CN106815876A - Image sparse characterizes the combined optimization training method of many dictionary learnings - Google Patents

Abstract

Image sparse characterizes many dictionary learning combined optimization training methods, belong to multimedia communication and image real time transfer field, it is characterized in that, the gradient matrix of training elementary area is regarded as through the nonzero element in the singular value matrix after singular value decomposition the energy value of correspondence gradient direction, elementary area is divided into isotropic image and anisotropic image by the energy value Parameters threshold according to setting, learn shared dictionary and specialized dictionary successively, with a reflection through the isotropism after sparse representation and the residual error of anisotropy image, the object function that the auto-correlation and the factor such as cross-correlation degree and nonzero element regularization of each dictionary are minimized is optimized, in optimization process, optimize A with orthogonal matching pursuit algorithm successively₀,A_k, then optimize D with gradient descent algorithm₀,D_k, when desire Optimal Parameters are retained, other items for not being related to be intended to Optimal Parameters are considered as constant.When the present invention is for compression of images, details is retained, and distortion rate is relatively low, and image quality is relatively preferable.

Description

Image sparse characterizes the combined optimization training method of many dictionary learnings

Technical field

The invention provides a kind of image data compression method, belong to multimedia communication and data compression crossing domain, it is special A kind of image data compression algorithm for low bit- rate is not designed, and cluster and the modeling of structuring dictionary are carried out to image texture, will Image carries out sparse representation, is mainly used in reducing the data volume transmitted during communication, is not only suitable for the image such as face of particular topic, It is applied to general natural image again, is widely used.

Background technology

Digital multimedia communications are most one of challenge, field with fastest developing speed in present communications technology various fields. Compression and transmission of the big data epoch to data propose demand higher.In order to effectively mitigate bandwidth pressure, data are carried out Effectively transmission, compression of images is widely studied by researchers.

Traditional method for compressing image can not produce good compression effectiveness in low bit- rate to image, in low bit- rate, Recover image to be difficult to produce preferable visual effect.Such as the JPEG image compression method based on discrete cosine transform (DCT) is in weight Obvious blocking effect can be produced when building, image block carries out transition coding, with the reduction of code check, be occurred in that not on the border of block Continuously.The wavelet coefficient of high frequency has been carried out threshold value contraction by the JPEG2000 compression methods based on wavelet transform (DWT), is made Into the loss of high-frequency information, ringing can be produced to image, its typical performance is that the field of gradation of image acute variation goes out The concussion of Gibbs distribution is now similar to, the quality of restored image is had a strong impact on, and cause that successive image treatment is difficult to.

In recent years, dictionary learning method achieves preferable compression effectiveness, will data (image) it is sparse with one group of base The base of linear combination represent that the dictionary is referred to " base ".It is identical with discrete cosine transform and wavelet transformation, dictionary Habit is also to enter line translation according to base, and image is characterized in the transform domain as illustrated, in the hope of obtaining the expression effect more superior than pixel domain Really, i.e., compression of images can be realized with less bit come phenogram picture in transform domain.Herein, corresponding to this group of base of dictionary Coefficient is sparse, and major part is zero, only small part nonzero coefficient, and sparse volume is carried out to image using this superior property Code (Sparse Coding, SC).Its difference is that discrete cosine base and wavelet basis are the bases obtained according to mathematical function, And the base of dictionary learning, it is to be obtained with the Algorithm Learning of machine learning from real image.This have the advantage that, from reality The border sample middle school more identical image of base out, and the base obtained according to mathematical function is difficult to the rule of perfect picture engraving. The principle of dictionary learning is that the image study to training set obtains one group of redundancy base, and the redundancy base refers to the atom of dictionary (i.e. a row of dictionary) number is more than its dimension, there is theoretical guarantee, and what the sample in test set can be with the redundancy base is several Individual component linear combination uniquely represents, claims this to be expressed as sparse representation.Sparse representation is intended to minimum dictionary atom A signal is represented, to realize representing image with a small number of data, the purpose of data compression is reached.Classical dictionary learning is calculated Method has K-SVD, every time one atom of study renewal sparse coefficient corresponding with its, until all of atomic update is finished, repeats Iteration can obtain complete dictionary several times.The deficiency of the algorithm is that the time of dictionary training is more long.Then, research carries Go out online dictionary learning algorithm (Online Dictionary Learning), the method is reached by stochastic gradient descent algorithm Optimal value, obtain dictionary by iteration several times, can quickly restrain.

