CN102842115A - Compressed sensing image super-resolution reconstruction method based on double dictionary learning - Google Patents

Abstract

The invention relates to a compressed sensing image super-resolution reconstruction method based on double dictionary learning. The method comprises the following steps of: redundant dictionary and encoding dictionary parameter training, autoregressive model weight value parameter training, and super-resolution reconstruction on a single-frame low-resolution image by virtue of a redundant dictionary, an encoding dictionary and autoregressive model weight value parameters which are trained well. The algorithm has the characteristic of good reconstruction effect, and is applicable to many fields of medical imaging, satellite remote sensing and telemetering, military reconnaissance and positioning, city security and the like.

Description

Compressed sensing image super-resolution rebuilding method based on dual dictionary study

Technical field:

The invention belongs to the digital image processing techniques field, a kind of specifically image super-resolution rebuilding method, the high-fidelity that is used for single image is amplified.

Background technology:

Along with popularizing of security protection equipment, the application of watch-dog also can be more and more widely, and role is also more and more important in our life; Because the visual field of monitoring is bigger or object scene is far away more from the distance of watch-dog, the pixel that is assigned on each scenery is few more, causes the loss in detail of object scene; Image thickens; Be unfavorable for subsequent treatment and Target Recognition, therefore, object scene carried out super-resolution rebuilding just seem particularly important.The super-resolution rebuilding technology is widely used in fields such as medical imaging, satellite remote sensing remote measurement, military surveillance and location and city security protections.

Mainly contain the three major types reconstruction algorithm at present:

One type is traditional multiframe Processing Algorithm; This type of algorithm is rebuild through the different information of the multiple image of fusion Same Scene, and this type of algorithm all is based on same model, through choosing different bound term; An ill-conditioning problem is found the solution; This type of algorithm input is had relatively high expectations, and accuracy of parameter estimation requires very high, so limited use.

Interpolation algorithm be one type the simplest; The highest ageing algorithm comprises bilinear interpolation, bicubic interpolation, cubic spline interpolation etc., and interpolation algorithm is not considered image immanent structure (edge); Cause image blurringly easily, this type of algorithm is generally as the pre-service of other super-resolution rebuilding algorithms.

Algorithm based on machine learning: such algorithm utilizes the information of learning to rebuild at first through the image library learning training being obtained the required information of super-resolution rebuilding then.Tradition can realize big multiple reconstruction based on the method for learn-by-example, is one type of image but require the image and the image in the image library of input, generally is applied to special image reconstructions such as people's face.Adopt the method for two redundant dictionary rarefaction representations when quality of input image is higher, can obtain result preferably, but to fuzzyyer, the image reconstruction ability that noise is bigger is just not enough.

The present invention adopts the single redundancy dictionary to carry out rarefaction representation, the method for rebuilding the contraction of equation employing iteration is carried out the target super resolution image find the solution, and reconstructed results is good.

Summary of the invention:

The purpose of this invention is to provide a kind of image super-resolution rebuilding method, it can keep the sharpness of image in enlarged image.

The technical scheme that the present invention adopts is following:

One, redundant dictionary, encoder dictionary parameter training:

Definition

Be redundant dictionary, Ψ=[ψ ₁, ψ ₂..., ψ _n] ∈ R ^{M * n}Be encoder dictionary, m, n are positive integer.Dual dictionary refers to redundant dictionary and encoder dictionary.

The first step: super-resolution image in the reading images storehouse, transfer the super-resolution coloured image to gray level image, be divided into size then and do

Image fritter sample, the image fritter that obtains is comply with left-to-right, from top to bottom, read mode by row and form column vector, use s _i∈ R ⁿ, i=1,2 ..., Q representes the column vector that each fritter forms, Q is the number of total column vector;

Second step: calculate s _iVariance Var (s _i), only keep Var (s _i) greater than the vector of threshold value TH, finally obtain training sample set S=[s ₁, s ₂... s _M];

The 3rd step: formula (1) is found the solution, adopt alternative manner to find the solution redundant dictionary Φ and encoder dictionary Ψ, establishing Θ is sparse coefficient, and λ, η are constant,

L is asked in expression ₂Norm, || ₁L is asked in expression ₁Norm:

$\{\mathrm{\Φ},\mathrm{\Ψ},\mathrm{\Θ}\}=\arg \underset{\mathrm{\Φ},\mathrm{\Ψ},\mathrm{\Θ}}{\min }\{{\left|\right|S-\mathrm{\Φ\Θ}\left|\right|}_2^2+\mathrm{\η}{\left|\right|\mathrm{\Θ}-\mathrm{\ΨS}\left|\right|}_2^2+\mathrm{\λ}{\left|\mathrm{\Θ}\right|}_1\}---\left(1\right)$

(1) with gaussian random matrix initialization redundant dictionary Φ, with unit matrix initialization codes dictionary Ψ,, establish iterations k=0 with the sparse coefficient Θ of full null matrix initialization, maximum iteration time is Max_Iter, the iteration convergence controlling elements are ε;

(2) definition (T _ζ[O]) _{I, j}=sign (O _{I, j}) max{|O _{I, j}|-ζ, 0} are the threshold operation operator, and ζ represents the threshold operation variable, and O represents threshold operation matrix variables, O _{I, j}Be designated as under among the representing matrix O that (sign () is the symbol manipulation operator, gets σ for i, element j) _Θ=2|| Φ ^TΦ+η I|| _F, wherein || || _FIt is unit matrix that Frobenius norm, I are asked in expression, uses formula (2) to upgrade current Θ value;

${\mathrm{\Θ}}^{k+1}=T_{\mathrm{\λ}/2{\mathrm{\σ}}_{\mathrm{\Θ}}}[(1-\frac{\mathrm{\η}}{{\mathrm{\σ}}_{\mathrm{\Θ}}}){\mathrm{\Θ}}^k+\frac{1}{{\mathrm{\σ}}_{\mathrm{\Θ}}}\left({\mathrm{\Φ}}^T(S-{\mathrm{\Φ\Θ}}^k\right)+\mathrm{\η\ΨS}]---\left(2\right)$

Θ wherein ^K+1, Θ ^kRepresent iteration k+1 and the k Θ value in step respectively, Φ ^TRepresent the transposition of Φ.

