CN108491868A - A kind of image processing method and device based on k-means cluster and dictionary learning - Google Patents
A kind of image processing method and device based on k-means cluster and dictionary learning Download PDFInfo
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Abstract
The present invention provides a kind of image processing methods and device based on k means cluster and dictionary learning, initialisation image parameter carries out piecemeal processing to noise image, given image block is clustered with k mean algorithms, MOD AK SVD dictionary training algorithms are used to each cluster, obtain training cluster dictionary { D1,D2,D3...Dk, then it polymerize each piecemeal dictionary { D1,D2,D3...DkFormed complete dictionary D so that D={ D1,D2,D3...Dk, it obtains each piecemeal dictionary and the excessively complete dictionary D of composition, then uses OMP (orthogonal matching pursuit) algorithm, solve corresponding sparse coefficient, by the way that certain iterations, the corresponding dictionary of renewal learning and sparse coefficient is arranged, to reconstruct the image after denoising.Algorithm provided by the invention and existing sparse coding algorithm (Sparse coding) algorithm, improved sparse coding (ISC) algorithm, PSNR (Y-PSNR) value of image denoising effect is compared under the conditions of different noise variance δ and mixed noise density d, it can be found that the denoising effect of the present invention will reach better effect.
Description
Technical field
The present invention relates to technical field of image processing more particularly to a kind of figures based on k-means cluster and dictionary learning
As processing method and processing device.
Background technology
21 century is stepped into this means that the stepped into information epoch, with the development of science and technology, the transmission form of information is no longer only
Various multimedia forms including being limited only to voice, but had evolved to image, data, word etc..And people are connecing
When by external information, 80% comes from visual information, and digital picture is the most important source that people obtain visual information, with this
Meanwhile with the development of computer technology, huge achievement is all achieved in the various aspects image procossing such as academic research and application,
And be deep into daily life, study and work many fields.The research contents of digital image processing techniques
Be related to extensively, including image denoising, image segmentation, image enhancement, image recognition, image restoration, image coding, at multiresolution
Reason etc..
Due to the influence of imaging device and environment, when obtaining the information of image, the capital that keeping away can not keep away occurs respectively for we
The interference of kind external cause or internal cause, causes image to be mingled with many noises, causes image that degradation phenomena occurs.To make us obtain
Information it is imperfect even wrong, such image can not clearly reflect original real information, therefore study
The technologies such as image denoising are of great significance and are widely applied foreground.
Consider a noise image, there is Y=Y0+ V, Y are the image observed, Y0It is unknown original image, V is superposition
Zero-mean white noise.Our target, which is one algorithm erased noise from Y of design, makes it as close as original image Y0。
It does not need Accurate Reconstruction generally when handling noise image, following sparse bayesian learning can be converted into and asked
Topic：
min||x||0s.t.||Y-DX||≤ε
Wherein, ε is a normal number, when ε is sufficiently small, it is believed that be accurately reconstructed signal, ε=0 to a certain extent
When as rarefaction representation problem.
Image denoising algorithm dictionary-based learning, dictionary learning algorithm is generally used typically to have image denoising at present
MOD dictionary learning algorithms, K-MOD dictionary learnings algorithm and AK-MOD algorithms, general process are：
If one group of signal Y=[y1,y2…yn], the target of MOD algorithms is to find a dictionary D and a sparse matrix X,
So that the reconstructed error of signal is minimum：
Here x is the row of matrix X, and MOD is a kind of renewal process of the alternating iteration between dictionary upgrading and sparse coding.
Sparse coding process is to each signal ynIndividually carry out rarefaction representation.
It is not examined such as sparse coding algorithm (Sparse coding) algorithm currently based on the Image denoising algorithm of dictionary learning
Consider the correlation between image block, using integrated solution method, denoising effect is general, improved sparse coding (ISC) algorithm, though
Correlation between the image block so considered, but its dictionary is undertrained fully, denoising effect is bad.
Invention content
An embodiment of the present invention provides it is a kind of based on k-means cluster and dictionary learning image processing method and device,
For solve traditional dictionary it is undertrained fully, the bad technical problem of denoising effect.
