CN106296606A - A kind of classification rarefaction representation image repair method of edge fitting - Google Patents

Abstract

The invention discloses the classification rarefaction representation image repair method of a kind of edge fitting.The present invention uses the extracting method that integral edge and local edge combine, the crack edge of area to be repaired is extracted, obtain the marginal information of reflecting edge feature, crack edge line is carried out curve fitting, to ensure that the reparation of image edge structure is strictly retrained by edge wheel profile by certain rule according to these marginal informations；Use and carry out dictionary training by tagsort, to strengthen the adaptivity of study dictionary；Near-hyperbolic tan is used to go to approximate l₀Norm, utilizes conjugate gradient method to solve this function, it is achieved the improvement to tradition SL0 algorithm, is applied in the image repair of non-edge damaged area by the SL0 restructing algorithm that need not estimate degree of rarefication.The picture quality that the present invention repairs is high, both can preferably repair the marginal texture of image, can keep again the overall flatness of structure.

Description

A kind of classification rarefaction representation image repair method of edge fitting

Technical field

The invention belongs to Digital Image Inpainting field, the classification rarefaction representation image repair of concrete a kind of edge fitting Method.

Background technology

Traditional image repair method is divided into two classes: a class is methods based on partial differential equation.The method is substantially A kind of diffusion process, but exist the fuzzyyest when repairing large area region.Another kind of is method based on textures synthesis.The party Method match block replaces multiblock to be repaired, will produce erroneous matching when can not find match block and continue mistake.In order to solve to covet The erroneous matching that greedy property causes, people have carried out a lot of improvement, but still have been not fee from coupling and the weighted graph of mistake algorithm As obscuring that block too much brings.Recently, a kind of new image sparse method for expressing is paid attention in image processing field, many Sparse theory is applied in the method for image repair by person.

Summary of the invention

Find in an experiment, image repair algorithm based on rarefaction representation all uses OMP restructing algorithm, to be repaired When image is reconstructed, generally requiring the degree of rarefication estimating signal, no matter degree of rarefication is estimated too small or excessively mostly can not reach Preferably quality reconstruction；Secondly, sparse representation method is not ideal enough to the holding of structure flatness, particularly repaiies curve Time multiple, some distortion can be produced at structure.In order to preferably repair the structural information of image, the present invention is from considering that structure is overall The angle of flatness, the advantage repaired in conjunction with sample rarefaction representation and structural constraint, the classification having invented a kind of edge fitting is dilute Relieving the exterior syndrome shows image repair method.

The present invention takes techniques below scheme:

The extracting method using integral edge and local edge to combine, carries the crack edge of area to be repaired Take, it is thus achieved that the various information of reflecting edge feature, by certain rule, crack edge line carried out curve fitting according to these information, To ensure that the reparation of image edge structure is strictly retrained by edge wheel profile；Use and carry out dictionary training by tagsort, To strengthen the adaptivity of study dictionary；Near-hyperbolic tan is used to go to approximate l₀Norm, utilizes conjugate gradient method to solve This function, it is achieved the improvement to tradition SL0 algorithm, is applied to non-edge by the SL0 restructing algorithm that need not to estimate degree of rarefication and breaks Damage in the image repair in region, to improve the reliability of rarefaction representation reparation texture information.Specifically comprise the following steps that

The first step: obtain and repair the marginal information of image.

1-1. passes through Sobel operator extraction integral edge, it is thus achieved that the strong edge of breakage image, provides image for image repair Integral edge structure；

1-2. uses the former of " by there are continuous 4 marginal points and above crack edge line is defined as agent structure edge " Then, use integral edge to extract and extract the method realization combined with damaged neighboring area local edge, effectively obtain damaged week The crack edge structural information of edge regions, finds the intersection point on border to be repaired and marginal information.These broken curves (are set fracture Curve is c₁,c₂,…,c_n, it is designated as gathering Q, wherein broken curve c_iStarting point be p_i1) connect correspondingly.By broken curve c_iIn its starting point p_i1On the most contrary two broken curves of direction vector be connected.From there through curve c_iDirection vector will Q is divided into two set Q₁,Q₂.After having classified, calculate the distance between each origin of curve, by two closest for starting point songs Line is attached by the method for quadratic polynomial curve matching.Specifically comprise the following steps that

1-2-1. is for arbitrary broken curve c_i, by starting point p_i1Set out, obtain c_iOn other each point p_i2,p_i3,p_i4,。 IfFor a p_i,jCoordinate vector, then curve c_iIn starting point p_i1On direction vector be defined as:

${\stackrel{\→}{s}}_i=0.5({\stackrel{\→}{p}}_{i,1}-{\stackrel{\→}{p}}_{i,2})+0.25({\stackrel{\→}{p}}_{i,2}-{\stackrel{\→}{p}}_{i,3})+0.125({\stackrel{\→}{p}}_{i,3}-{\stackrel{\→}{p}}_{i,4})---\left(1\right)$

Wherein,WillIt is unitization,

1-2-2. circulation step 1-2-1 obtains every broken curve c_iDirection vector, by c₁Put into set Q₁In, then Travel through remaining all curve c_i, obtain and Q₁In all direction of curve vector angles and minimum curve, be designated as c_min, and put Enter to gather Q₁, until Q₁In the half that element is master curve quantity, remaining curve put into set Q₂。

$c_{\min }\∈Q_1,iff\underset{c_i\∈Q_1}{\mathrm{\Σ}}\mathrm{\θ}({\stackrel{\→}{s}}_i,{\stackrel{\→}{s}}_{\min })=\underset{c_j\∈Q-Q_1}{\min }\left\{\underset{c_j\∈Q_1}{\mathrm{\Σ}}\mathrm{\θ}({\stackrel{\→}{s}}_i,{\stackrel{\→}{s}}_j)\right\}---\left(2\right)$

1-2-3., by after the curve classification in Q, takes Q₁In a curve, at Q₂Middle searching and Q₁In the curve chosen rise These two curves are carried out quadratic polynomial curve matching, i.e. complete the connection of broken curve by the curve that point is closest；When complete After becoming the connection of these two broken curves, by these two curves respectively from set Q₁,Q₂Middle rejecting, then according to said method pair Remaining curve processes, until the curve of fracture has all connected, obtains the edge contour information repaired.

Second step: to image block by tagsort and K-SVD dictionary training.In order to strengthen the self adaptation of study dictionary Property, use the method combining image block gradient information and local variance that image block is classified.It is known that edge and texture Information is frequently found in the image block containing abundant structural information, otherwise, the smooth region of image contains less structure letter Breath.Graded according to pixel the most violent, image block inner structure information is the abundantest；And the image that structural information is rare Block, the gradient of its interior pixels is smaller.Therefore, gradient information can well reflect that the structural information of image block is enriched Degree (i.e. smoothness).