(3) defining operation π (d)=d/max (1, || d||), d is a vector, this operation expression with vector projection to unit length, definition σ _Φ=2|| Θ Θ ^T|| _F, use formula (3) to upgrade current Φ value:

${\mathrm{\Φ}}^{k+1}=\mathrm{\π}({\mathrm{\Φ}}^k+\frac{1}{{\mathrm{\σ}}_{\mathrm{\Φ}}}(S-{\mathrm{\Φ}}^k\mathrm{\Θ}){\mathrm{\Θ}}^T)---\left(3\right)$

π () expression is here carried out unit length projection, wherein Φ to each row of Φ ^K+1, Φ ^kRepresent iteration k+1 and the k Φ value in step respectively, Θ ^TRepresent the transposition of Θ.

(4) calculate σ _Ψ=2||SS ^T|| _F, use formula (4) to upgrade current Ψ value:

${\mathrm{\Ψ}}^{k+1}=\mathrm{\π}({\mathrm{\Ψ}}^k+\frac{1}{{\mathrm{\σ}}_{\mathrm{\Ψ}}}(\mathrm{\Θ}-{\mathrm{\Ψ}}^{k}S)S^T)---\left(4\right)$

π () expression is here carried out unit length projection, wherein Ψ to each row of Ψ ^K+1, Ψ ^kRepresent iteration k+1 and the k Ψ value in step respectively, S ^TRepresent the transposition of S.

(5) iterations k=k+1;

(6) repeat (2) to (5) and stopped iteration in enough hour up to the value variation that arrives maximum iterations or formula (1).Output Φ value and Ψ value.

Two, autoregressive model weighting parameter training:

The first step: super-resolution image in the reading images storehouse; Transfer image to gray level image; Carry out convolution with a low frequency Gaussian convolution nuclear then, obtain low-frequency image, then original image and low-frequency image are subtracted each other; Difference reflects the high-frequency information (here with its called after high frequency imaging) of image, high frequency imaging is divided into size does

The image fritter, find with super-resolution image in s _iThe image fritter of corresponding position, and comply with left-to-rightly, from top to bottom, read mode by row and form column vector, be designated as

All S=[s ₁, s ₂... s _M] corresponding high frequency fritter vector set is combined into

Second step: use the K-means sorting algorithm with S ^hBe divided into K class { C ₁, C ₂... C _K,

m _kExpression C _kThe number of middle vector uses formula (5) to calculate the barycenter μ of each type _k, k=1,2 ..., K is according to S ^hClassification results, with S=[s ₁, s ₂... s _M] also be divided into the K class, be expressed as { S ₁, S ₂... S _K}:

${\mathrm{\μ}}_k=\frac{1}{m_k}\underset{i=1}{\overset{m_k}{\mathrm{\Σ}}}{s}_i^h$ $s_i^h\∈C_k---\left(5\right)$

The 3rd step: if s ' _iExpression s _iCenter pixel value, q _iBe s _iMiddle s ' _iThe vector formed of neighborhood territory pixel value, use minimum secondary method calculating formula

In α _k, identical processing is carried out in all classification, obtain autoregressive model weighting parameter combination { α ₁, α ₂... α _K;

The 4th step: output autoregressive model weighting parameter combination { α ₁, α ₂... α _KAnd the barycenter { μ of each type ₁, μ ₂... μ _K;

Three, image super-resolution rebuilding

Redundant dictionary Φ, encoder dictionary Ψ, autoregressive model weighting parameter combination { α ₁, α ₂... α _K, the barycenter { μ of each type ₁, μ ₂... μ _KFor training in advance obtains, once training can be used always.

The first step: read in the low-resolution image Y that need rebuild,, be expressed as X if gray level image uses two cube interpolation that Y is interpolated into the size that needs ⁽⁰⁾If image is the RGB image three-colo(u)r, be the YCbCr color space then with image transformation, the Y component is interpolated into the size that needs, be expressed as X ⁽⁰⁾, establish X (0) ∈ R ^{N " * 1}, then defining A, B is the matrix of coefficients of N " * N " dimension;

Second step: the value of design factor matrix A and B, it is divided into following a few step:

(1) with X ⁽⁰⁾Being divided into size does

The image fritter, be designated as into x _i, i=1,2 ... N, the number of N presentation video piecemeal has overlapping between the adjacent piece in the time of piecemeal; With X ⁽⁰⁾Carry out convolution with a low frequency Gaussian convolution nuclear, obtain low-frequency image, then with X ⁽⁰⁾Subtract each other difference reflection X with low-frequency image ⁽⁰⁾High-frequency information (here with its called after high frequency imaging), high frequency imaging be divided into size do

The image fritter, find and x _iThe image fritter of corresponding position, and comply with left-to-rightly, from top to bottom, read mode by row and form column vector, be designated as

(2) calculate With all { μ ₁, μ ₂... μ _KBetween Euclidean distance, find minimum that of distance, its following k that is labeled as _i, find { α ₁, α ₂... α _KIn under be designated as k _iWeighting parameter, as x _iThe autoregressive model weighting parameter

The center pixel value of (3) establishing, χ _iBe x _iMiddle x ' _iThe vector formed of neighborhood territory pixel value, use formula (6) compute matrix A;

I, j are coordinate variables, get positive integer, and span is 1～N ".

(4) at X ⁽⁰⁾In the fritter that image is divided into, seek

L similar fritter, variable l=1,2 ... L, L represent the quantity of similar fritter, are positive integer,

Represent X ⁽⁰⁾In and x _iSimilar fritter calculates

In

Value, wherein

The expression normalized factor, h is a constant, establishes

Be weight vector,

Represent the center pixel set of all similar fritters, then use formula (7) compute matrix B:

I, l are coordinate variables, get positive integer, and span is 1～N ".

The 3rd step: set the constant γ in the formula of back ₁, γ ₂, γ ₃, P, e, Mid_Iter and maximum iterations Max_Iter, set constant matrices τ, initialization iterations k=0;

The 4th step: establish I representation unit matrix, I matrix size and matrix A, B are the same, and D representes the down-sampling matrix; D sets according to rebuilding multiple, and H is the Gaussian Blur matrix, and it is the matrix form of Gaussian convolution nuclear; Setting according to Gaussian convolution nuclear, is a circular matrix, computing formula (8):

X ^(k+1/2)＝X ^(k)+γ ₃[(DH) ^TY-(DH) ^TDHX ^(k)]

-γ ₁(I-A) ^T(I-A)X ^(k)-γ ₂(I-B) ^T(I-B)X ^(k) (8)

X ^(k+1/2), X ^(k)Represent iteration k+1/2 and the k reconstructed results in step respectively.