Sparse coding is carried out to image, dictionary is generally divided into two kinds of forms of single dictionary and many dictionaries.Single dictionary format It is that, to one unified dictionary of all image studies, this dictionary compacts, but lacks the resolution capability of different characteristic, it is difficult to Optimal sign is carried out to all of feature.The representative algorithm that this unified dictionary is compressed sign to image has scholar Recurrence least square dictionary learning algorithm (the Recursive Least Squares that Karl Skretting are proposed Dictionary Learning Algorithm, RLS_DLA), the method is from pixel domain or wavelet field to different iconologies Unified dictionary is practised out, low bit coding is carried out to image with sparse coefficient, algorithm iteration convergence is very fast.Many dictionary formats are Feature different in image is modeled respectively, the dictionary of the multiple specializations of study, this dictionary has resolution capability.Scholar Michael Elad propose to be characterized with the face image to people of multiple specialization dictionaries at first, i.e., to the feature of face such as Eye, nose, eyebrow, mouth etc. set up the K-SVD dictionaries of specialization respectively, and each image block is independently characterized, this face characteristic word Allusion quotation is compacted very much, realizes that low bit is encoded, and effect is better than coding standards such as traditional JPEG2000.But, the method adapts to energy Power is limited, it is impossible to being compressed for other images in addition to face.Scholar Li Shaoyang is using the non-side for joining Bayesian learning Natural image data are learnt multiple dictionaries by method, and the number of dictionary is automatically determined by algorithm according to prior information, this side Method can learn to one group of optimal dictionary, and different images is characterized.

On the other hand, natural image has the general character of many inherences, and identical feature possibly be present in different images, or even It is that most of images have.Image also has the characteristic of itself, and such as some image blocks have the directionality of distinctness, and geometric properties are bright Really.Based on considerations above, it is necessary to set up a kind of new compression algorithm, the common feature to image sets up unified shared dictionary, And multiple specialized dictionaries are set up to the property feature of image, and two kinds of mutual supplement with each other's advantages of the dictionary of form are realized, share dictionary The sign that can be compacted to the realization of most of features, the dictionary of specialization can more added with resolving power, to shared dictionary and specialized word Allusion quotation is optimized in combination, and study carries out sparse representation to one group of optimal dictionary to image.

The content of the invention

It is a kind of by learn shared dictionary that the general character of the isotropic images in image obtains and by learning image in The proprietary dictionary that obtains of individual character carry out combined optimization training method, to realize that compression image is ensureing containing abundant information amount While, compression ratio can be to greatest extent improved again.

It is an advantage of the current invention that different with multiple by the geometric component of modeled images different characteristic, i.e. low frequency component The high fdrequency component of gradient direction so that the image rebuild after compression retains more complete details, there is more preferable Objective image quality, And more meet the subjective feeling of people.

It is a feature of the present invention that being a kind of natural image coding method, learn optimal base carries out sparse table to image Levy, realize according to the following steps successively in a computer：

Step (1), computer initialization sets following each parameters and coefficient：

Each image fritter will be obtained after training image X cuttingsI=1,2 ..., i ..., I, I are x_iSum, x_i ∈R^m, m is the row of matrix R, abbreviation x_i,

Image fritter x_iIn pixel useRepresent, write a Chinese character in simplified form into j, j=1,2 ..., J, meanwhile, j is also the sequence number of pixel, J It is the sum of pixel, the horizontal component of the pixel is represented with u, vertical component is represented with v.

Use g_jThe gradient of the pixel j is represented,Use G_iRepresent described image fritter x_i's Gradient matrix, G_i=[g₁,g₂,…,g_J]^T,G_i∈R^J×2, columns n=2 represent the number J of pixel gradient, row expression pixel with row The level and vertical component of gradient, use respectivelyRepresent.

Deflections of the pixel j in gradient direction is represented with ω

Use K₀Represent that the collection of isotropism subimage block is combined into, abbreviation K₀, use D₀Represent study K₀The shared dictionary for obtaining.

The set of anisotropic image block, K={ K are represented with K₁,K₂,…,K_k,…,K₆}={ K_k, referred to as 6 class gradients The region k of deflection, wherein, K₁Correspondence (0 °, 30 °), K₂Correspondence (30 °+, 60 °), K₃Correspondence (60 °+, 90 °), K₄(90 ° of correspondence +, 120 °), K₅Correspondence (120 °+, 150 °), K₆Correspondence (150 °+, 180 °), wherein, 30 °+represent that the rest may be inferred by analogy for it more than 30 °, symbol Number " { } " expression " contains " element, similarly hereinafter.

Use D_KRepresent the proprietary dictionary obtained after study K, abbreviation D_K, correspondingly, use D₁~D₆Corresponding study is represented respectively The 6 proprietary sub- dictionaries obtained after 6 anisotropy image blocks of the gradient angular zone, and D_KBy 6 proprietary sub- dictionary groups Into D_K={ D₁,D₂,…,D₆}={ D_k}。

The shared dictionary D is represented with D₀With proprietary sub- dictionary D_kSet, be expressed as：D={ D₀, D_K}={ D₀,D₁,D₂, D₃,D₄,D₅,D₆}。

With k=1,2 ..., 6 represent the subscript sequence of each proprietary sub- dictionaries.Dictionary D is represented with k '=0,1,2,3,4,5,6 In the contained sub- dictionary of whole subscript sequence.

