formula optimization problem:

$Z=\arg \underset{\text{Z}}{\min }{\left|\right|\mathrm{\&Theta;\&Psi;Z}-Y_0\left|\right|}_2^2+c{\left|\right|Z-Z^{\&prime;}\left|\right|}_2^2$

Wherein Ψ represents fuzzy matrix, and Θ represents down-sampled matrix, Y ₀for the low-resolution image of N × M size of input.

8. the image super-resolution reconstructing method building based on cognitive regularization parameter according to claim 2, is characterized in that, described step 7) is specific as follows:

If input picture is gray level image, the Z obtaining in step 6) is the image obtaining after super-resolution reconstruction;

If input picture is coloured image, according to Cb temporary in the Z obtaining in step 6) and step 1) and Cr matrix, (Z, Cb, Cr) is transformed into rgb space, that is:

R=Z+1.402Cr

G=Z-0.344Cb-0.714Cr

B=Z+1.772Cb

Then make Z=(R, G, B) ∈ R ^{aN × aM × 3}.

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