A kind of image processing method based on k-means cluster and dictionary learning provided by the invention, including：
Initialisation image parameter obtains waiting for the noise image of piecemeal, and the noise image for treating piecemeal carries out image block acquisition
Image block；
It runs k-means algorithms and K cluster of cluster calculation acquisition is carried out to image block, MOD-AK- is run to each cluster
SVD dictionary learning algorithms obtain training cluster dictionary { D1,D2,D3...Dk}；
By training cluster dictionary { D1,D2,D3…DkIt was polymerized to complete dictionary D={ D1,D2,D3…Dk}；
Operation OMP orthogonal matching pursuit algorithms solve the sparse coefficient of corresponding excessively complete dictionary D
According to sparse coefficientCalculate reconstruct denoising image；
Judge whether iterations reach preset targeted number, if so, output reconstruct denoising image, if it is not, then will
Iterations add the step of returning to initialisation image parameter together, and the initial value of the iterations is 1.
Preferably, the initialisation image parameter obtains waiting for the noise image of piecemeal, and the noise image for treating piecemeal carries out
Image block obtains image block and specifically includes：
It enables
Be arranged image block size be n*n, dictionary size k, Lagrange multiplier λ1, cluster numbers K, image is big
The small fragmental image processing for N*N obtains (N-n+1)2A image block；
Wherein, y is pending noise image,To wait for the noise image of piecemeal,For the weight after last iteration
Structure denoising image, β are preset related coefficient, and j is iterations and initial value is 1.
Preferably, the operation k-means algorithms obtain k cluster to image block progress cluster calculation and specifically include：
Image block is divided into K classes by calculating the Euclidean distance between each segment, forms K cluster.
Preferably, described that training cluster dictionary { D is obtained to each cluster operation MOD-AK-SVD dictionary learning algorithms1,D2,
D3...DkSpecifically include：
Randomly build a dictionary Dk, to DkExecute normalized；
Main iterative process is executed according to k-th of cluster；
JudgeWhether preset minimum value is less than or equal to, if so, output dictionary Dk, if it is not, then returning
Execute main iterative process；
Wherein, the main iterative process is：
Operation OMP orthogonal matching pursuit algorithms solve dictionary DkSparse coefficient；
It runs MOD and AK-AVD algorithms and updates dictionary, that is, calculate following equation：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
Dictionary atom d is updated according to following equationj0And sparse coefficient
dj0=Ej0xj0；
Wherein, Y indicates picture signal matrix, XKIndicate sparse coefficient matrix, dj0Represent DKIn jth 0 arrange,Represent XK
In 0 row of jth, Ωj0Indicate that corresponding set of circumstances, M are constant.
Preferably, the operation OMP orthogonal matching pursuit algorithms solve the sparse coefficient of corresponding excessively complete dictionary D
Specially：
According to the sparse coefficient of excessively complete dictionary DThe sparse coefficient of complete dictionary D was calculated in solution formula
The sparse coefficient of the excessively complete dictionary DSolution formula be：
Wherein,For the corresponding sparse coefficient of iteration j ith cluster, RijIndicate corresponding piece of extraction operator, X tables
Diagram indicates error parameter as signal matrix, T (σ).
Preferably, described according to sparse coefficientCalculating reconstruct denoising image is specially：
Reconstruct denoising image is calculated according to denoising image formula；
The denoising image formula is：
Wherein,Indicate that the hot-tempered image that goes after iteration j, R are that image block extracts operator, λ1For Lagrangian constant, X
For noise image, D is updated dictionary,For the corresponding sparse coefficient of iteration j ith cluster, I is cell matrix.
A kind of image processing apparatus based on k-means cluster and dictionary learning provided by the invention, including：
Image block module obtains waiting for the noise image of piecemeal for initialisation image parameter, treats the noise pattern of piecemeal
Image block is obtained as carrying out image block；
Cluster and dictionary learning module, it is poly- to image block progress cluster calculation acquisition K for running k-means algorithms
Class obtains training cluster dictionary { D to each cluster operation MOD-AK-SVD dictionary learning algorithms1,D2,D3...Dk}；
Dictionary aggregation module, for cluster dictionary { D will to be trained1,D2,D3...DkIt was polymerized to complete dictionary D={ D1,
D2,D3...Dk}；
Sparse coefficient computing module solves corresponding excessively complete dictionary D's for running OMP orthogonal matching pursuit algorithms
Sparse coefficient
Denoising image module is reconstructed, for according to sparse coefficientCalculate reconstruct denoising image；
Loop iteration module, for judging whether iterations reach preset targeted number, if so, output reconstruct is gone
It makes an uproar image, executes image block module if it is not, then adding iterations to return together, the initial value of the iterations is 1.