Make optional position in image (x, pixel value y) be f (x, y), the Grad in its 4 directions up and down is:

$\left\{\begin{array}{c}{g}_1(x,y)=|f(x,y)-f(x-1,y)|\\ g_2(x,y)=|f(x,y)-f(x+1,y)|\\ g_3(x,y)=|f(x,y)-f(x,y-1)|\\ g_4(x,y)=|f(x,y)-f(x,y+1)|\end{array}\right.---\left(3\right)$

Take the weights that greatest gradient value is this pixel on these 4 directions:

G (x, y)=max{g₁(x,y),g₂(x,y),g₃(x,y),g₄(x,y)} (4)

Each pixel in each image block (size is n × m) is carried out gradient weighting, and its size is:

$u_k=\frac{\underset{x=1}{\overset{n}{\mathrm{\Σ}}}\underset{y=1}{\overset{m}{\mathrm{\Σ}}}g(x,y)\×f(x,y)}{\underset{x=1}{\overset{n}{\mathrm{\Σ}}}\underset{y=1}{\overset{m}{\mathrm{\Σ}}}g(x,y)}---\left(5\right)$

u_kGradient weighted value for kth image block.In order to be classified by image block, set threshold value T₁, wherein T₁ For empirical, typically take T₁=100.Work as u_k＜ T₁Time, expression image block is smooth area, otherwise image block is structure-rich district. Although the graded in marginal texture district and irregular grain region is all universal relatively big, but the local variance of image tends to preferably The detailed information embodying image, it comprises a large amount of structural informations of image.Therefore, utilize local variance to said structure Classify again and obtain marginal texture district and irregular grain district in abundant district.

The local variance of kth image block is:

${\mathrm{Var}}_k=\frac{1}{n\×m}\underset{x=1}{\overset{n}{\mathrm{\Σ}}}\underset{y=1}{\overset{m}{\mathrm{\Σ}}}{|f(x,y)-{\stackrel{\‾}{f}}_k|}^2---\left(6\right)$

Wherein,For the average pixel value in image block.Set threshold value T₂, wherein T₂For empirical, typically take T₂ =300.Work as Var_k＜ T₂Time, image block is irregular grain district, otherwise image block is marginal texture district.

Image block is being divided into, by architectural feature, the sub-district that marginal texture district, irregular grain district are different with smooth area three Behind territory, the image pattern block of zones of different is carried out dictionary training, obtain the complete dictionary of corresponding mistake.Below with smooth Dictionary D_sAs a example by, illustrate that K-SVD algorithm realizes process to dictionary training.

According to sparse representation model:

$\begin{array}{ccc}\underset{D,X}{\min }\left|\right|Y-DX|{|}_2& s.t& \left|\right|x_i|{|}_0<K\end{array}---\left(7\right)$

Wherein, D=[d₁,d₂,…,d_L] it was complete dictionary, K ＜ ＜ L represents x_iMaximum degree of rarefication be K； Represent and treat training signal, the sample image block of the most same feature.Algorithm while solving D also to sparse coefficient x_iCarry out sparse Coding.Due to l₀The nonconvex property of problem, generally uses OMP algorithm to solve.But dictionary training algorithm is otherwise varied with formula (7) , training signalIt is known that and cross complete dictionary D be unknown, it needs to be obtained by dictionary training algorithm.

Assume Y_s={ y_i|i∈Ω_sRepresent that select from smooth region image block treats training sample set of blocks, Ω_sTable Show smooth region image block, can be described as by the process of the characteristics dictionary corresponding to this sample set of K-SVD Algorithm for Training:

$\begin{array}{ccc}\underset{D_s,X_s}{\min }\left|\right|Y_s-D_s{x}_s|{|}_2& s.t& \left|\right|x_i|{|}_0<K,i\&Element;{\mathrm{\&Omega;}}_s\end{array}---\left(8\right)$

In order to solve formula (8), it is necessary to first initialize dictionary D_s.In order to accelerate convergence of algorithm speed, select at this algorithm Select image sorted smoothed image block to D_sInitialize.

K-SVD algorithm is the estimation that the step according to sparse coding provides sample block set, thus update in dictionary each Individual atom.Specifically, smooth dictionary D to be updated_sIn kth row d_k, then formula (8) can be rewritten as:

$\left|\right|Y_s-D_s{x}_s|{|}_2=||Y_s-\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{d}_j{x}_j|{|}_2=\left|\right|(Y_s-\underset{j\&NotEqual;k}{\overset{K}{\mathrm{\&Sigma;}}}{d}_j{x}_j)-d_k{x}_k|{|}_2=||E_k-d_k{x}_k|{|}_2---\left(9\right)$

Wherein, D_sX_sBe broken down into matrix that K order is 1 and, remaining K-1 item is all fixing, and remaining 1 row seek to The row updated, E_kRepresent and remove atom d_kThe error afterwards all samples caused, and then to E_kCarry out SVD decomposition, update d_k.With Said method, by { d₁,d₂,…,d_LAll atoms in } are all updated, i.e. to smooth dictionary D_sComplete training.

So, according to the training method of above K-SVD, the image block classified just can obtain and cross complete dictionary accordingly: limit Edge dictionary D_e, irregular grain dictionary D_tAnd smooth dictionary D_s。

3rd step: l will be approximated₀The sparse restructing algorithm SL0 of norm is applied to the image repair of rarefaction representation.Use approximation Hyperbolic tangent function goes to approximate l₀Norm, utilizes conjugate gradient method to solve this function.

Owing to the mathematical model of SL0 is:

min||X||₀, s.t.Y=DX (10)

Vector X=[x₁ x₂ … x_n]^T, its l₀Norm represents the number of non-zero element in vector X, if assuming:

$f\left(x\right)=\left\{\begin{array}{cc}1,& x\&NotEqual;0\\ 0,& x=0\end{array}\right.---\left(11\right)$

Then:

$\left|\right|X|{|}_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}f\left(x_i\right)---\left(12\right)$

Therefore, as long as finding continuous function f (x) the most smooth, it is possible to well approach | | X | |₀Value. There is " abruptness " significantly smooth continuous function to construct, and this continuous function can accurately approach l₀Norm.Therefore originally Patent uses the near-hyperbolic tan shown in formula (13) as approximate evaluation l₀The function of norm.

$f_{\mathrm{\&sigma;}}\left(x\right)=\frac{1}{8}\frac{e^{\frac{x^2}{2{\mathrm{\&sigma;}}^2}}-e^{\frac{-x^2}{2{\mathrm{\&sigma;}}^2}}}{e^{\frac{x^2}{2{\mathrm{\&sigma;}}^2}}+e^{\frac{-x^2}{2{\mathrm{\&sigma;}}^2}}}+\frac{7}{8}(1-e^{\frac{-8x^2}{{\mathrm{\&sigma;}}^2}})---\left(13\right)$

Knowable to formula (13), variable σ value is the least, and near-hyperbolic tan " abruptness " is the most obvious, more approaches l₀Norm, But along with constantly diminishing of σ value, function curve is more and more rough.Therefore, choosing of σ parameter is the most crucial, choosing of it L must approached₀Degree and the smoothing of functions degree of norm take compromise between the two.To this end, use one group of σ sequence { σ successively decreased₁, σ₂,…,σ_nBe used for approaching object function, carry out the optimum of solved function to utilizing steepest descent method while σ each time value.