Dictionary encoding coefficient matrix, A={ A are represented with A₀,A_K, wherein：A₀Represent the shared dictionary D₀Code coefficient Matrix, A_KRepresent the proprietary dictionary D_KCode coefficient matrix, wherein,Represent A_KIncluding：Proprietary son Dictionary set { D_kIn correspond to the set of anisotropy subimage block in each general character image part dictionary code coefficientAnd 6 class anisotropy subgraph each proprietary sub- dictionary D_kCode coefficient matrixK=1,2 ..., 6.

The element of each code coefficient matrix is referred to as code coefficient a, δ<A ＜ ＜ 1, set code coefficient as combined optimization One of parameter of training, its object is to：In follow-up study, when judge first through step (2.3) in target obtain, afterwards again pass through When the compression image of parametric variable combined optimization is unsatisfactory for error requirements with the original input image of reality on image similarity, energy By improving the similarity of compression image and original image to the regulation of each code coefficient, to overcome error.

WithThe autocorrelation matrix of shared dictionary is represented, is usedRepresent the autocorrelation matrix of each proprietary dictionary.WithRepresent the dictionary D={ D₀,D₁,D₂,D₃,D₄,D₅,D₆Remaining each word after Zhong-1 block any one sub- dictionary The connection matrix of allusion quotation.

Autocorrelation matrix adjustment factor sequence is represented with η, including：

Shared dictionary D₀Autocorrelation matrixAdjustment factor η₀, 0<η₀＜ ＜ 1, each proprietary sub- dictionary D_kFrom phase Close matrixAdjustment factor η_k, k=1,2 ..., 6,0<η_k＜ ＜ 1.

With the cross correlation matrix number between each sub- dictionary in η ' expression dictionaries DAdjustment factor, k '=0, 1,2,…,6,0<η_k′' ＜ ＜ 1,

Being represented with λ carries out the regularization coefficient of regularization, 0 to the dictionary encoding coefficient matrices A<λ ＜ ＜ 1.

Step (2), from the X_iIt is middle to extract the K₀And K：

Step (2.1), randomly selects the equal training image of arbitrary size from image data base, each Zhang Suoshu instructions It is setting quantity and equal-sized image fritter x to practice image cutting_i, x is expressed as with vector form_i∈R^m；

Step (2.2), asks for each described x_iIn each pixel j horizontal and vertical directions gradient g_j, obtain described x_iGradient matrix G_i, abbreviation G_i, then by formula G_i=U Σ W^TSingular value decomposition is carried out, is obtained：

M × m rank unitary matrice U, positive semidefinite m × 2 rank diagonal matrix Σ ∈ R^m×2, the element on diagonal is referred to as singular value, its In nonzero element represent the energy size of corresponding gradient direction；2 × 2 rank unitary matrice W, W ∈ R^2×2, each column vector represents institute State x_iThe gradient direction of interior each pixel；

Step (2.3), the difference parameter of gradient direction energy is represented with ρ, target x_iMiddle all directions energy relative equilibrium And relatively more stable subimage block is used as isotropic image block K₀, as the publicly-owned feature；And it is obvious having The subimage block of directionality as the anisotropic image block K, as proprietary feature, according to gradient direction angle ω, the K It is divided into the gradient direction angular zone described in 6,ρ value, Σ between (0,1)_1,1,Σ_2,2It is two ladders The degree each self-corresponding singular value in direction；

Step (3), to the shared dictionary D₀With proprietary dictionary D_kCombined optimization training is carried out according to the following steps：

If the object function of combined optimization is：

Wherein, d_jIt is unit vector, representing matrix D_iColumn vector.Expression is asked so that object function is minimum Variables D_i,A_iValue；[D₀,D_k] represent matrix D₀With D_kIt is horizontally-spliced into a big matrix；||.||_FRepresent square The Frobenius norms of battle array；||.||₀The L of representing matrix₀The number of norm, i.e. nonzero element；Q_k′Correspond to auto-correlation square Battle arrayUnit matrix；||.||₂It is the Euclid norm of vector.

Step (3.1), with recurrence least square dictionary learning algorithm RLA_DLA to the D₀And D_kInitialized.It is i.e. right The image block K of the isotropic₀Dictionary learning is carried out, the shared dictionary D for being initialized₀, and its corresponding initialization Code coefficient matrix A₀To the image block K of the anisotropic_k, k=1,2 ..., 6, dictionary learning is carried out respectively, initialized Proprietary sub- dictionary D_k, k=1,2 ..., 6, and its corresponding initialization code coefficient matrix

Step (3.2), solves the proprietary dictionary D_kAnd it is corresponding

Step (3.2.1), changes the expression-form of the object function of the combined optimization training occurred in step (3)：Find out And ignore constant term, retain D_k,, alternately solve.