The 5th step: if R _iExpression is with x _iCutting is come out from X, that is: x _i=R _iX is if iterations k, uses formula (9) compute sparse coefficient Θ less than Mid_Iter ^(k+1/2), Θ ^(k+1/2)=[α ₁, α ₂... α _N]; Otherwise, use formula (10) calculation of alpha _i:

Θ ^(k+1/2)＝[ΨR ₁X ^(k+1/2)，ΨR ₂X ^(k+1/2)，…ΨR _NX ^(k+1/2)] (9)

${\mathrm{\α}}_i=\underset{\mathrm{\α}}{\arg \min }\{{\left|\right|x_i-\mathrm{\Φ\α}\left|\right|}^2+{\mathrm{\γ}}_4{\left|\mathrm{\α}\right|}_1\}---\left(10\right)$

Wherein, γ ₄Be constant, formula (10) adopts the characteristic symbol finding algorithm to find the solution, and detailed process is following:

(a) the vectorial θ ∈ R of definition ^{M * 1}, θ _jJ element among the representation vector θ, θ _j∈ 1,0,1}, initialization

Definition of activities is gathered β={ }, and it is initialized as empty set;

(b), calculate for the element that among the α is 0

Find out the j value, α _jRepresent each element of j of α, if

θ then _j=-1, β=β ∪ j}, if:

θ then _j=1, β=β ∪ { j};

(c) select among the Φ be designated as β down column vector is formed

selects the element that is designated as β among α and the θ down and form and calculating

respectively and check

and

relevant position element then one by one; See that which element has changed symbol (refer to by just become negative or just become by negative); Be provided with the value reindexing of Num position; The element of negate position is put 0 (each Value Operations to a position in ; The value of other position remains unchanged); Be worth altered new vector with

expression; Then

has Num kind value; In the Num kind value difference substitution with

; Find out the value that makes

value minimum that

; Make identical change for the element relevant position middle element that is designated as β among

α down with

its assignment; Element becomes 0 subscript and from β, removes with

and among the α, upgrades θ=sign (α);

(d) judge among the α be not whether 0 element satisfies:

If do not satisfy, then carry out (c) step, otherwise judge among the α to be whether 0 element is satisfied:

Then do not carry out (b) step if do not satisfy, otherwise the value of returning α (is α _i=α).

The 6th step: calculate Θ with formula (11) ^(k+1), defining operation (T _τ[Z]) _{I, j}=sign (Z _{I, j}) max{|Z _{I, j}|-τ _{I, j}, 0}, Z are the objects of this operation.

Θ ^(k+1)＝T _τ[Θ ^(k+1/2)] (11)

The 7th step: use formula (12) to calculate X ^(k+1)

$X^{(k+1)}={\left(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{R}_i^T{R}_i\right)}^{-1}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{R}_i^T\mathrm{\Φ}{\mathrm{\α}}_i---\left(12\right)$

The 8th step: if mod (k, P)==0, and k>=Mid_Iter, with X ^(k+1)Replace the X in second step ⁽⁰⁾, recomputate A and B, and use formula (13) to calculate τ _{I, j}

${\mathrm{\τ}}_{i,j}=\frac{c{\mathrm{\σ}}_n^2}{{\mathrm{\σ}}_{i,j}+\mathrm{\δ}}---\left(13\right)$

C is a constant, σ _nBe the standard deviation of picture noise, δ is a smaller constant, σ _{I, j}Calculate as follows: use X ^(k+1), extract fritter, and ask and x _iSimilar fritter is to all and x _iSimilar fritter vector

Calculate

Propose then

L=1,2 ... the j number of L, the standard deviation of calculating these numbers is σ _{I, j}

The 9th step: iterations k=k+1;

The tenth step: judge

and k>=Max_Iter; Wherein there is a condition to set up; Then stop iteration, return super-resolution image X; Otherwise repeat the 4th and went on foot for the tenth step;

The 11 step: if input picture is a gray level image, directly export X,, then brightness X and color CbCr are converted into rgb space, the image after output is rebuild if coloured image then is interpolated into the size identical with X with the CbCr component.

The present invention is a kind of image super-resolution rebuilding method, compared with prior art, the invention has the advantages that the image reconstruction better quality.

For the validity after the verification algorithm reconstruction; With [the Jianchao Yang of the result after this paper reconstruction with two cube interpolation, Jianchao Yang proposition; John Wright; Thomas S.Huang; Yi Ma.Image super-resolution via sparse representation [J] .IEEE Transaction on image processing.2010; 19 (11): 2861-2873.] contrast based on the method for rarefaction representation and [Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization [J] .IEEE Transaction on image processing.2011,20 (7): 1838-1857.] ASDS reconstruction algorithm of Weisheng Dong proposition.

Description of drawings: shown in Figure 1 is visual effect contrast after the reconstruction of four kinds of methods, and the image among Fig. 1 is through dwindling processing, and the upper left corner is the local original image of intercepting.Among Fig. 1 first classifies the low-resolution image of input as; Second classifies the result of two cube interpolation as; The 3rd classifies the result that Jianchao Yang algorithm (being called for short the Yang algorithm) is rebuild as; The 4th classifies the result that Weisheng Dong algorithm (being called for short the Dong algorithm) is rebuild as, and the 5th classifies the result that the inventive method is rebuild as.Can see that from result (the image upper left corner) result that two cube interpolation obtain is the fuzzyyest; And the edge of image recovery extent that obtains based on the method for rarefaction representation is not enough, and image visual effect is also not as the ASDS method, and the picture quality of ASDS after rebuilding is very high; But it is in butterfly's wing figure; Caused partial distortion, method of the present invention can obtain best visual effect, does not almost have visible distortion.

The contrast of Fig. 1 simulation result

Table one

For four kinds of super resolution ratio reconstruction methods of objective appraisal, table one has provided the Y-PSNR (PSNR:Peak Signal to Noise Ratio) and the structural similarity sex index data such as (SSIM:Structure Similarity Index) of four kinds of super resolution ratio reconstruction methods.Can obtain from table one; The PSNR of two cubes of interpolation and the value of SSIM are minimum; The Yang algorithm is with respect to two cubes of interpolation; PSNR and SSIM value have lifting largely, and it is the highest that Dong algorithm and algorithm each item index of the present invention are improved degree, and PSNR and SSIM index slightly are better than the Dong algorithm under the most of situation of algorithm of the present invention.