The direction of search of steepest descent method is the negative gradient direction of function, and closer to desired value, step-length is the least, advances more Slowly, solution procedure exists sawtooth effect so that l₀The accuracy that norm is estimated reduces.And the direction of search of conjugate gradient method For the linear combination in negative gradient direction with the direction of search of last iteration, the sawtooth effect that steepest descent method is brought can be solved Should.

For solving this kind of nothing of minf (x) about fasciculation problem, it is assumed that an initial value x₀, obtain x through series of iterations_n。 If current iterative value is x_k, then next iterative value i.e. x_k+1=x_k+u×d_k, u represents iteration step length, d_kRepresent and ask minimum The direction of search of value, use conjugate gradient method solution formula is:

$d_k=\left\{\begin{array}{cc}-g_k,& k=1\\ -g_k+{\mathrm{\&beta;}}_k{d}_{k-1},& k\&GreaterEqual;2\end{array}\right.---\left(14\right)$

Wherein, g_kThe gradient of representative function f (x), β_kCan be solved by different conjugate gradient methods.To β_kSolve Method uses mixing conjugate gradient method, i.e. mixes FR (Fletcher-Reeves) conjugate gradient method and PRP (Polak, Ribiere And Polyar) conjugate gradient method:

${\mathrm{\&beta;}}_k=\left\{\begin{array}{cc}{\mathrm{\&beta;}}_k^{PRP},& 0<{\mathrm{\&beta;}}_k^{PRP}<{\mathrm{\&beta;}}_k^{FR}\\ {\mathrm{\&beta;}}_k^{FR},& else\end{array}\right.---\left(15\right)$

The conjugate gradient method of this mixing avoids the shortcoming that may produce continuous little step-length；Simultaneously as conjugate gradient The direction of the iteration each time of method is all that last iteration direction forms with negative gradient directional combination, it is possible to overcome steepest descent method The crenellated phenomena brought.

Therefore, utilize the sparse representation method of SL0, classification repair all kinds of characteristic information of image to realize step as follows:

(1) initial value is made to be respectively X=D^T(DD^T)^-1Y, σ₁=2max (X), k=1；

(2) j=1,2 ..., L, (L is conjugate gradient method iterations, L=5) utilizes conjugate gradient method to solve g_nThe gradient of representative function f (x):

1. direction is searched:

②X←X+μd_n, wherein step factor μ=1.5；

③X←X-D^T(DD^T)^-1(DX-Y)；

4. n=n+1, j=j+1；If j is ＜ L, then repeat step 1., 2., 3.；

(3) k=k+1, σ_k=η σ_k-1, η ∈ [0.51], repeat step (2), until σ_k＜ ε, ε=0.01, now obtain X's Optimal solution.

The present invention has the beneficial effect that:

When being reconstructed image to be repaired, generally requiring the degree of rarefication estimating signal, no matter degree of rarefication is estimated too small Or cross and mostly can not reach preferable quality reconstruction；Secondly, sparse representation method is not ideal enough to the holding of structure flatness, When particularly curve being repaired, some distortion can be produced at structure.In order to preferably repair the structural information of image, this Invent from the angle considering structure entirety flatness, the advantage repaired in conjunction with sample rarefaction representation and structural constraint.

The crack edge of area to be repaired is extracted by the present invention, it is thus achieved that the various information of reflecting edge feature, according to Crack edge line is carried out curve fitting, to ensure that the reparation of image edge structure is strictly by limit by these information by certain rule The constraint of edge contour line；Use and carry out dictionary training by tagsort, to strengthen the adaptivity of study dictionary；Use approximate Double Bent tan goes to approximate l₀Norm, utilizes conjugate gradient method to solve this function, it is achieved the improvement to tradition SL0 algorithm, will not Need the SL0 restructing algorithm estimating degree of rarefication to be applied in the image repair of non-edge damaged area, repair improving rarefaction representation The reliability of multiple texture information.

Accompanying drawing explanation

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

Fig. 2 is the overall structural edge schematic diagram extracted with local approach, and Fig. 2 (a) is damaged Lena image；Fig. 2 (b) is overall The structural edge that method is extracted；The overall structural edge extracted with local approach of Fig. 2 (c)；Fig. 2 (d) edge fitting design sketch, Qi Zhongtu In ' △ ' represent without screening before the starting point at agent structure edge, ' o ' represents rising of the agent structure edge after screening Point.

Fig. 3 (a)-(d) is the matching repairing model of crack edge.

Fig. 4 (a)-(b) is that marginal information repairs schematic diagram.

Fig. 5 (a)-(c) is that image block is by the schematic diagram of tagsort.

Fig. 6 (a)-(f) is for being respectively adopted reparation algorithm [1], repairing algorithm [2], reparation algorithm [3] and inventive algorithm Comparison to damaged Baboon image repair result.

Fig. 7 (a)-(f) is for using the comparison to damaged Barb image repair effect of the above-mentioned algorithm.

Fig. 8 (a)-(f) removes the comparison of result for using above-mentioned algorithm that Baboon image carries out English alphabet.

Fig. 9 (a)-(f) removes the comparison of design sketch for using above-mentioned algorithm to material object.

Figure 10 (a)-(f) is for using the comparison to large area breakage Lena repairing effect of the above-mentioned algorithm.

Figure 11 (a)-(f) removes the comparison of effect for using above-mentioned algorithm to personage.

Illustrate: in order to compare the superiority of inventive algorithm, compare with following associated restoration algorithm.

Reparation algorithm [1]: Criminisi A, Perez P, Toyama K.Region filling and object removal by Eexemplar-based inpainting[J].IEEE Transactions on Image Processing,2004,13(9):1200-1212.

Reparation algorithm [2]: Xu Z, Sun J.Image inpainting by patch propagation using patch sparsity[J].IEEE Transactions on Image Processing,2010,19(5):1153-1165.

Reparation algorithm [3]: Konka's human relations, Tang Xianghong, Zhang Dong, slaughter Artline. the structure sparse propagation image of tagsort study Restorative procedure [J]. computer-aided design and graphics journal, 2015,27 (5): 864-872.

It is embodied as explanation

Below in conjunction with the accompanying drawings the embodiment of the present invention is elaborated.

In the present embodiment, the flow chart of the present invention that Fig. 1 is given.