Step (3.2.1.1),Represent the isotropic image collection K₀With shared dictionary D₀Enter Residual error after row sparse representation, this is constant, and object function value is not influenceed, negligible；

Step (3.2.1.2), due to A={ A₀,A_K},Thus in λ | | A | |₀Xiang Zhong, ignores A₀And, just it is reduced to

Step (3.2.1.3), rewrites

It is written over item and represents K_kAnisotropy subimage block K in individual gradient direction angular zone_kWith corresponding code coefficient MatrixShared dictionary D after regulation₀With corresponding code coefficient matrixProprietary sub- dictionary D after regulation_kCarry out jointly Residual error after sparse representation.Similarly, can handleItem is rewritten asOrderBeing written over the expression formula of result because obtained from is：

Step (3.2.1.3), the object function of the combined optimization training after being changed：

Wherein, k=1,2 ..., 6, λ, η_k,η′_kIt is setting value.

Step (3.2.2), solves the code coefficient matrix of each proprietary sub- dictionary

Step (3.2.2.1), only retains and the code coefficientRelated item, ignores other,

Step (3.2.2.2), in D_kUnder conditions of constant, obtain for solving the code coefficient matrixTarget letter Number：

Step (3.2.2.3), sets degree of rarefication L, according to known K_kAnd D₀, tried to achieve with orthogonal matching pursuit algorithm OMPSo as to obtain Y_k.Obtain corresponding in the object function for bringing step (3.2.2.2) into

Step (3.2.3), solves proprietary dictionary D_K=[D₁,D₂,…,D₆]:

Step (3.2.3.1), in the object function of step (3.2.1.3) the combined optimization training, ignores constant termRetain and each proprietary sub- dictionary D_kRelated item, obtains：

Step (3.2.3.2), clicks each proprietary sub- dictionary D ' after step obtains combined optimization training_k:

Step (3.2.3.3) makes：d_γRepresent D_kColumn vector, referred to as dictionary atom, γ is the sequence number of the column vector,

Step (3.2.3.4), d is updated with following gradient descent algorithms_γ, the d that γ is obtained after updating_γ' sub- the dictionary for constituting With D '_kRepresent：

K=1,2 ..., 6, symbolRepresent to variable derivation, a^γRepresent coefficient matrixγ rows, obtain：ζ₁It is step-length.Step-length ζ₁Determined by armijo criterions, the armi jo criterions, be linear search step Algorithm long.

Step (3.3), solves shared dictionary D₀：

Step (3.3.1), changes the expression-form of the object function of combined optimization training in step (3)：

Step (3.3.1.1), each D_kAnd the auto-correlation adjustment factor sequence η of correlation_k, cross-correlation adjustment factor η '_k, respectively Proprietary sub- dictionary encoding coefficient matrixIt is considered as constant, and A={ A₀,A_K},Retain D₀,

Step (3.3.1.2) rewrites following every expression formulas

It is rewritten as：

It is rewritten as：

It is rewritten asWith

λ||A||₀It is rewritten asAlso one λ | | A₀||₀。

Step (3.3.1.3), the revised combined optimization training objective function is：

Step (3.3.1.4), A is solved by step (3.3.1.3)₀:

Specialized dictionary D ' after fixed renewal_k, make D_k=D '_k, keepD₀It is constant, obtain for solving A₀It is described Combined optimization training objective function：

A is tried to achieve with the orthogonal matching pursuit algorithm OMP algorithms described in step (3.2.2.3)₀。

Step (3.3.1.5), the combined optimization training objective function proposed according to step (3.3.1.3) is solved

In Z_k,A₀,D₀Under conditions of constant, exceptWithIt is able to retain outer, ignores other , obtain for solvingThe combined optimization training objective function：

Obtained with step (3.3.1.4) identical method

Step (3.3.1.6), the combined optimization training objective function proposed by step (3.3.1.3) solves D₀:

Step (3.3.1.6.1), the specialized dictionary D ' after fixed renewal_k, retain and shared dictionary D₀Related item, obtains To solution D₀The combined optimization training objective function：

Wherein, D_-0The horizontally-spliced matrix of all of proprietary sub- dictionary is represented, its expression formula is D_-0=[D '₁,D ′₂,…,D′₆]。

Step (3.3.1.6.2), it is described updated proprietary with the gradient descent algorithm described in step (3.2.3.4) Sub- dictionary D_k' and atom d_γ', the atom after updating again is designated as d "_γ, obtain：

Wherein：RepresentIn γ ' OK, ζ₂Represent step-length, the armijo criterions described in step (3.2.3.4) It is determined that.

Brief description of the drawings

Fig. 1, many geometry dictionary method for compressing image system block diagrams.

Fig. 2, combined optimization training program FB(flow block).

Fig. 3, image block energy differences parameter ρ probability distribution statistical figure, abscissa represents energy differences, and ordinate represents figure As number of blocks.

Fig. 4, trains the dictionary for completing：

Fig. 4 .1, share dictionary, Fig. 4 .2, the specialized dictionary in part.

Fig. 5, Lena compression of images objective evaluation index：

Fig. 5 .1, coefficient nonzero value number,

Fig. 5 .2, rate-distortion curve.