Embodiment:

The technical scheme that the present invention adopts is:

One, redundant dictionary, encoder dictionary parameter training:

Be redundant dictionary, Ψ=[ψ ₁, ψ ₂..., ψ _n] ∈ R ^{M * n does}Encoder dictionary, m, n are positive integer, m=512 wherein, n=49, dual dictionary refers to redundant dictionary and encoder dictionary.

The first step: super-resolution image in the reading images storehouse, transfer super-resolution image to gray level image, be divided into size then and do

The fritter sample, the image fritter that obtains is comply with from left to right, from top to bottom, read mode by row and form column vector, use s _i∈ R ⁿ, i=1,2 ..., Q representes the column vector that each fritter forms, Q is the number of total column vector;

Second step: calculate s _iVariance Var (s _i), only keep Var (s _i) greater than the vector of threshold value TH, wherein the TH span is: 4.5～20, finally obtain training sample set S=[s ₁, s ₂... s _M], M is greater than 120000;

The 3rd step: formula (1) is found the solution, adopt alternative manner to find the solution redundant dictionary Φ, encoder dictionary Ψ, Θ are sparse coefficient, and λ, η are constant, and η gets and is approximately equal to 1 numerical value, and the λ span is 0.05～0.2, L is asked in expression ₂Norm, || ₁L is asked in expression ₁Norm:

$\mathrm{fuction}=\{\mathrm{\Φ},\mathrm{\Ψ},\mathrm{\Θ}\}=\arg \underset{\mathrm{\Φ},\mathrm{\Ψ},\mathrm{\Θ}}{\min }\{{\left|\right|S-\mathrm{\Φ\Θ}\left|\right|}_2^2+\mathrm{\η}{\left|\right|\mathrm{\Θ}-\mathrm{\ΨS}\left|\right|}_2^2+\mathrm{\λ}{\left|\mathrm{\Θ}\right|}_1\}---\left(1\right)$

(1) with gaussian random matrix initialization redundant dictionary Φ, with unit matrix initialization codes dictionary Ψ, with the sparse coefficient Θ of full null matrix initialization, iterations k=0, maximum iteration time Max_Iter gets 800～1500, iteration convergence controlling elements ε=10 ^-6

(2) definition (T _ζ[O]) _{I, j}=sign (O _{I, j}) max{|O _{I, j}|-ζ, 0} are the threshold operation operator, and ζ represents the threshold operation variable, and O represents threshold operation matrix variables, O _{I, j}Be designated as under among the representing matrix O that (sign () is the symbol manipulation operator, gets σ for i, element j) _Θ=2|| Φ ^TΦ+η I|| _F, || || _FIt is unit matrix that Frobenius norm, I are asked in expression, uses formula (2) to upgrade current Θ value;

${\mathrm{\Θ}}^{k+1}=T_{\mathrm{\λ}/2{\mathrm{\σ}}_{\mathrm{\Θ}}}[(1-\frac{\mathrm{\η}}{{\mathrm{\σ}}_{\mathrm{\Θ}}}){\mathrm{\Θ}}^k+\frac{1}{{\mathrm{\σ}}_{\mathrm{\Θ}}}\left({\mathrm{\Φ}}^T(S-{\mathrm{\Φ\Θ}}^k\right)+\mathrm{\η\ΨS}]---\left(2\right)$

Θ wherein ^K+1, Θ ^kRepresent iteration k+1 and the k Θ value in step respectively, Φ ^TRepresent the transposition of Φ.

(3) defining operation π (d)=d/max (1, || d||), d is a vector, this operation expression with vector projection to unit length, definition σ _Φ=2|| Θ Θ ^T|| _F, use formula (3) to upgrade current Φ value:

${\mathrm{\Φ}}^{k+1}=\mathrm{\π}({\mathrm{\Φ}}^k+\frac{1}{{\mathrm{\σ}}_{\mathrm{\Φ}}}(S-{\mathrm{\Φ}}^k\mathrm{\Θ}){\mathrm{\Θ}}^T)---\left(3\right)$

π () expression is here carried out unit length projection, wherein Φ to each row of Φ ^K+1, Φ ^kRepresent iteration k+1 and the k Φ value in step respectively, Θ ^TRepresent the transposition of Θ.

(4) calculate σ _Ψ=2||SS ^T|| _F, use formula (4) to upgrade current Ψ value:

${\mathrm{\Ψ}}^{k+1}=\mathrm{\π}({\mathrm{\Ψ}}^k+\frac{1}{{\mathrm{\σ}}_{\mathrm{\Ψ}}}(\mathrm{\Θ}-{\mathrm{\Ψ}}^{k}S)S^T)---\left(4\right)$

π () expression is here carried out unit length projection, wherein Ψ to each row of Ψ ^K+1, Ψ ^kRepresent iteration k+1 and the k Ψ value in step respectively, S ^TRepresent the transposition of S.

(5) iterations k=k+1;

(6) with Θ, Ψ, Φ value and the preceding value difference substitution formula (1) that once calculates of current calculating, the value of calculating target function is judged ${\left|\right|{\mathrm{Function}}^{(k+1)}-{\mathrm{Function}}^{\left(k\right)}\left|\right|}_2^2/{\left|\right|{\mathrm{Function}}^{\left(k\right)}\left|\right|}_2^2<\mathrm{\&epsiv;}$ (function ^(k+1), function ^kRepresent the function value that k+1 and the k step calculates respectively) whether satisfy with k>=Max_Iter condition, satisfied wherein any one, stop iteration, export Φ value and Ψ value; Otherwise repeat (2) to (5).