The first step: first, by Sobel operator extraction integral edge, it is thus achieved that the strong edge of breakage image, for image repair The integral edge structure of image is provided, as shown in Fig. 2 (b), gives the structural edge that damaged Lena image wholeness method is extracted； Then using the principle of " by there are continuous 4 marginal points and above crack edge line is defined as agent structure edge ", using Integral edge is extracted and is extracted the method realization combined with damaged neighboring area local edge, effectively obtains damaged neighboring area Crack edge structural information, finds the intersection point on border to be repaired and marginal information, as shown in Fig. 2 (c).In order to by these points one by one Correspondingly connected, Fig. 3 (a) gives a plurality of crack edge line and is respectively c₁,c₂,…,c_N, it is designated as gathering Q, wherein curve c_i's Starting point is p_i1.Regulation is by curve c_iIn its starting point p_i1On the most contrary two broken curves of direction vector be connected.Thus lead to Cross curve c_iDirection vector Q is divided into two set Q₁,Q₂.After having classified, calculate the distance between each origin of curve, will The method of two curve negotiating quadratic polynomial curve matchings that starting point is closest is attached.Specifically comprise the following steps that

(1) for arbitrary broken curve c_i, by starting point p_i1Set out, obtain c_iOn other each point p_i2,p_i3,p_i4,.IfFor a p_i,jCoordinate vector, then curve c_iIn starting point p_i1On direction vector be defined as:

${\stackrel{\&RightArrow;}{s}}_i=0.5({\stackrel{\&RightArrow;}{p}}_{i,1}-{\stackrel{\&RightArrow;}{p}}_{i,2})+0.25({\stackrel{\&RightArrow;}{p}}_{i,2}-{\stackrel{\&RightArrow;}{p}}_{i,3})+0.125({\stackrel{\&RightArrow;}{p}}_{i,3}-{\stackrel{\&RightArrow;}{p}}_{i,4})---\left(1\right)$

Wherein,WillIt is unitization,

(2) circulation step (1) obtains every curve c_iDirection vector, by c₁Put into set Q₁In, then travel through remaining All curve c_i, obtain and Q₁In all direction of curve vector angles and minimum curve, be designated as c_min, and put into set Q₁, Until Q₁In the half that element is master curve quantity, remaining curve put into set Q₂。

$c_{\min }\&Element;Q_1,iff\underset{c_i\&Element;Q_1}{\mathrm{\&Sigma;}}\mathrm{\&theta;}({\stackrel{\&RightArrow;}{s}}_i,{\stackrel{\&RightArrow;}{s}}_{\min })=\underset{c_j\&Element;Q-Q_1}{\min }\left\{\underset{c_j\&Element;Q_1}{\mathrm{\&Sigma;}}\mathrm{\&theta;}({\stackrel{\&RightArrow;}{s}}_i,{\stackrel{\&RightArrow;}{s}}_j)\right\}---\left(2\right)$

(3) by after the curve classification in Q, Q is taken₁In a curve, at Q₂The song that middle searching is closest with its starting point These two curves are carried out quadratic polynomial curve matching, i.e. complete the connection of broken curve by line；When completing these two fracture songs After the connection of line, by these two curves respectively from set Q₁,Q₂Middle rejecting, then according to remaining curve is carried out by said method Process, until the curve of fracture has all connected.Shown in broken curve repairing effect such as Fig. 3 (b):

(4) when broken curve sum N is odd number, n (Q₁)≠n(Q₂) (as shown in Fig. 3 (c)).In this case, it is achieved Step does following adjustment:

1. in performing step (2), if n is (Q₁)=(N-1)/2, the most ensuing curve c_iSort out by following rule:

$c_{\min }\&Element;\left\{\begin{array}{cc}{Q}_1,& \underset{c_i\&Element;Q_1}{\mathrm{\&Sigma;}}\mathrm{\&theta;}({\stackrel{\&RightArrow;}{S}}_i,{\stackrel{\&RightArrow;}{S}}_{\min })\&le;\frac{\mathrm{\&pi;}(N-1)/2}{2}\\ Q_2,& \underset{c_i\&Element;Q_1}{\mathrm{\&Sigma;}}\mathrm{\&theta;}({\stackrel{\&RightArrow;}{S}}_i,{\stackrel{\&RightArrow;}{S}}_{\min })>\frac{\mathrm{\&pi;}(N-1)/2}{2}\end{array}\right.$

After completing the classification of (N-1)/2+1 bar curve, remaining curve puts into set Q₂In.

2., in step (3), Q is compared₁,Q₂In element number, choose the set that number is few, it is assumed that n (Q₁) ＜ n (Q₂), Then take set Q₁In a curve, at Q₂These two curves are carried out secondary many by the curve that middle searching is closest with its starting point Item formula curve matching.The like, complete to gather Q₁In all curves pairing after, Q₂In also to remain a curve unpaired, then exist Q₁The curve that middle searching is closest with its starting point, completes to connect.All curves in so Q have matched, such as Fig. 3 (d) institute Show.

Shown to fitting effect such as Fig. 2 (d) of the crack edge of damaged Lena figure (Fig. 2 (a)) by above-mentioned matching rule.

After image border curve completes matching, the constraint information that this matched curve just can be repaired as edge so that The reparation of edge epigraph block is carried out by the track at edge.Centered by point on present invention edge line after matching, take reparation Window size is 3 × 3 (for the accuracys repaired, repair window value less), utilizes the error sum of squares (SSD) of pixel to exist ψ₁,ψ₂,ψ₃... (the known pixels block on edge line, size is 3 × 3, as shown in Fig. 4 (a)) is found mate most like with ψ Block, then the pixel value of best matching blocks is filled into the unknown pixel point of the image block to be repaired of correspondence.The most successively Complete the reparation of little image block on edge.Repair shown in result such as Fig. 4 (b).

Second step: to image block by tagsort and K-SVD dictionary training.In order to strengthen the self adaptation of study dictionary Property, use the method combining image block gradient information and local variance that image block is classified.It is known that edge and texture Information is frequently found in the image block containing abundant structural information, otherwise, the smooth region of image contains less structure letter Breath.Graded according to pixel the most violent, image block inner structure information is the abundantest；And the image that structural information is rare Block, the gradient of its interior pixels is smaller.Therefore, gradient information can well reflect that the structural information of image block is enriched Degree (i.e. smoothness).

If make optional position in image (x, pixel value y) be f (x, y), the Grad in its 4 directions up and down is:

$\left\{\begin{array}{c}{g}_1(x,y)=|f(x,y)-f(x-1,y)|\\ g_2(x,y)=|f(x,y)-f(x+1,y)|\\ g_3(x,y)=|f(x,y)-f(x,y-1)|\\ g_4(x,y)=|f(x,y)-f(x,y+1)|\end{array}\right.---\left(3\right)$

Take the weights that greatest gradient value is this pixel on these 4 directions:

G (x, y)=max{g₁(x,y),g₂(x,y),g₃(x,y),g₄(x,y)} (4)

Each pixel in each image block (size is n × m) is carried out gradient weighting, and its size is:

$u_k=\frac{\underset{x=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{m}{\mathrm{\&Sigma;}}}g(x,y)\&times;f(x,y)}{\underset{x=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{m}{\mathrm{\&Sigma;}}}g(x,y)}---\left(5\right)$

u_kGradient weighted value for kth image block.In order to be classified by image block, set threshold value T₁, wherein T₁ For empirical, typically take T₁=100.Work as u_k＜ T₁Time, expression image block is smooth area, otherwise image block is structure-rich district. Fig. 5 (b) gives the result using gradient weighted value that Fig. 5 (a) carries out image block classification.In Fig. 5 (b), black part represents Smooth region, white portion represents structure-rich region.But due to marginal texture district and the graded in irregular grain region All generally bigger, it is impossible to go to identify marginal texture district and irregular grain district by gradient weighted value.Therefore, local variance pair is utilized Said structure enriches district and classifies and obtain marginal texture district and irregular grain district.