Fig. 6, the image that image woman is encoded in code check for 0.15bpp：

Fig. 6 .1, JPEG (PSNR=28.68dB, SSIM=0.63),

Fig. 6 .2, JPEG2000 (PSNR=29.29dB, SSIM=0.77),

Fig. 6 .3, RLS_DLA (PSNR=28.5dB, SSIM=0.73),

Fig. 6 .4, the present invention, PSNR=29.76dB, SSIM=0.77).

Specific embodiment

Berkeley Segmentation Image database are chosen as training image collection, 200 are randomly selected In image 8 × 10⁴Used as training set, the size of each image block is 8 × 8 to individual image block.Test image comes from USC-SIPI Data set, including some standard pictures, such as Lena, boat, man, couple, camera man, woman etc..What training was obtained The size of dictionary is 200 dimensions, i.e., each dictionary has 200 atoms.The distribution situation of the energy differences parameter of image block.Will test Image block seeks gradient, counts the energy difference of the main gradient direction of the Energy distribution of the gradient direction of each image block, i.e., two Value, its probability-distribution function is as shown in Figure of description 2.The specialized dictionary of shared dictionary and part that training is obtained is illustrated in In bright book accompanying drawing 3.

Experiment parameter is as shown in Table 1.

The experiment parameter of table 1.

Image compression standard JPEG, JPEG2000 methods, and dictionary learning algorithm RLS_DLA are chosen, K-SVD is used as right Ratio method is tested.

By taking Lena images as an example, the number of the nonzero value corresponding to its dictionary, and rate-distortion curve is displayed in specification In accompanying drawing 4.By taking woman images as an example, it is encoded when bit rate is 0.15bpp, and it is attached that reconstruction image is displayed in specification In Fig. 5.Other test images are encoded in 0.5bpp and 0.4bpp, and its objective evaluating index PSNR is displayed in table 2.

The encoding efficiency when code check of table 2. is 0.5bpp (up) and 0.4bpp (descending)

It can be inferred that institute's pressure-raising compression method can obtain the more high-quality image of relative other method in low bit- rate, Details retains more intact, and distortion rate is relatively low.

Claims (1)

1. image sparse characterizes the combined optimization training method of many dictionary learnings, it is characterised in that be one kind by learning image In isotropic images the general character shared dictionary for obtaining and the proprietary dictionary that is obtained by learning the individual character in image carry out Combined optimization training method, to realize that compression image while ensureing containing abundant information amount, can be improved to greatest extent again Compression ratio, realizes according to the following steps successively in a computer：

Step (1), computer initialization sets following each parameters and coefficient：

Each image fritter will be obtained after training image X cuttingsI is x_iSum, x_i∈ R^m, m is the row of matrix R, abbreviation x_i,

Image fritter x_iIn pixel useRepresent, write a Chinese character in simplified form into j, j=1,2 ..., J, meanwhile, j is also the sequence number of pixel, and J is picture The sum of element, the horizontal component of the pixel is represented with u, and vertical component is represented with v；

Use g_jThe gradient of the pixel j is represented,Use G_iRepresent described image fritter x_iGradient Matrix, G_i=[g₁,g₂,…,g_J]^T,G_i∈R^J×2, columns n=2 represent the number J of pixel gradient, row expression pixel gradient with row Level and vertical component, use respectively Represent；

Deflections of the pixel j in gradient direction is represented with ω

Use K₀Represent that the collection of isotropism subimage block is combined into, abbreviation K₀, use D₀Represent study K₀The shared dictionary for obtaining；

The set of anisotropic image block, K={ K are represented with K₁,K₂,…,K_k,…,K₆}={ K_k, referred to as 6 class gradient directions The region k at angle, wherein, K₁Correspondence (0 °, 30 °), K₂Correspondence (30 °+, 60 °), K₃Correspondence (60 °+, 90 °), K₄Correspondence (90 °+, 120 °), K₅Correspondence (120 °+, 150 °), K₆Correspondence (150 °+, 180 °), wherein, 30 °+represent that the rest may be inferred by analogy for it, symbol more than 30 ° " { } " expression " contains " element, similarly hereinafter；

Use D_KRepresent the proprietary dictionary obtained after study K, abbreviation D_K, correspondingly, use D₁~D₆6 institutes of corresponding study are represented respectively The 6 proprietary sub- dictionaries obtained after the anisotropy image block for stating gradient angular zone, and D_KIt is made up of 6 proprietary sub- dictionaries, D_K= {D₁,D₂,…,D₆}={ D_k}；

The shared dictionary D is represented with D₀With proprietary sub- dictionary D_kSet, be expressed as：D={ D₀, D_K}={ D₀,D₁,D₂,D₃, D₄,D₅,D₆}；

With k=1,2 ..., 6 represent the subscript sequence of each proprietary sub- dictionaries；Institute in dictionary D is represented with k '=0,1,2,3,4,5,6 The subscript sequence of the sub- dictionary of whole for containing；