Preferably, described image piecemeal module specifically includes：
Image initial unit, for enabling
Image block unit for image block size to be arranged is n*n, dictionary size k, Lagrange multiplier λ1、
Cluster numbers are K, and the fragmental image processing that image size is N*N is obtained (N-n+1)2A image block；
Wherein, y is pending noise image,To wait for the noise image of piecemeal,For the weight after last iteration
Structure denoising image, β are preset related coefficient, and j is iterations and initial value is 1.
Preferably, the cluster and dictionary learning module specifically include：
Cluster cell forms K cluster for image block to be divided into K classes by calculating the Euclidean distance between each segment；
Normalization unit, for randomly building a dictionary Dk, to DkExecute normalized；
Main iteration unit, for executing main iterative process according to k-th of cluster；
Judging unit, for judgingWhether preset minimum value is less than or equal to, if so, output dictionary
Dk, main iterative process is executed if it is not, then returning；
Wherein, the main iterative process is：
Operation OMP orthogonal matching pursuit algorithms solve dictionary DkSparse coefficient；
It runs MOD and AK-AVD algorithms and updates dictionary, that is, calculate following equation：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
Dictionary atom d is updated according to following equationj0And sparse coefficient
dj0=Ej0xj0；
Wherein, Y indicates picture signal matrix, XKIndicate sparse coefficient matrix, dj0Represent DKIn jth 0 arrange,Represent XK
In 0 row of jth, Ωj0Indicate that corresponding set of circumstances, M are constant.
Preferably,
The sparse coefficient computing module is specifically used for the sparse coefficient according to excessively complete dictionary DSolution formula calculates
To the sparse coefficient of excessively complete dictionary D
The reconstruct denoising image module is specifically used for calculating reconstruct denoising image according to denoising image formula；
The sparse coefficient of the excessively complete dictionary DSolution formula be：
Wherein,For the corresponding sparse coefficient of iteration j ith cluster, RijIndicate corresponding piece of extraction operator, X tables
Diagram indicates error parameter as signal matrix, T (σ).
The denoising image formula is：
Wherein,Indicate that the hot-tempered image that goes after iteration j, R are that image block extracts operator, λ1For Lagrangian constant, X
For noise image, D is updated dictionary,For the corresponding sparse coefficient of iteration j ith cluster, I is cell matrix.
As can be seen from the above technical solutions, the embodiment of the present invention has the following advantages：
A kind of image processing method based on k-means cluster and dictionary learning provided by the invention, including：Initialization figure
As parameter obtains waiting for the noise image of piecemeal, the noise image for treating piecemeal carries out image block and obtains image block；Run k-
Means algorithms carry out cluster calculation to image block and obtain K cluster, and MOD-AK-SVD dictionary learning algorithms are run to each cluster
Obtain training cluster dictionary { D1,D2,D3...Dk}；By training cluster dictionary { D1,D2,D3...DkIt was polymerized to complete dictionary D=
{D1,D2,D3...Dk}；Operation OMP orthogonal matching pursuit algorithms solve the sparse coefficient of corresponding excessively complete dictionary DAccording to
Sparse coefficientCalculate reconstruct denoising image；Judge whether iterations reach preset targeted number, if so, output reconstruct
Denoising image, if it is not, iterations are then added the step of returning to initialisation image parameter together, the initial value of the iterations
It is 1.Initialisation image parameter of the present invention carries out piecemeal processing to noise image, with k mean algorithms to given image block into
Row cluster uses MOD-AK-SVD dictionary training algorithms to each cluster, obtains training cluster dictionary { D1,D2,D3...Dk, so
After polymerize each piecemeal dictionary { D1,D2,D3...DkFormed complete dictionary D so that D={ D1,D2,D3...Dk, obtain each piecemeal
Then dictionary and the excessively complete dictionary D of composition use OMP (orthogonal matching pursuit) algorithm, solve corresponding sparse coefficient, pass through
Certain iterations, the corresponding dictionary of renewal learning and sparse coefficient are set, to reconstruct the image after denoising.The present invention
The algorithm of offer and existing sparse coding algorithm (Sparse coding) algorithm, improved sparse coding (ISC) algorithm,
PSNR (Y-PSNR) value of image denoising effect is compared under the conditions of different noise variance δ and mixed noise density d, can
With discovery, our denoising effect will reach better effect.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention without having to pay creative labor, may be used also for those of ordinary skill in the art
To obtain other attached drawings according to these attached drawings.