The local variance of kth image block is:

${\mathrm{Var}}_k=\frac{1}{n\&times;m}\underset{x=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{m}{\mathrm{\&Sigma;}}}{|f(x,y)-{\stackrel{\&OverBar;}{f}}_k|}^2---\left(6\right)$

Wherein,For the average pixel value in image block.Set threshold value T₂, wherein T₂For empirical, typically take T₂ =300.Work as Var_k＜ T₂Time, image block is irregular grain district, otherwise image block is marginal texture district.Fig. 5 (c) is given and finishes Closing gradient weighted value and the image classification results of local variance, wherein black region represents smooth area, and grey parts represents and do not advises Then texture area, white portion represents structural area, edge.It can be seen that the figure that gradient weighted value and local variance combine As tagsort effect is preferable.

Image block is being divided into, by architectural feature, the sub-district that marginal texture district, irregular grain district are different with smooth area three Behind territory, the image pattern block of zones of different is carried out dictionary training, obtain the complete dictionary of corresponding mistake.Below with smooth Dictionary D_sAs a example by, illustrate that K-SVD algorithm realizes process to dictionary training.

According to sparse representation model:

$\begin{array}{ccc}\underset{D,X}{\min }\left|\right|Y-DX|{|}_2& s.t& \left|\right|x_i|{|}_0<K\end{array}---\left(7\right)$

Wherein, D=[d₁,d₂,…,d_L] it was complete dictionary, K ＜ ＜ L represents x_iMaximum degree of rarefication be K； Represent and treat training signal, the sample image block of the most same feature.Algorithm while solving D also to sparse coefficient x_iCarry out sparse Coding.Due to l₀The nonconvex property of problem, generally uses OMP algorithm to solve.But dictionary training algorithm is otherwise varied with formula (7) , training signalIt is known that and cross complete dictionary D be unknown, it needs to be obtained by dictionary training algorithm.

Assume Y_s={ y_i|i∈Ω_sRepresent that select from smooth region image block treats training sample set of blocks, Ω_sTable Show smooth region image block, can be described as by the process of the characteristics dictionary corresponding to this sample set of K-SVD Algorithm for Training:

$\begin{array}{ccc}\underset{D_s,X_s}{\min }\left|\right|Y_s-D_s{x}_s|{|}_2& s.t& \left|\right|x_i|{|}_0<K,i\&Element;{\mathrm{\&Omega;}}_s\end{array}---\left(8\right)$

In order to solve formula (8), it is necessary to first initialize dictionary D_s.In order to accelerate convergence of algorithm speed, select in the present invention Select image sorted smoothed image block to D_sInitialize.

K-SVD algorithm is the estimation that the step according to sparse coding provides sample block set, thus update in dictionary each Individual atom.Specifically, D to be updated_sIn kth row d_k, then formula (8) can be rewritten as:

Wherein, D_sX_sBe broken down into matrix that K order is 1 and, remaining K-1 item is all fixing, and remaining 1 row seek to The row updated, E_kRepresent and remove atom d_kThe error afterwards all samples caused, and then to E_kCarry out SVD decomposition, update d_k.With Said method, by { d₁,d₂,…,d_LAll atoms in } are all updated, i.e. to dictionary D_sComplete training.

So, according to the training method of above K-SVD, the image block classified just can obtain and cross complete dictionary accordingly: limit Edge dictionary D_e, irregular grain dictionary D_tAnd smooth dictionary D_s。

3rd step: l will be approximated₀The sparse restructing algorithm SL0 of norm is applied to the image repair of rarefaction representation.Use approximation Hyperbolic tangent function goes to approximate l₀Norm, utilizes conjugate gradient method to solve this function.

Owing to the mathematical model of SL0 is:

min||X||₀, s.t.Y=DX (10)

Vector X=[x₁ x₂ … x_n]^T, its l₀Norm represents the number of non-zero element in vector X, if assuming:

$f\left(x\right)=\left\{\begin{array}{cc}1,& x\&NotEqual;0\\ 0,& x=0\end{array}\right.---\left(11\right)$

Then:

$\left|\right|X|{|}_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}f\left(x_i\right)---\left(12\right)$

Therefore, as long as finding continuous function f (x) the most smooth, it is possible to well approach | | X | |₀Value. There is " abruptness " significantly smooth continuous function to construct, and this continuous function can accurately approach l₀Norm.Therefore originally Near-hyperbolic tan shown in invention employing formula (13) is as approximate evaluation l₀The function of norm.

$f_{\mathrm{\&sigma;}}\left(x\right)=\frac{1}{8}\frac{e^{\frac{x^2}{2{\mathrm{\&sigma;}}^2}}-e^{\frac{-x^2}{2{\mathrm{\&sigma;}}^2}}}{e^{\frac{x^2}{2{\mathrm{\&sigma;}}^2}}+e^{\frac{-x^2}{2{\mathrm{\&sigma;}}^2}}}+\frac{7}{8}(1-e^{\frac{-8x^2}{{\mathrm{\&sigma;}}^2}})---\left(13\right)$

Knowable to formula (13), variable σ value is the least, and near-hyperbolic tan " abruptness " is the most obvious, more approaches l₀Norm, But along with constantly diminishing of σ value, function curve is more and more rough.Therefore, choosing of σ parameter is the most crucial, choosing of it L must approached₀Degree and the smoothing of functions degree of norm take compromise between the two.To this end, use one group of σ sequence { σ successively decreased₁, σ₂,…,σ_nBe used for approaching object function, carry out the optimum of solved function to utilizing steepest descent method while σ each time value.

The direction of search of steepest descent method is the negative gradient direction of function, and closer to desired value, step-length is the least, advances more Slowly, solution procedure exists sawtooth effect so that l₀The accuracy that norm is estimated reduces.And the direction of search of conjugate gradient method For the linear combination in negative gradient direction with the direction of search of last iteration, the sawtooth effect that steepest descent method is brought can be solved Should.

For solving this kind of nothing of minf (x) about fasciculation problem, it is assumed that an initial value x₀, obtain x through series of iterations_n。 If current iterative value is x_k, then next iterative value i.e. x_k+1=x_k+u×d_k, u represents iteration step length, d_kRepresent and ask minimum The direction of search of value, use conjugate gradient method solution formula is:

$d_k=\left\{\begin{array}{cc}-g_k,& k=1\\ -g_k+{\mathrm{\&beta;}}_k{d}_{k-1},& k\&GreaterEqual;2\end{array}\right.---\left(14\right)$

Wherein, g_kThe gradient of representative function f (x), β_kCan be solved by different conjugate gradient methods.To β_kSolve Method uses mixing conjugate gradient method, i.e. mixes FR (Fletcher-Reeves) conjugate gradient method and PRP (Polak, Ribiere And Polyar) conjugate gradient method:

${\mathrm{\&beta;}}_k=\left\{\begin{array}{cc}{\mathrm{\&beta;}}_k^{PRP},& 0<{\mathrm{\&beta;}}_k^{PRP}<{\mathrm{\&beta;}}_k^{FR}\\ {\mathrm{\&beta;}}_k^{FR},& else\end{array}\right.---\left(15\right)$

The conjugate gradient method of this mixing avoids the shortcoming that may produce continuous little step-length；Simultaneously as conjugate gradient The direction of the iteration each time of method is all that last iteration direction forms with negative gradient directional combination, it is possible to overcome steepest descent method The crenellated phenomena brought.