Dictionary encoding coefficient matrix, A={ A are represented with A₀,A_K, wherein：A₀Represent the shared dictionary D₀Code coefficient matrix, A_KRepresent the proprietary dictionary D_KCode coefficient matrix, wherein,Represent A_KIncluding：Proprietary sub- wordbook Close { D_kIn correspond to the set of anisotropy subimage block in each general character image part dictionary code coefficientAnd Each proprietary sub- dictionary D of 6 class anisotropy subgraphs_kCode coefficient matrix

The element of each code coefficient matrix is referred to as code coefficient a, δ<A ＜ ＜ 1, set code coefficient as combined optimization is trained One of parameter, its object is to：In follow-up study, when judge first through step (2.3) in target obtain, afterwards again through parameter When the compression image of variable combined optimization is unsatisfactory for error requirements with the original input image of reality on image similarity, can pass through The similarity of compression image and original image is improved to the regulation of each code coefficient, to overcome error；

WithThe autocorrelation matrix of shared dictionary is represented, is usedRepresent the autocorrelation matrix of each proprietary dictionary；WithRepresent the dictionary D={ D₀,D₁,D₂,D₃,D₄,D₅,D₆Remaining each word after Zhong-1 block any one sub- dictionary The connection matrix of allusion quotation；

Autocorrelation matrix adjustment factor sequence is represented with η, including：

Shared dictionary D₀Autocorrelation matrixAdjustment factor η₀, 0<η₀＜ ＜ 1, each proprietary sub- dictionary D_kAuto-correlation square Battle arrayAdjustment factor η_k, k=1,2 ..., 6,0<η_k＜ ＜ 1；

With the cross correlation matrix number between each sub- dictionary in η ' expression dictionaries DAdjustment factor, k '=0,1, 2,…,6,0<η_k′' ＜ ＜ 1,

Being represented with λ carries out the regularization coefficient of regularization, 0 to the dictionary encoding coefficient matrices A<λ ＜ ＜ 1；

Step (2), from the X_iIt is middle to extract the K₀And K：

Step (2.1), randomly selects the equal training image of arbitrary size from image data base, each Zhang Suoshu is trained and is schemed As cutting is setting quantity and equal-sized image fritter x_i, x is expressed as with vector form_i∈R^m；

Step (2.2), asks for each described x_iIn each pixel j horizontal and vertical directions gradient g_j, obtain the x_i's Gradient matrix G_i, abbreviation G_i, then by formula G_i=U Σ W^TSingular value decomposition is carried out, is obtained：

M × m rank unitary matrice U, positive semidefinite m × 2 rank diagonal matrix Σ ∈ R^m×2, the element on diagonal is referred to as singular value, therein Nonzero element represents the energy size of corresponding gradient direction；2 × 2 rank unitary matrice W, W ∈ R^2×2, each column vector represents the x_i The gradient direction of interior each pixel；

Step (2.3), the difference parameter of gradient direction energy is represented with ρ, target x_iMiddle all directions energy relative equilibrium and compare Stable subimage block is used as isotropic image block K₀, as the publicly-owned feature；And with obvious directionality Subimage block as the anisotropic image block K, be 6 the K points according to gradient direction angle ω as proprietary feature Individual described gradient direction angular zone,ρ value, Σ between (0,1)_1,1,Σ_2,2It is two gradient directions Each self-corresponding singular value；

Step (3), to the shared dictionary D₀With proprietary dictionary D_kCombined optimization training is carried out according to the following steps：

If the object function of combined optimization is：

$\begin{array}{c}\underset{D_i,A_i}{\min }\left\{\right||K_0-D_0{A}_0|{|}_F^2\\ +\underset{k=1}{\overset{6}{\&Sigma;}}\left|\right|K_k-\&lsqb;D_0,D_k\&rsqb;A_K^k|{|}_F^2\\ +\underset{k^{\&prime;}=0}{\overset{6}{\&Sigma;}}\left({\mathrm{\&eta;}}_{k^{\&prime;}}\right||D_{k^{\&prime;}}^T{D}_{k^{\&prime;}}-Q_{k^{\&prime;}}|{|}_F^2)\\ +\underset{k^{\&prime;}=0}{\overset{6}{\&Sigma;}}\left({\mathrm{\&eta;}}_{k^{\&prime;}}^{\&prime;}\right|\left|D_{k^{\&prime;}}^T{D}_{-k^{\&prime;}}\right|{|}_F^2)+\mathrm{\&lambda;}\left|\right|A\left|{|}_0\right\}\end{array}$

$s.t.\left|\right|d_j|{|}_2=1,\&ForAll;j\&Element;J$

Wherein, d_jIt is unit vector, representing matrix D_iColumn vector；The change for causing that object function is minimum is asked in expression Amount D_i,A_iValue；[D₀,D_k] represent matrix D₀With D_kIt is horizontally-spliced into a big matrix；||.||_FRepresenting matrix Frobenius norms；||.||₀The L of representing matrix₀The number of norm, i.e. nonzero element；Q_k′Correspond to autocorrelation matrixUnit matrix；||.||₂It is the Euclid norm of vector；