Two, autoregressive model weighting parameter training:

The first step: super-resolution image in the reading images storehouse; Transfer image to gray level image, carry out convolution (Gaussian convolution nuclear size is 7 * 7, and standard deviation is 1.6) with a low frequency Gaussian convolution nuclear then; Obtain low-frequency image; Then original image and low-frequency image are subtracted each other, difference reflects the high-frequency information (here with its called after high frequency imaging) of image, high frequency imaging is divided into size does

The image fritter, n=49, find with super-resolution image in s _iThe image fritter of corresponding position, and comply with left-to-rightly, from top to bottom, read mode by row and form column vector, be designated as

All S=[s ₁, s ₂... s _M] corresponding high frequency fritter vector set is combined into $S^h=[s_1^h,s_2^h,...s_M^h].$

Second step: use the K-means sorting algorithm with S ^hBe divided into K class { C ₁, C ₂... C _K,

K gets 200, m _kExpression C _kThe number of middle vector uses formula (5) to calculate the barycenter μ of each type _k, k=1,2 ..., K is according to S ^hClassification results, with S=[s ₁, s ₂... s _M] also be divided into the K class, be expressed as { S ₁, S ₂... S _K}:

${\mathrm{\&mu;}}_k=\frac{1}{m_k}\underset{i=1}{\overset{m_k}{\mathrm{\&Sigma;}}}{s}_i^h$ $s_i^h\&Element;C_k---\left(5\right)$

The 3rd step: if s ' _iExpression s _iCenter pixel value, q _iBe s _iMiddle s ' _iThe vector formed of neighborhood territory pixel value, the neighborhood size is got 3 * 3 and (is comprised center pixel, q _iFor removing the vector of forming behind the center pixel, be the column vector of 8 elements), use minimum secondary method calculating formula

In α _k, α _kBe 8 * 1 vector, identical processing is carried out in all classification, obtain autoregressive model weighting parameter combination { α ₁, α ₂... α _K;

The 4th step: output autoregressive model weighting parameter combination { α ₁, α ₂... α _KAnd the barycenter { μ of each type ₁, μ ₂... μ _K;

Three, image super-resolution rebuilding

Redundant dictionary Φ, encoder dictionary Ψ, autoregressive model weighting parameter combination { α ₁, α ₂... α _K, the barycenter { μ of each type ₁, μ ₂... μ _KFor training in advance obtains, once training can be used always.

The first step: read in the low-resolution image Y that need rebuild,, be expressed as X if gray level image uses two cube interpolation that Y is interpolated into the size that needs ⁽⁰⁾If image is the RGB image three-colo(u)r, be the YCbCr color space then with image transformation, the Y component is interpolated into the size that needs, be expressed as X ⁽⁰⁾, establish X (0) ∈ R ^{N " * 1}, then defining A, B is the matrix of coefficients of N " * N " dimension;

Second step: design factor matrix A and B, it is divided into following a few step:

(1) with X ⁽⁰⁾Being divided into size does

The image fritter, be designated as into x _i, i=1,2 ... N, the number of N presentation video piecemeal (with the size variation of input picture) has overlapping (laterally or 4 pixel width of longitudinal overlap) between the adjacent piece in the time of piecemeal; With X ⁽⁰⁾Carry out convolution with a low frequency Gaussian convolution nuclear, obtain low-frequency image, then with X ⁽⁰⁾Subtract each other difference reflection X with low-frequency image ⁽⁰⁾High-frequency information (here with its called after high frequency imaging), high frequency imaging be divided into size do

The image fritter, find and x _iThe image fritter of corresponding position, and comply with left-to-rightly, from top to bottom, read mode by row and form column vector, be designated as

(2) calculate

With all { μ ₁, μ ₂... μ _KBetween Euclidean distance, find minimum that of distance, its following k that is labeled as _i, find { α ₁, α ₂... α _KIn under be designated as k _iWeighting parameter, as x _iThe autoregressive model weighting parameter

(3) if x ' _iExpression x _iCenter pixel value, χ _iBe x _iMiddle x ' _iThe vector formed of neighborhood territory pixel value, use formula (6) compute matrix A;

I, j are coordinate variables, get positive integer, and span is 1～N ".

(4) at X ⁽⁰⁾In the fritter that is divided in the image, seek

L similar fritter, variable l=1,2 ... L, L represent the quantity of similar fritter, are positive integer, and the L span is 7～10,

Represent X ⁽⁰⁾In the fritter similar with xi, calculate In

Value, wherein

The expression normalized factor, h is a constant, span is 65～70, establishes

Be weight vector,

Represent the center pixel set of all similar fritters, then use formula (7) compute matrix B:

I, l are coordinate variables, get positive integer, and span is 1～N ".

The 3rd step: preset: γ ₁Span 0.008～0.01, γ ₂Span 0.04～0.1, γ ₃Get value, P=20, e=10 about 6.5 ^-6, Mid_Iter=100 and maximum iterations Max_Iter=150, set constant matrices τ=0, initialization iterations k=0;

The 4th step: establish I representation unit matrix, I matrix size and matrix A, B are the same, and D representes the down-sampling matrix, and D is according to rebuilding the multiple setting; H is the Gaussian Blur matrix, and it is that (rebuilding the factor is 3 o'clock to Gaussian convolution nuclear, and Gaussian convolution nuclear size is 7 * 7, and standard deviation is 1.6; Rebuilding the factor is 2 o'clock, and Gaussian convolution nuclear size is 5 * 5, and standard deviation is about 0.9～1.1; Rebuilding the factor is 4 o'clock, and Gaussian convolution nuclear size is 7 * 7, and standard deviation is 1.7～1.8) matrix form; Setting according to Gaussian convolution nuclear, is a circular matrix, computing formula (8):

X ^(k+1/2)＝X ^(k)+γ ₃[(DH) ^TY-(DH) ^TDHX ^(k)]

-γ ₁(I-A) ^T(I-A)X ^(k)-γ ₂(I-B) ^T(I-B)X ^(k) (8)

X ^(k+1/2), X ^(k)Represent iteration k+1/2 and the k reconstructed results in step respectively.

The 5th step: if R _iExpression is with x _iCutting is come out from X, that is: x _i=R _iX is if iterations k, uses formula (9) compute sparse coefficient Θ less than Mid_Iter ^(k+1/2), Θ ^(k+1/2)=[α ₁, α ₂... α _N]; Otherwise, use formula (10) calculation of alpha _i:

Θ ^(k+1/2)＝[ΨR ₁X ^(k+1/2)，ΨR ₂X ^(k+1/2)，…ΨR _NX ^(k+1/2)] (9)

${\mathrm{\&alpha;}}_i=\underset{\mathrm{\&alpha;}}{\arg \min }\{{\left|\right|x_i-\mathrm{\&Phi;\&alpha;}\left|\right|}^2+{\mathrm{\&gamma;}}_4{\left|\mathrm{\&alpha;}\right|}_1\}---\left(10\right)$

Wherein, γ ₄Be constant, span is 0.1～0.2, and formula (10) adopts the characteristic symbol finding algorithm to find the solution, and detailed process is following:

(a) the vectorial θ ∈ R of definition ^{M * 1}, θ _jJ element among the representation vector θ, θ _j∈ 1,0,1}, initialization

Definition of activities is gathered β={ }, and it is initialized as empty set;

(b), calculate for the element that among the α is 0

Find out the j value, α _jRepresent each element of j of α, if θ then _j=-1, β=β ∪ j}, if:

θ then _j=1, β=β ∪ { j};

(c) select among the Φ be designated as β down column vector is formed

selects the element that is designated as β among α and the θ down and form

and

calculating respectively and check

and

relevant position element then one by one; See that which element has changed symbol (refer to by just become negative or just become by negative); Be provided with the value reindexing of Num position; The element of negate position is put 0 (each Value Operations to a position in

; The value of other position remains unchanged); Be worth altered new vector with

expression; Then has Num kind value; In the Num kind value difference substitution with

; Find out the value that makes value minimum that

; Make identical change for the element relevant position middle element that is designated as β among

α down with

its assignment; Element becomes 0 subscript and from β, removes with

and among the α, upgrades θ=sign (α);

(d) judge among the α be not whether 0 element satisfies:

If do not satisfy, then carry out (c) step, otherwise judge among the α to be whether 0 element is satisfied:

Then do not carry out (b) step if do not satisfy, otherwise the value of returning α (is α _i=α);

The 6th step: calculate Θ with formula (11) ^(k+1), defining operation (T _τ[Z]) _{I, j}=sign (Z _{I, j}) max{|Z _{I, j}|-τ _{I, j}, 0}, Z are the objects of this operation:

Θ ^(k+1)＝T _τ[Θ ^(k+1/2)] (11)

The 7th step: use formula (12) to calculate X ^(k+1):

$X^{(k+1)}={\left(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{R}_i^T{R}_i\right)}^{-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{R}_i^T\mathrm{\&Phi;}{\mathrm{\&alpha;}}_i---\left(12\right)$

The 8th step: if mod (k, P)==0, and k>=Mid_Iter, with X ^(k+1) replace the X in second step ⁽⁰⁾, recomputate A and B, and use formula (13) to calculate τ _{I, j}:

${\mathrm{\&tau;}}_{i,j}=\frac{c{\mathrm{\&sigma;}}_n^2}{{\mathrm{\&sigma;}}_{i,j}+\mathrm{\&delta;}}---\left(13\right)$

C is a constant, σ _nBe the standard deviation of picture noise, c σ _nSpan is 0.1～3.6, and normal image gets 0.1～0.6; δ is a smaller constant, gets 0.35, σ _{I, j}Calculate as follows: use X ^(k+1), extract fritter, and ask and x _iSimilar fritter is to all and x _iSimilar fritter vector Calculate

Propose then

L=1,2 ... the j number of L, the standard deviation of calculating these numbers is σ _{I, j}

The 9th step: iterations k=k+1;

The tenth step: judge and k>=Max_Iter; Wherein there is a condition to set up; Then stop iteration, return super-resolution image X; Otherwise repeat the 4th and went on foot for the tenth step;

The 11 step: if input picture is a gray level image, directly export X,, then brightness X and color CbCr are converted into rgb space, the image after output is rebuild if coloured image then is interpolated into the size identical with X with the CbCr component.

Claims (1)

1. based on the compressed sensing image super-resolution rebuilding method of dual dictionary study, it is characterized in that following steps:

1, redundant dictionary, encoder dictionary parameter training:

Be redundant dictionary, Ψ=[ψ ₁, ψ ₂..., ψ _n] ∈ R ^{M * n}Be encoder dictionary, m, n are positive integer, m=512 wherein, and n=49, dual dictionary refer to the present invention and produce redundant dictionary and two dictionaries of encoder dictionary simultaneously.

The first step: super-resolution image in the reading images storehouse, transfer super-resolution image to gray level image, be divided into size then and do

The fritter sample, the image fritter that obtains is comply with from left to right, from top to bottom, read mode by row and form column vector, use s _i∈ R ⁿ, i=1,2 ..., Q representes the column vector that each fritter forms, Q is the number of total column vector;

Second step: calculate s _iVariance Var (s _i), only keep Var (s _i) greater than the vector of threshold value TH, wherein the TH span is: 4.5～20, finally obtain training sample set S=[s ₁, s ₂... s _M], M is greater than 120000;

The 3rd step: formula (1) is found the solution, adopt alternative manner to find the solution redundant dictionary Φ, encoder dictionary Ψ, Θ are sparse coefficient, and λ, η are constant, and η gets and is approximately equal to 1 numerical value, and the λ span is 0.05～0.2,

L is asked in expression ₂Norm, || ₁L is asked in expression ₁Norm:

$\mathrm{fuction}=\{\mathrm{\&Phi;},\mathrm{\&Psi;},\mathrm{\&Theta;}\}=\arg \underset{\mathrm{\&Phi;},\mathrm{\&Psi;},\mathrm{\&Theta;}}{\min }\{{\left|\right|S-\mathrm{\&Phi;\&Theta;}\left|\right|}_2^2+\mathrm{\&eta;}{\left|\right|\mathrm{\&Theta;}-\mathrm{\&Psi;S}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\mathrm{\&Theta;}\right|}_1\}---\left(1\right)$

(1) with gaussian random matrix initialization redundant dictionary Φ, with unit matrix initialization codes dictionary Ψ, with the sparse coefficient Θ of full null matrix initialization, iterations k=0, maximum iteration time Max_Iter gets 800～1500, iteration convergence controlling elements ε=10 ^-6

(2) definition (T _ζ[O]) _{I, j}=sign (O _{I, j}) max{|O _{I, j}|-ζ, 0} are the threshold operation operator, and ζ represents the threshold operation variable, and O represents threshold operation matrix variables, O _{I, j}Be designated as under among the representing matrix O that (sign () is the symbol manipulation operator, gets σ for i, element j) _Θ=2|| Φ ^TΦ+η I|| _F, || || _FIt is unit matrix that Frobenius norm, I are asked in expression, uses formula (2) to upgrade current Θ value;

${\mathrm{\&Theta;}}^{k+1}=T_{\mathrm{\&lambda;}/2{\mathrm{\&sigma;}}_{\mathrm{\&Theta;}}}[(1-\frac{\mathrm{\&eta;}}{{\mathrm{\&sigma;}}_{\mathrm{\&Theta;}}}){\mathrm{\&Theta;}}^k+\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&Theta;}}}\left({\mathrm{\&Phi;}}^T(S-{\mathrm{\&Phi;\&Theta;}}^k\right)+\mathrm{\&eta;\&Psi;S}]---\left(2\right)$

Θ wherein ^K+1, Θ ^kRepresent iteration k+1 and the k Θ value in step respectively, Φ ^TRepresent the transposition of Φ.