Therefore, utilize the sparse representation method of SL0, classification repair all kinds of characteristic information of image to realize step as follows:

(1) initial value is made to be respectively X=D^T(DD^T)^-1Y, σ₁=2max (X), k=1；

(2) j=1,2 ..., L, (L is conjugate gradient method iterations, L=5) utilizes conjugate gradient method to solve g_nThe gradient of representative function f (x):

1. direction is searched:

②X←X+μd_n, wherein step factor μ=1.5；

③X←X-D^T(DD^T)^-1(DX-Y)；

4. n=n+1, j=j+1；If j is ＜ L, then repeat step 1., 2., 3.；

(3) k=k+1, σ_k=η σ_k-1, η ∈ [0.51], repeat step (2), until σ_k＜ ε, ε=0.01, now obtain X's Optimal solution.

In order to check the repairing effect of inventive algorithm, image is simulated emulation, and carries out with other algorithms Contrast experiment.Emulation experiment is carried out under MATLAB environment.When image repair effect is commented, in addition to using subjective assessment, It is also adopted by Y-PSNR (PSNR) simultaneously and carries out objective evaluation.

Fig. 6 and Fig. 7 gives reparation algorithm [1], repairs algorithm [2], reparation algorithm [3] and this algorithm to breakage image Baboon and Barb carries out the result of repair process.From Fig. 6 Baboon repairing effect figure it can be seen that at nose mid portion (smooth region), the repairing effect of four kinds of algorithms is the most more satisfactory；In the breakage of nose Yu cheek junction, repair algorithm [1], All there is structural break phenomenon (Fig. 6 (c), Fig. 6 (d) and Fig. 6 (e) shown in) in algorithm [2] and algorithm [3] after repairing, but this algorithm The marginal texture of nose smooths after repair；For the reparation of eye portion, this part-structure and texture information are the most complicated, calculate In the upper right portion of eyes, method [1] and algorithm [2] occur that the factitious white of bulk extends (shown in Fig. 6 (c), Fig. 6 (d)), Eye structure is caused heavy damage, after algorithm [3] reparation, occurs in that certain extension phenomenon (shown in Fig. 6 (e)) at canthus, And this algorithm canthus after repair maintains clear nothing around good architectural feature and eyeball and extends phenomenon, repairing effect compares Natural (shown in Fig. 6 (f)).

From the result of Fig. 7 Barb figure repair process it can be seen that four kinds of algorithms are equal at arm (smooth region) repairing effect Well；Four kinds of algorithms are preferable at table leg marginal portion (smooth area and edge calmodulin binding domain CaM) repairing effect；Repairing scarf part Time (texture with edge calmodulin binding domain CaM), algorithm [1], algorithm [2] and algorithm [3] all occur the incoherent phenomenon of texture (Fig. 7 (c), Shown in Fig. 7 (d) and Fig. 7 (e)), repairing effect is fuzzyyer；And first this algorithm owing to being repaired the edge of scarf, Define certain structural constraint, therefore repair back edge structure and be maintained, and clean mark, the most natural (Fig. 7 of trend Shown in (f)).

Fig. 8 and Fig. 9 sets forth the comparison of object removal treatment effect.Fig. 8 gives and Baboon figure is carried out English The result that letter removal processes.It can be seen that repair Baboon figure nose in the middle part of etc. image smoothing district time, four kinds The repairing effect of algorithm is the best；But algorithm [2] and algorithm [3] are when repairing nose with cheek intersection, and nose border occurs Phenomenon of rupture (Fig. 8 (d) and Fig. 8 (e) draws black circle part), structure is destroyed, and other two kinds of algorithms can keep structure herein Coherent；When repairing the lines of cheek, all there is factitious extension (Fig. 8 (c), Fig. 8 in algorithm [1], algorithm [2] and algorithm [3] Shown in (d) and Fig. 8 (e)), do not meet visual law, and this algorithm repairing effect is more satisfactory；Beard part in Baboon figure belongs to In texture structure complex region, algorithm [1], algorithm [2] and algorithm [3] these three algorithm all occur fuzzy or factitious prolong Stretch phenomenon (Fig. 8 (c), Fig. 8 (d) and Fig. 8 (e) are shown), and this algorithm is at texture part repairing effect natural (shown in Fig. 8 (f)).

Fig. 9 gives the simulation experiment result removing material object.It can be seen that algorithm [1], algorithm [2] and calculation There is edge distortion and discontinuous phenomenon (Fig. 9 (c), Fig. 9 (d) and Fig. 9 (e) are shown) when repairing bank in method [3], and edge is tied Structure cannot keep continuity, and repairing mark is obvious so that repairing effect is unnatural.And this algorithm removes effect very certainly to object So, visual law is met.

Figure 10 and Figure 11 sets forth the comparison that large area breakage is repaiied effect.Figure 10 gives and carries out Lena figure greatly The simulation experiment result that area is repaired, wherein damaged area is 10.1% (every fritter breakage size is 20 × 20 pixels).From figure In it can be seen that the reparation of the left cheek in Lena figure and part background area (smooth) is imitated by algorithm [1] and algorithm [2] Fruit the best (Figure 10 (c), Figure 10 (d) draw black circle part), and other two kinds of algorithms are the best to the repairing effect of this part；Hair The texture structure of part is complicated, and algorithm [1], algorithm [2] and algorithm [3] these three algorithm all occur when repairing hair portion Phenomenon of rupture (Figure 10 (c), Figure 10 (d) and Figure 10 (e) are shown), and the repairing effect of this algorithm is more satisfactory, hair portion after reparation The most there is not factitious phenomenon of rupture (shown in Figure 10 (f)) in proportion by subtraction.In parts such as crown, the brim of a hat and right cheek (drawing black circle part), all there is a certain degree of concavo-convex and factitious extension phenomenon when repairing its edge in first three algorithm, And the crack edge line of area to be repaired is first fitted by this algorithm, ensure the flatness of image border so that repair effect Fruit meets human eye vision effect (shown in Figure 10 (f)).

Figure 11 gives the simulation experiment result removing large area material object.It can be seen that algorithm [2] (Figure 11 Shown in (d)) when repairing sea level at a distance and these two parts of wave, discontinuous phenomenon all occurs, structural information is destroyed, There is obvious repairing mark；And algorithm [1], algorithm [2] and algorithm [3] are when repairing wave part, its edge lines are not Enough smooth, make material object remove effect unnatural (Figure 11 (c), Figure 11 (d) and Figure 11 (e) are shown)；And this algorithm repairing effect is certainly So, visual law is met.