Step (3.1), with recurrence least square dictionary learning algorithm RLA_DLA to the D₀And D_kInitialized；I.e. to described The image block K of isotropic₀Dictionary learning is carried out, the shared dictionary D for being initialized₀, and its corresponding initialization coding Coefficient matrices A₀To the image block K of the anisotropic_k, k=1,2 ..., 6, dictionary learning is carried out respectively, what is initialized is special There is sub- dictionary D_k, k=1,2 ..., 6, and its corresponding initialization code coefficient matrix

Step (3.2), solves the proprietary dictionary D_kAnd it is corresponding

Step (3.2.1), changes the expression-form of the object function of the combined optimization training occurred in step (3)：Find out and neglect Slightly constant term, retains D_k,, alternately solve；

Step (3.2.1.1),Represent the isotropic image collection K₀With shared dictionary D₀Carry out sparse Residual error after sign, this is constant, and object function value is not influenceed, negligible；

Step (3.2.1.2), due toThus in λ | | A | |₀Xiang Zhong, ignores A₀And, just it is reduced to

Step (3.2.1.3), rewrites

It is written over item and represents K_kAnisotropy subimage block K in individual gradient direction angular zone_kWith corresponding code coefficient matrixShared dictionary D after regulation₀With corresponding code coefficient matrixProprietary sub- dictionary D after regulation_kCarry out jointly sparse Residual error after sign；Similarly, can handleItem is rewritten asOrderBeing written over the expression formula of result because obtained from is：

Step (3.2.1.3), the object function of the combined optimization training after being changed：

$\begin{array}{c}\underset{A_K^k,D_k}{\min }\left|\right|Y_k-D_k{A}_K^2|{|}_F^2+\mathrm{\&lambda;}|\left|A_K^k\right|{|}_0^2+{\mathrm{\&eta;}}_k\left|\right|D_k^T{D}_k-Q_k|{|}_F^2\\ \begin{array}{cc}+{\mathrm{\&eta;}}_{k^{\&prime;}}^{\&prime;}\left|\right|D_k^T{D}_{-k}|{|}_F^2& s.t.\left|\right|d_j|{|}_2=1,\&ForAll;j\&Element;J\end{array}\end{array}$

Wherein, k=1,2 ..., 6, λ, η_k, η '_kIt is setting value；

Step (3.2.2), solves the code coefficient matrix of each proprietary sub- dictionary

Step (3.2.2.1), only retains and the code coefficientRelated item, ignores other,

Step (3.2.2.2), in D_kUnder conditions of constant, obtain for solving the code coefficient matrixObject function：

$\underset{A_K^k}{min}\left|\right|Y_k-D_k{A}_K^k|{|}_F^2+\mathrm{\&lambda;}|\left|A_K^k\right|{|}_0$

Step (3.2.2.3), sets degree of rarefication L, according to known K_kAnd D₀,

Tried to achieve with orthogonal matching pursuit algorithm OMPSo as to obtain Y_k；Obtained in the object function for bringing step (3.2.2.2) into It is corresponding

Step (3.2.3), solves proprietary dictionary D_K=[D₁,D₂,…,D₆]:

Step (3.2.3.1), in the object function of step (3.2.1.3) the combined optimization training, ignores constant termRetain and each proprietary sub- dictionary D_kRelated item, obtains：

$\underset{D_k}{\min }\left\{\right||Y_k-D_k{A}_K^k|{|}_F^2+{\mathrm{\&eta;}}_k\left|\right|D_k^T{D}_k-Q_k|{|}_F^2+{\mathrm{\&eta;}}_k^{\&prime;}|\left|D_k^T{D}_{-k}\right|{|}_F^2\},$

$s.t.\left|\right|d_j|{|}_2=1,\&ForAll;j\&Element;J$

Step (3.2.3.2), clicks each proprietary sub- dictionary D ' after step obtains combined optimization training_k:

Step (3.2.3.3) makes：d_γRepresent D_kColumn vector, referred to as dictionary atom, γ is the sequence number of the column vector,

Step (3.2.3.4), d is updated with following gradient descent algorithms_γ, the d that γ is obtained after updating_γ' sub- dictionary the D ' for constituting_k Represent：

$\&dtri;d_{\mathrm{\&gamma;}}=2(D_k{A}_K^k-Y_k){\left(a^{\mathrm{\&gamma;}}\right)}^T+4{\mathrm{\&eta;}}_k(D_k{D}_k^T-Q_k)d_{\mathrm{\&gamma;}}+2{\mathrm{\&eta;}}_k^{\&prime;}\left(D_{-k}{D}_{-k}^T\right)d_{\mathrm{\&gamma;}},$

K=1,2 ..., 6, symbolRepresent to variable derivation, a^γRepresent coefficient matrixγ rows, obtain：ζ₁It is step-length；Step-length ζ₁Determined by armijo criterions, the armi jo criterions, be linear search step Algorithm long；