(3) defining operation π (d)=d/max (1, || d||), d is a vector, this operation expression with vector projection to unit length, definition σ _Φ=2|| Θ Θ ^T|| _F, use formula (3) to upgrade current Φ value:

${\mathrm{\&Phi;}}^{k+1}=\mathrm{\&pi;}({\mathrm{\&Phi;}}^k+\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&Phi;}}}(S-{\mathrm{\&Phi;}}^k\mathrm{\&Theta;}){\mathrm{\&Theta;}}^T)---\left(3\right)$

π () expression is here carried out unit length projection, wherein Φ to each row of Φ ^K+1, Φ ^kRepresent iteration k+1 and the k Φ value in step respectively, Θ ^TRepresent the transposition of Θ.

(4) calculate σ _Ψ=2||SS ^T|| _F, use formula (4) to upgrade current Ψ value:

${\mathrm{\&Psi;}}^{k+1}=\mathrm{\&pi;}({\mathrm{\&Psi;}}^k+\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&Psi;}}}(\mathrm{\&Theta;}-{\mathrm{\&Psi;}}^{k}S)S^T)---\left(4\right)$

π () expression is here carried out unit length projection, wherein Ψ to each row of Ψ ^K+1, Ψ ^kRepresent iteration k+1 and the k Ψ value in step respectively, S ^TRepresent the transposition of S.

(5) iterations k=k+1;

(6) with Θ, Ψ, Φ value and the preceding value difference substitution formula (1) that once calculates of current calculating, the value of calculating target function is judged ${\left|\right|{\mathrm{Function}}^{(k+1)}-{\mathrm{Function}}^{\left(k\right)}\left|\right|}_2^2/{\left|\right|{\mathrm{Function}}^{\left(k\right)}\left|\right|}_2^2<\mathrm{\&epsiv;}$ (function ^(k+1), function ^kRepresent the function value that k+1 and the k step calculates respectively) whether satisfy with k>=Max_Iter condition, satisfied wherein any one, stop iteration, export Φ value and Ψ value; Otherwise repeat (2) to (5).

2, autoregressive model weighting parameter training:

The first step: super-resolution image in the reading images storehouse; Transfer image to gray level image, carry out convolution (Gaussian convolution nuclear size is 7 * 7, and standard deviation is 1.6) with a low frequency Gaussian convolution nuclear then; Obtain low-frequency image; Then original image and low-frequency image are subtracted each other, difference reflects the high-frequency information (here with its called after high frequency imaging) of image, high frequency imaging is divided into size does

The image fritter, n=49, find with super-resolution image in s _iThe image fritter of corresponding position, and comply with left-to-rightly, from top to bottom, read mode by row and form column vector, be designated as

All S=[s ₁, s ₂... s _M] corresponding high frequency fritter vector set is combined into $S^h=[s_1^h,s_2^h,...s_M^h].$

Second step: use the K-means sorting algorithm with S ^hBe divided into K class { C ₁, C ₂... C _K,

K gets 200, m _kExpression C _kThe number of middle vector uses formula (5) to calculate the barycenter μ of each type _k, k=1,2 ..., K is according to S ^hClassification results, with S=[s ₁, s ₂... s _M] also be divided into the K class, be expressed as { S ₁, S ₂... S _K}:

${\mathrm{\&mu;}}_k=\frac{1}{m_k}\underset{i=1}{\overset{m_k}{\mathrm{\&Sigma;}}}{s}_i^h$ $s_i^h\&Element;C_k---\left(5\right)$

The 3rd step: if s ' _iExpression s _iCenter pixel value, q _iBe s _iMiddle s ' _iThe vector formed of neighborhood territory pixel value, the neighborhood size is got 3 * 3 and (is comprised center pixel, q _iFor removing the vector of forming behind the center pixel, be the column vector of 8 elements), use minimum secondary method calculating formula

In α _k, α _kBe 8 * 1 vector, identical processing is carried out in all classification, obtain autoregressive model weighting parameter combination { α ₁, α ₂... α _K;

The 4th step: output autoregressive model weighting parameter combination { α ₁, α ₂... α _KAnd the barycenter { μ of each type ₁, μ ₂... μ _K;

3, image super-resolution rebuilding

Redundant dictionary Φ, encoder dictionary Ψ, autoregressive model weighting parameter combination { α ₁, α ₂... α _K, the barycenter { μ of each type ₁, μ ₂... μ _KFor training in advance obtains, once training can be used always.

The first step: read in the low-resolution image Y that need rebuild,, be expressed as X if gray level image uses two cube interpolation that Y is interpolated into the size that needs ⁽⁰⁾If image is the RGB image three-colo(u)r, be the YCbCr color space then with image transformation, the Y component is interpolated into the size that needs, be expressed as X ⁽⁰⁾, establish X ⁽⁰⁾∈ R ^{N " * 1}, then defining A, B is the matrix of coefficients of N " * N " dimension;

Second step: design factor matrix A and B, it is divided into following a few step:

(1) with X ⁽⁰⁾Being divided into size does

The image fritter, be designated as into x _i, i=1,2 ... N, the number of N presentation video piecemeal (with the size variation of input picture) has overlapping (laterally or 4 pixel width of longitudinal overlap) between the adjacent piece in the time of piecemeal; With X ⁽⁰⁾Carry out convolution with a low frequency Gaussian convolution nuclear, obtain low-frequency image, then with X ⁽⁰⁾Subtract each other difference reflection X with low-frequency image ⁽⁰⁾High-frequency information (here with its called after high frequency imaging), high frequency imaging be divided into size do

The image fritter, find and x _iThe image fritter of corresponding position, and comply with left-to-rightly, from top to bottom, read mode by row and form column vector, be designated as

(2) calculate

With all { μ ₁, μ ₂... μ _KBetween Euclidean distance, find minimum that of distance, its following k that is labeled as _i, find { α ₁, α ₂... α _KIn under be designated as k _iWeighting parameter, as x _iThe autoregressive model weighting parameter

(3) if x ' _iExpression x _iCenter pixel value, χ _iBe x _iMiddle x ' _iThe vector formed of neighborhood territory pixel value, use formula (6) compute matrix A;

I, j are coordinate variables, get positive integer, and span is 1～N ".