Above the preferred embodiments of the present invention and principle are described in detail, to those of ordinary skill in the art Speech, the thought provided according to the present invention, detailed description of the invention will change, and these changes also should be regarded as the present invention Protection domain.

Claims (8)

1. the classification rarefaction representation image repair method of an edge fitting, it is characterised in that: use integral edge and local edge The extracting method that edge combines, extracts the crack edge of area to be repaired, it is thus achieved that the marginal information of reflecting edge feature, Crack edge line is carried out curve fitting by certain rule according to these marginal informations, tight to ensure the reparation of image edge structure Lattice are retrained by edge wheel profile；Use and carry out dictionary training by tagsort, to strengthen the adaptivity of study dictionary；Adopt Go to approximate l with near-hyperbolic tan₀Norm, utilizes conjugate gradient method to solve this function, it is achieved change tradition SL0 algorithm Enter, the SL0 restructing algorithm that need not estimate degree of rarefication is applied in the image repair of non-edge damaged area.

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 1, it is characterised in that: obtain Take and repair the marginal information of image；

1-1. passes through Sobel operator extraction integral edge, it is thus achieved that the strong edge of breakage image, provides the whole of image for image repair Body marginal texture；

1-2. uses the principle of " by there are continuous 4 marginal points and above crack edge line is defined as agent structure edge ", Use integral edge to extract and extract the method realization combined with damaged neighboring area local edge, effectively obtain damaged surrounding zone The crack edge structural information in territory, finds the intersection point on border to be repaired and marginal information；By these broken curves correspondingly Connect, if broken curve is c₁,c₂,…,c_n, it is designated as gathering Q, wherein broken curve c_iStarting point be p_i1；By broken curve c_i? Its starting point p_i1On the most contrary two broken curves of direction vector be connected；From there through curve c_iDirection vector Q is divided It is two set Q₁,Q₂；After having classified, calculate the distance between each origin of curve, two closest for starting point curves are led to The method crossing quadratic polynomial curve matching is attached.

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 2, it is characterised in that institute The method by two closest for starting point curve negotiating quadratic polynomial curve matchings stated is attached, and concrete steps are such as Under:

1-2-1. is for arbitrary broken curve c_i, by starting point p_i1Set out, obtain c_iOn other each point p_i2,p_i3,p_i4,；IfFor a p_i,jCoordinate vector, then curve c_iIn starting point p_i1On direction vector be defined as:

${\stackrel{\&RightArrow;}{s}}_i=0.5({\stackrel{\&RightArrow;}{p}}_{i,1}-{\stackrel{\&RightArrow;}{p}}_{i,2})+0.25({\stackrel{\&RightArrow;}{p}}_{i,2}-{\stackrel{\&RightArrow;}{p}}_{i,3})+0.125({\stackrel{\&RightArrow;}{p}}_{i,3}-{\stackrel{\&RightArrow;}{p}}_{i,4})---\left(1\right)$

Wherein,WillIt is unitization,

1-2-2. circulation step 1-2-1 obtains every broken curve c_iDirection vector, by c₁Put into set Q₁In, then travel through Remaining all curve c_i, obtain and Q₁In all direction of curve vector angles and minimum curve, be designated as c_min, and put into collection Close Q₁, until Q₁In the half that element is master curve quantity, remaining curve put into set Q₂；

$c_{\min }\&Element;Q_1,iff\underset{c_i\&Element;Q_1}{\mathrm{\&Sigma;}}\mathrm{\&theta;}({\stackrel{\&RightArrow;}{s}}_i,{\stackrel{\&RightArrow;}{s}}_{\min })=\underset{c_j\&Element;Q-Q_1}{\min }\left\{\underset{c_j\&Element;Q_1}{\mathrm{\&Sigma;}}\mathrm{\&theta;}({\stackrel{\&RightArrow;}{s}}_i,{\stackrel{\&RightArrow;}{s}}_j)\right\}---\left(2\right)$

1-2-3., by after the curve classification in Q, takes Q₁In a curve, at Q₂Middle searching and Q₁In the origin of curve chosen away from From nearest curve, these two curves are carried out quadratic polynomial curve matching, i.e. completes the connection of broken curve；When completing this Article two, after the connection of broken curve, by these two curves respectively from set Q₁,Q₂Middle rejecting, then according to said method is to remaining Curve process, until fracture curve all connected, obtain repair edge contour information.

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 1, it is characterised in that institute The employing stated carries out dictionary training by tagsort, specific as follows:

Use the method combining image block gradient information and local variance that image block is classified, make optional position in image (x, pixel value y) be f (x, y), the Grad in its 4 directions up and down is:

$\left\{\begin{array}{c}{g}_1(x,y)=|f(x,y)-f(x-1,y)|\\ g_2(x,y)=|f(x,y)-f(x+1,y)|\\ g_3(x,y)=|f(x,y)-f(x,y-1)|\\ g_4(x,y)=|f(x,y)-f(x,y+1)|\end{array}\right.---\left(3\right)$

Take the weights that greatest gradient value is this pixel on these 4 directions:

G (x, y)=max{g₁(x,y),g₂(x,y),g₃(x,y),g₄(x, y) } (4) by each image block (size is n × m) Each pixel carry out gradient weighting, its size is:

$u_k=\frac{\underset{x=1}{\overset{n}{\&Sigma;}}\underset{y=1}{\overset{m}{\&Sigma;}}g(x,y)\&times;f(x,y)}{\underset{x=1}{\overset{n}{\&Sigma;}}\underset{y=1}{\overset{m}{\&Sigma;}}g(x,y)}---\left(5\right)$

u_kGradient weighted value for kth image block；In order to be classified by image block, set threshold value T₁, wherein T₁For warp Test constant, work as u_k＜ T₁Time, expression image block is smooth area, otherwise image block is structure-rich district；Although marginal texture district and not The graded in regular veins region is all universal relatively big, but the local variance of image tends to preferably embody the details of image Information, it comprises a large amount of structural informations of image；Therefore, utilize local variance that said structure is enriched district to classify again To marginal texture district and irregular grain district；

The local variance of kth image block is:

${\mathrm{Var}}_k=\frac{1}{n\&times;m}\underset{x=1}{\overset{n}{\&Sigma;}}\underset{y=1}{\overset{m}{\&Sigma;}}|f(x,y)-{\stackrel{\&OverBar;}{f}}_k{|}^2---\left(6\right)$

Wherein,For the average pixel value in image block；Set threshold value T₂, wherein T₂For empirical, work as Var_k＜ T₂Time, Image block is irregular grain district, otherwise image block is marginal texture district；

Image block is being divided into marginal texture district, three the different subregions in irregular grain district and smooth area by architectural feature After, the image pattern block of zones of different is carried out dictionary training, obtains the complete dictionary of corresponding mistake.

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 1, it is characterised in that institute The T stated₁=100, T₂=300.