Fig. 1 is an a kind of reality of image processing method based on k-means clusters and dictionary learning provided by the invention
Apply the flow chart of example；
Fig. 2 is another of a kind of image processing method based on k-means clusters and dictionary learning provided by the invention
The schematic diagram of embodiment；
Fig. 3 is an a kind of reality of image processing apparatus based on k-means clusters and dictionary learning provided by the invention
Apply the schematic diagram of example；
Fig. 4 is an a kind of reality of image processing apparatus based on k-means clusters and dictionary learning provided by the invention
Apply the schematic diagram of cluster and dictionary learning module in example.
Specific implementation mode
An embodiment of the present invention provides it is a kind of based on k-means cluster and dictionary learning image processing method and device,
For solve traditional dictionary it is undertrained fully, the bad technical problem of denoising effect.
In order to make the invention's purpose, features and advantages of the invention more obvious and easy to understand, below in conjunction with the present invention
Attached drawing in embodiment, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that disclosed below
Embodiment be only a part of the embodiment of the present invention, and not all embodiment.Based on the embodiments of the present invention, this field
All other embodiment that those of ordinary skill is obtained without making creative work, belongs to protection of the present invention
Range.
Referring to Fig. 1, the one of a kind of image processing method based on k-means clusters and dictionary learning provided by the invention
A embodiment, including：
101, initialisation image parameter obtains waiting for the noise image of piecemeal, and the noise image for treating piecemeal carries out image block
Obtain image block；
102, operation k-means algorithms carry out cluster calculation to image block and obtain K cluster, and MOD- is run to each cluster
AK-SVD dictionary learning algorithms obtain training cluster dictionary { D1,D2,D3...Dk}；
103, by training cluster dictionary { D1,D2,D3...DkIt was polymerized to complete dictionary D={ D1,D2,D3...Dk}；
104, operation OMP orthogonal matching pursuit algorithms solve the sparse coefficient of corresponding excessively complete dictionary D
105, according to sparse coefficientCalculate reconstruct denoising image；
106, judge whether iterations reach preset targeted number, if so, output reconstruct denoising image, if it is not,
Iterations are then added into the step of returning to initialisation image parameter together, the initial value of iterations is 1.
Please refer to table 1, algorithm provided by the invention and existing sparse coding algorithm (Sparse coding) algorithm change
Into sparse coding (ISC) algorithm, the PSNR of image denoising effect under the conditions of different noise variance δ and mixed noise density d
(Y-PSNR) value is compared, it can be found that our denoising effect will reach better effect.
Table 1
Referring to Fig. 2, a kind of image processing method based on k-means clusters and dictionary learning provided by the invention is another
One embodiment, including：
(1) algorithm iteration number j=1,2...J are set, enabled
That is initialisation image parameter.Wherein, y is pending noise image,To wait for the noise image of piecemeal,For the last time
Reconstruct denoising image after iteration, β are preset related coefficient, and j is iterations and initial value is 1.
Be arranged image block size be n*n, dictionary size k, Lagrange multiplier λ1, cluster numbers K, image is big
The small fragmental image processing for N*N obtains (N-n+1)2A image block.
(2) given image block is clustered with k mean algorithms, each cluster is instructed with MOD-AK-SVD dictionaries
Practice algorithm, obtains training cluster dictionary { D1,D2,D3...Dk, i.e.,：
Image block is divided into K classes by calculating the Euclidean distance between each segment, forms K cluster.