(4) at X ⁽⁰⁾In the fritter that is divided in the image, seek

L similar fritter, variable l=1,2 ... L, L represent the quantity of similar fritter, are positive integer, and the L span is 7～10,

Represent X ⁽⁰⁾In and x _iSimilar fritter calculates In

Value, wherein

The expression normalized factor, h is a constant, span is 65～70, establishes

Be weight vector,

Represent the center pixel set of all similar fritters, then use formula (7) compute matrix B:

I, l are coordinate variables, get positive integer, and span is 1～N ".

The 3rd step: preset: γ ₁Span 0.008～0.01, γ ₂Span 0.04～0.1, γ ₃Get value, P=20, e=10 about 6.5 ^-6, Mid_Iter=100 and maximum iterations Max_Iter=150, set constant matrices τ=0, initialization iterations k=0;

The 4th step: establish I representation unit matrix, I matrix size and matrix A, B are the same, and D representes the down-sampling matrix, and D is according to rebuilding the multiple setting; H is the Gaussian Blur matrix, and it is that (rebuilding the factor is 3 o'clock to Gaussian convolution nuclear, and Gaussian convolution nuclear size is 7 * 7, and standard deviation is 1.6; Rebuilding the factor is 2 o'clock, and Gaussian convolution nuclear size is 5 * 5, and standard deviation is about 0.9～1.1; Rebuilding the factor is 4 o'clock, and Gaussian convolution nuclear size is 7 * 7, and standard deviation is 1.7～1.8) matrix form; Setting according to Gaussian convolution nuclear, is a circular matrix, computing formula (8):

X ^(k+1/2)＝X ^(k)+γ ₃[(DH) ^TY-(DH) ^TDHX ^(k)]

-γ ₁(I-A) ^T(I-A)X ^(k)-γ ₂(I-B) ^T(I-B)X ^(k) (8)

X ^(k+1/2), X ^(k)Represent iteration k+1/2 and the k reconstructed results in step respectively.

The 5th step: if R _iExpression is with x _iCutting is come out from X, that is: x _i=R _iX is if iterations k, uses formula (9) compute sparse coefficient Θ less than Mid_Iter ^(k+1/2), Θ ^(k+1/2)=[α ₁, α ₂... α _N]; Otherwise, use formula (10) calculation of alpha _i:

Θ ^(k+1/2)＝[ΨR ₁X ^(k+1/2)，ΨR ₂X ^(k+1/2)，…ΨR _NX ^(k+1/2)] (9)

${\mathrm{\&alpha;}}_i=\underset{\mathrm{\&alpha;}}{\arg \min }\{{\left|\right|x_i-\mathrm{\&Phi;\&alpha;}\left|\right|}^2+{\mathrm{\&gamma;}}_4{\left|\mathrm{\&alpha;}\right|}_1\}---\left(10\right)$

Wherein, γ ₄Be constant, span is 0.1～0.2, and formula (10) adopts the characteristic symbol finding algorithm to find the solution, and detailed process is following:

(a) the vectorial θ ∈ R of definition ^{M * 1}, θ _jJ element among the representation vector θ, θ _j∈ 1,0,1}, initialization

Definition of activities is gathered β={ }, and it is initialized as empty set;

(b), calculate for the element that among the α is 0

Find out the j value, α _jRepresent each element of j of α, if

θ then _j=-1, β=β ∪ j}, if: θ then _j=1, β=β ∪ { j};

(c) select among the Φ be designated as β down column vector is formed

selects the element that is designated as β among α and the θ down and form

and

calculating

respectively and check

and

relevant position element then one by one; See that which element has changed symbol (refer to by just become negative or just become by negative); Be provided with the value reindexing of Num position; The element of negate position is put 0 (each Value Operations to a position in ; The value of other position remains unchanged); Be worth altered new vector with

expression; Then

has Num kind value; In the Num kind value difference substitution with

; Find out the value that makes

value minimum that

; Make identical change for the element relevant position middle element that is designated as β among

α down with

its assignment; Element becomes 0 subscript and from β, removes with

and among the α, upgrades θ=sign (α);

(d) judge among the α be not whether 0 element satisfies:

If do not satisfy, then carry out (c) step, otherwise judge among the α to be whether 0 element is satisfied:

Then do not carry out (b) step if do not satisfy, otherwise the value of returning α (is α _i=α);

The 6th step: calculate Θ with formula (11) ^(k+1), defining operation (T _τ[Z]) _{I, j}=sign (Z _{I, j}) max{|Z _{I, j}|-τ _{I, j}, 0}, Z are the objects of this operation:

Θ ^(k+1)＝T _τ[Θ ^(k+1/2)] (11)

The 7th step: use formula (12) to calculate X ^(k+1):

$X^{(k+1)}={\left(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{R}_i^T{R}_i\right)}^{-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{R}_i^T\mathrm{\&Phi;}{\mathrm{\&alpha;}}_i---\left(12\right)$

The 8th step: if mod (k, P)==0, and k>=Mid_Iter, with X ^(k+1)Replace the X in second step ⁽⁰⁾, recomputate A and B, and use formula (13) to calculate τ _{I, j}:

${\mathrm{\&tau;}}_{i,j}=\frac{c{\mathrm{\&sigma;}}_n^2}{{\mathrm{\&sigma;}}_{i,j}+\mathrm{\&delta;}}---\left(13\right)$

C is a constant, σ _nBe the standard deviation of picture noise, c σ _nSpan is 0.1～3.6, and normal image gets 0.1～0.6; δ is a smaller constant, gets 0.35, σ _{I, j}Calculate as follows: use X ^(k+1), extract fritter, and ask and x _iSimilar fritter is to all and x _iSimilar fritter vector Calculate

Propose then

L=1,2 ... the j number of L, the standard deviation of calculating these numbers is σ _{I, j}

The 9th step: iterations k=k+1;

The tenth step: judge

and k>=Max_Iter; Wherein there is a condition to set up; Then stop iteration, return super-resolution image X; Otherwise repeat the 4th and went on foot for the tenth step;

The 11 step: if input picture is a gray level image, directly export X,, then brightness X and color CbCr are converted into rgb space, the image after output is rebuild if coloured image then is interpolated into the size identical with X with the CbCr component.

Images