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 4, it is characterised in that make With K-SVD algorithm to dictionary training, by specific as follows for the process that the image pattern block of smooth area carries out dictionary training:

According to sparse representation model:

$\begin{array}{ccc}\underset{D,X}{\min }\left|\right|Y-DX|{|}_2& s.t& \left|\right|x_i|{|}_0<K\end{array}---\left(7\right)$

Wherein, D=[d₁,d₂,…,d_L] it was complete dictionary, K ＜ ＜ L represents x_iMaximum degree of rarefication be K；Represent Treat training signal, the sample image block of the most same feature；Algorithm while solving D also to sparse coefficient x_iCarry out sparse volume Code；Due to l₀The nonconvex property of problem, generally uses OMP algorithm to solve；But dictionary training algorithm is otherwise varied with formula (7) It is, training signalIt is known that and cross complete dictionary D be unknown, it needs to be obtained by dictionary training algorithm；

Assume Y_s={ y_i|i∈Ω_sRepresent that select from smooth region image block treats training sample set of blocks, Ω_sRepresent smooth Area image block, can be described as by the process of the characteristics dictionary corresponding to this sample set of K-SVD Algorithm for Training:

$\begin{array}{ccc}\underset{D_s,X_s}{\min }\left|\right|Y_s-D_s{x}_s|{|}_2& s.t& \left|\right|x_i|{|}_0<K,i\&Element;{\mathrm{\&Omega;}}_s\end{array}---\left(8\right)$

In order to solve formula (8), it is necessary to first initialize dictionary D_s；In order to accelerate convergence of algorithm speed, at this algorithms selection image Sorted smoothed image block is to D_sInitialize；

K-SVD algorithm is the estimation that the step according to sparse coding provides sample block set, thus it is former to update each in dictionary Son；Specifically, smooth dictionary D to be updated_sIn kth row d_k, then formula (8) can be rewritten as:

$\left|\right|Y_s-D_s{x}_s|{|}_2=||Y_s-\underset{j=1}{\overset{K}{\&Sigma;}}{d}_j{x}_j|{|}_2=\left|\right|(Y_s-\underset{j\&NotEqual;k}{\overset{K}{\&Sigma;}}{d}_j{x}_j)-d_k{x}_k|{|}_2=||E_k-d_k{x}_k|{|}_2---\left(9\right)$

Wherein, D_sX_sBe broken down into matrix that K order is 1 and, remaining K-1 item is all fixing, and remaining 1 row seek to update Row, E_kRepresent and remove atom d_kThe error afterwards all samples caused, and then to E_kCarry out SVD decomposition, update d_k；With above-mentioned Method, by { d₁,d₂,…,d_LAll atoms in } are all updated, i.e. to smooth dictionary D_sComplete training.

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 6, it is characterised in that root According to the training method of K-SVD, same structural area, edge and irregular grain block are carried out dictionary training, thus by classifying Image block obtained accordingly cross complete dictionary: edge dictionary D_e, irregular grain dictionary D_t。

The classification rarefaction representation image repair method of a kind of edge fitting the most according to claim 1, it is characterised in that adopt Go to approximate l with near-hyperbolic tan₀Norm, utilizes conjugate gradient method to solve this function, the improvement tool to tradition SL0 algorithm Body is accomplished by

Owing to the mathematical model of SL0 is:

min||X||₀, s.t. Y=DX (10)

Vector X=[x₁ x₂ … x_n]^T, its l₀Norm represents the number of non-zero element in vector X, if assuming:

$f\left(x\right)=\left\{\begin{array}{cc}1,& x\&NotEqual;0\\ 0,& x=0\end{array}\right.---\left(11\right)$

Then:

$\left|\right|X|{|}_0=\underset{i=1}{\overset{n}{\&Sigma;}}f\left(x_i\right)---\left(12\right)$

Therefore, as long as finding continuous function f (x) the most smooth, it is possible to well approach | | X | |₀Value；In order to Structure has " abruptness " and significantly smooths continuous function, and this continuous function can accurately approach l₀Norm；Employing formula (13) Shown near-hyperbolic tan is as approximate evaluation l₀The function of norm；

$f_{\mathrm{\&sigma;}}\left(x\right)=\frac{1}{8}\frac{e^{\frac{x^2}{2{\mathrm{\&sigma;}}^2}}-e^{\frac{-x^2}{2{\mathrm{\&sigma;}}^2}}}{e^{\frac{x^2}{2{\mathrm{\&sigma;}}^2}}+e^{\frac{-x^2}{2{\mathrm{\&sigma;}}^2}}}+\frac{7}{8}(1-e^{\frac{-8x^2}{{\mathrm{\&sigma;}}^2}})---\left(13\right)$

Knowable to formula (13), variable σ value is the least, and near-hyperbolic tan " abruptness " is the most obvious, more approaches l₀Norm, but with Constantly diminishing of σ value, function curve is more and more rough；Therefore, choosing of σ parameter is the most crucial, and choosing of it is necessary Approaching l₀Degree and the smoothing of functions degree of norm take compromise between the two；To this end, use one group of σ sequence { σ successively decreased₁, σ₂,…,σ_nBe used for approaching object function, carry out the optimum of solved function to utilizing steepest descent method while σ each time value；

For solving this kind of nothing of minf (x) about fasciculation problem, it is assumed that an initial value x₀, obtain x through series of iterations_n；If Current iterative value is x_k, then next iterative value i.e. x_k+1=x_k+u×d_k, u represents iteration step length, d_kExpression is minimized The direction of search, use conjugate gradient method solution formula is:

$d_k=\left\{\begin{array}{cc}-g_k& k=1\\ -g_k+{\mathrm{\&beta;}}_k{d}_{k-1},& k\&GreaterEqual;2\end{array}\right.---\left(14\right)$

Wherein, g_kThe gradient of representative function f (x), β_kCan be solved by different conjugate gradient methods；To β_kMethod for solving Use mixing conjugate gradient method, i.e. mix FR (Fletcher-Reeves) conjugate gradient method and PRP conjugate gradient method:

${\mathrm{\&beta;}}_k=\left\{\begin{array}{cc}{\mathrm{\&beta;}}_k^{PRP},& 0<{\mathrm{\&beta;}}_k^{PRP}<{\mathrm{\&beta;}}_k^{FR}\\ {\mathrm{\&beta;}}_k^{ER},& else\end{array}\right.---\left(15\right)$

Therefore, utilize the sparse representation method of SL0, classification repair all kinds of characteristic information of image to realize step as follows:

(1) initial value is made to be respectively X=D^T(DD^T)^-1Y, σ₁=2max (X), k=1；

(2) j=1,2 ..., L, (L is conjugate gradient method iterations, L=5) utilizes conjugate gradient method to solveg_nGeneration The gradient of table function f (x):

1. direction is searched:②X ←X+μd_n, wherein step factor μ=1.5；

③X←X-D^T(DD^T)^-1(DX-Y)；

4. n=n+1, j=j+1；If j is ＜ L, then repeat step 1., 2., 3.；

(3) k=k+1, σ_k=η σ_k-1, η ∈ [0.5 1], repeat step (2), until σ_k＜ ε, ε=0.01, now obtain X Excellent solution.