Randomly build a dictionary Dk, to DkExecute normalized；
Main iterative process is executed according to k-th of cluster；
JudgeWhether preset minimum value is less than or equal to, if so, output dictionary Dk, if it is not, then returning
Execute main iterative process；
It should be noted that the dictionary D exported at this timekIt is exactly the corresponding piecemeal dictionary of k-th of cluster, repeats (2) step
Calculating process (can also algorithm be carried out to each cluster simultaneously), k is calculated from 1 update to K, so that it may to obtain K piecemeal word
Allusion quotation clusters dictionary { D to get to training1,D2,D3...Dk}。
Wherein, main iterative process is：
Operation OMP orthogonal matching pursuit algorithms solve dictionary DkSparse coefficient；
It runs MOD and AK-AVD algorithms and updates dictionary, that is, calculate following equation：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
Dictionary atom d is updated according to following equationj0And sparse coefficient
dj0=Ej0xj0；
Wherein, Y indicates picture signal matrix, XKIndicate sparse coefficient matrix, dj0Represent DKIn jth 0 arrange,Represent XK
In 0 row of jth, Ωj0Indicate that corresponding set of circumstances, M are constant.
(3) by training cluster dictionary { D1,D2,D3…DkIt was polymerized to complete dictionary D={ D1,D2,D3…Dk}；
(4) OMP (orthogonal matching pursuit) algorithm is used, solves corresponding sparse coefficient, i.e.,：
According to the sparse coefficient of excessively complete dictionary DThe sparse coefficient of complete dictionary D was calculated in solution formula
Cross the sparse coefficient of complete dictionary DSolution formula be：
Wherein,For the corresponding sparse coefficient of iteration j ith cluster, RijIndicate corresponding piece of extraction operator, X tables
Diagram indicates error parameter as signal matrix, T (σ).
(5) denoising image is reconstructed, i.e.,：
Reconstruct denoising image is calculated according to denoising image formula；
Denoising image formula is：
Wherein,Indicate that the hot-tempered image that goes after iteration j, R are that image block extracts operator, λ1For Lagrangian constant, X
For noise image, D is updated dictionary,For the corresponding sparse coefficient of iteration j ith cluster, I is cell matrix.
It should be noted that formula is to calculate the formula for removing hot-tempered image, and when also to carry out next iteration, denoising at this time
Image formulaReplace formulaInThe initialization for carrying out image parameter, when no longer
When iteration, denoising image formula calculatesIt is exactly the image of final output.
(6) judge whether iterations reach preset targeted number, if so, output reconstruct denoising image, if it is not, then
The initial value of the step of returning to initialisation image parameter by iterations plus together, iterations is 1.Iterations j=1,2 ...
J, the i.e. initial value of iterations j are 1, J are iterated to since 1, J is targeted number.
To be clearly understood that technical scheme of the present invention, relevant speciality term will be explained below：
K-means algorithms, i.e. k mean algorithms, specially：By calculating corresponding Euclidean distance, constantly it polymerize from k
The point of the nearest mean value of central point enables Euclidean distance aggregating into one kind very close to point, reaches classifying quality.
Dictionary learning algorithm typically has MOD dictionary learning algorithms, K-MOD dictionary learnings algorithm and AK-MOD, if one group
Signal Y=[y1,y2…yn], the target of MOD algorithms is to find a dictionary D and a sparse matrix X so that the reconstruct of signal
Error is minimum：
Here x is the row of matrix X, and MOD is a kind of renewal process of the alternating iteration between dictionary upgrading and sparse coding.
Sparse coding process is to each signal ynIndividually carry out rarefaction representation.
The step of excessively complete dictionary training based on MOD algorithms：
Initialize dictionary：Random one dictionary D0 of construction, standardizes to D0.
Main iterative process：
Sparse coding step：Sparse coefficient is found out using OMP tracing algorithms：
Dictionary is updated using MOD algorithms：
IfReach enough fractional values of setting, stops calculating.Otherwise, next iteration is carried out.D(k)
It is exactly the dictionary that we finally obtain.
K-SVD algorithms are proposed by Aharon et al..Keep dictionary in addition to jth 0 arrange other than all row fix, dj0 this
Row can be realized with the multiplication in same X to be updated, and object function is as follows：
Wherein,It is residual matrix,Represent the jth row in X.To dj0WithIt is simple by one
To Ej0Rank-l approach to make above formula minimum, thus obtain the update of dictionary atom.