Step (3.3), solves shared dictionary D₀：

Step (3.3.1), changes the expression-form of the object function of combined optimization training in step (3)：

Step (3.3.1.1), each D_kAnd the auto-correlation adjustment factor sequence η of correlation_k, cross-correlation adjustment factor η '_k, it is each proprietary Sub- dictionary encoding coefficient matrixIt is considered as constant, andRetain

Step (3.3.1.2) rewrites following every expression formulas

It is rewritten as：

It is rewritten as：

It is rewritten asWith

λ||A||₀It is rewritten asAlso one λ | | A₀||₀；

Step (3.3.1.3), the revised combined optimization training objective function is：

$\begin{array}{c}\underset{D_0,A_0^k,A_0}{\min }\{{\&Sigma;}_{k=1}^6\left(\right||Z_k-D_0{A}_0^k|{|}_F^2+\mathrm{\&lambda;}\left|\right|A_k^0\left|{|}_0\right)+||K_0-D_0{A}_0|{|}_F^2+\mathrm{\&lambda;}\left|\right|A_0^k|{|}_0\\ +\mathrm{\&lambda;}\left|\right|A_0|{|}_0+{\mathrm{\&eta;}}_k||D_0^T{D}_0-Q_0|{|}_F^2+{\mathrm{\&eta;}}_k^{\&prime;}\left|\right|D_0^T{D}_{-0}\left|{|}_F^2\right\},\end{array}$

$s.t.\left|\right|d_j|{|}_2=1,\&ForAll;j\&Element;J,Z_k=K_k-D_k{A}_K^k$

Step (3.3.1.4), A is solved by step (3.3.1.3)₀:

Specialized dictionary D ' after fixed renewal_k, make D_k=D '_k, keepD₀It is constant, obtain for solving A₀The joint Optimization training objective function：

$\underset{A_0}{\min }\left\{\right||K_0-D_0{A}_0|{|}_F^2+\mathrm{\&lambda;}\left|\right|A_0\left|{|}_0\right\}$

A is tried to achieve with the orthogonal matching pursuit algorithm OMP algorithms described in step (3.2.2.3)₀；

Step (3.3.1.5), the combined optimization training objective function proposed according to step (3.3.1.3) is solved

In Z_k,A₀,D₀Under conditions of constant, exceptWithIt is able to retain outer, ignores other, Obtain for solvingThe combined optimization training objective function：

$\underset{A_0^k}{min}\left\{\right||Z_k-D_0{A}_0^k|{|}_F^2+\mathrm{\&lambda;}\left|\right|A_0^k\left|{|}_0\right\}$

Obtained with step (3.3.1.4) identical method

Step (3.3.1.6), the combined optimization training objective function proposed by step (3.3.1.3) solves D₀:

Step (3.3.1.6.1), the specialized dictionary D ' after fixed renewal_k, retain and shared dictionary D₀Related item, is asked Solution D₀The combined optimization training objective function：

${\min }_{D_0}\left\{{\&Sigma;}_{k=1}^6\right||Z_k-D_0{A}_k^0|{|}_F^2+\left|\right|K_0-D_0{A}_0|{|}_F^2+{\mathrm{\&eta;}}_k||D_0^T{D}_0-$ $Q_0|{|}_F^2+{\mathrm{\&eta;}}_k^{\&prime;}|\left|D_0^T{D}_{-0}\right|{|}_F^2\}$

Wherein, D_-0The horizontally-spliced matrix of all of proprietary sub- dictionary is represented, its expression formula is D_-0=[D '₁,D′₂,…, D′₆]；

Step (3.3.1.6.2), with the gradient descent algorithm described in step (3.2.3.4), the updated proprietary sub- word Allusion quotation D_k' and atom d_γ', the atom after updating again is designated as d "_γ, obtain：

$\begin{array}{c}\&dtri;d_{\mathrm{\&gamma;}}^{\&prime;\&prime;}=2(D_0{A}_k^0-Z_k){\left(a_k^{{\mathrm{\&gamma;}}^{\&prime;}}\right)}^T+2(D_0{A}_0-K_0){\left(a_k^{{\mathrm{\&gamma;}}^{\&prime;}}\right)}^T\\ +4{\mathrm{\&eta;}}_k(D_0{D}_0^T-I_0)d_{\mathrm{\&gamma;}}^{\&prime;\&prime;}+2{\mathrm{\&eta;}}_k^{\&prime;}\left(D_{-0}{D}_{-0}^T\right)d_{\mathrm{\&gamma;}}^{\&prime;\&prime;}\end{array}$

$d_{\mathrm{\&gamma;}}^{\&prime;\&prime;}=d_{\mathrm{\&gamma;}}^{\&prime;}-{\mathrm{\&zeta;}}_2\&dtri;d_{\mathrm{\&gamma;}}^{\&prime;\&prime;}$

Wherein：RepresentIn γ ' OK, ζ₂Step-length is represented, armi jo criterions are true described in step (3.2.3.4) It is fixed.