The step of excessively complete dictionary training based on K-SVD algorithms：
Initialize dictionary：Random one dictionary D0 of construction, standardizes to D0.
Main iterative process：
Sparse coding step：Sparse coefficient is found out using OMP (orthogonal matching pursuit) algorithm.
Dictionary is updated using K-SVD algorithms：The following steps update each column and coefficient X (k) of dictionary, define sample group dj0：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
djIt is the jth row in X (k), is decomposed using SVD：
Update dictionary atom dj0, sparse coefficientdj0=u1,
IfReach enough fractional values of setting, stops calculating.Otherwise, next iteration is carried out.D(k)
It is exactly the dictionary that we finally obtain.
AK-SVD algorithms：
Calculation amount is reduced by providing the approximate solution that SVD is decomposed.AK-SVD utilizes residual matrix Ej0To dj0WithIt carries out
It alternately updates, as follows：
djo=Ej0xj0；
Dictionary training generally can be divided into two processes：One is sparse coding, that is to say sparse decomposition, another is word
The update of allusion quotation
MOD-AK-SVD dictionary learning algorithms are to combine MOD algorithms and AK-SVD algorithms to carry out repeatedly dictionary
Update solves the algorithm of dictionary.
It is to a kind of implementation of the image processing method based on k-means clusters and dictionary learning provided by the invention above
Example is described in detail, below will be to a kind of image procossing based on k-means cluster and dictionary learning provided by the invention
Device is described in detail.
Referring to Fig. 3, the one of a kind of image processing apparatus based on k-means clusters and dictionary learning provided by the invention
A embodiment, including：
Image block module 201 obtains waiting for the noise image of piecemeal for initialisation image parameter, treats the noise of piecemeal
Image carries out image block and obtains image block；
Cluster and dictionary learning module 202 carry out cluster calculation acquisition K for running k-means algorithms to image block
Cluster obtains training cluster dictionary { D to each cluster operation MOD-AK-SVD dictionary learning algorithms1,D2,D3...Dk}；
Dictionary aggregation module 203, for cluster dictionary { D will to be trained1,D2,D3…DkIt was polymerized to complete dictionary D={ D1,
D2,D3…Dk}；
Sparse coefficient computing module 204 solves corresponding excessively complete dictionary for running OMP orthogonal matching pursuit algorithms
The sparse coefficient of D
Denoising image module 205 is reconstructed, for according to sparse coefficientCalculate reconstruct denoising image；
Loop iteration module 206, for judging whether iterations reach preset targeted number, if so, output weight
Structure denoising image executes image block module if it is not, then adding iterations to return together, and the initial value of iterations is 1.
Further, image block module 201 specifically includes：
Image initial unit, for enabling
Image block unit for image block size to be arranged is n*n, dictionary size k, Lagrange multiplier λ1、
Cluster numbers are K, and the fragmental image processing that image size is N*N is obtained (N-n+1)2A image block；
Wherein, y is pending noise image,To wait for the noise image of piecemeal,For the weight after last iteration
Structure denoising image, β are preset related coefficient, and j is iterations and initial value is 1.
Referring to Fig. 4, further, cluster and dictionary learning module 202 specifically include：
Cluster cell 301, for image block to be divided into K classes by calculating the Euclidean distance between each segment, composition K is poly-
Class；
Normalization unit 302, for randomly building a dictionary Dk, to DkExecute normalized；
Main iteration unit 303, for executing main iterative process according to k-th of cluster；
Judging unit 304, for judgingWhether preset minimum value is less than or equal to, if so, output
Dictionary Dk, main iterative process is executed if it is not, then returning；
Wherein, main iterative process is：
Operation OMP orthogonal matching pursuit algorithms solve dictionary DkSparse coefficient；
It runs MOD and AK-AVD algorithms and updates dictionary, that is, calculate following equation：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
Dictionary atom d is updated according to following equationj0And sparse coefficient
dj0=Ej0xj0；
Wherein, Y indicates picture signal matrix, XKIndicate sparse coefficient matrix, dj0Represent DKIn jth 0 arrange,Represent XK
In 0 row of jth, Ωj0Indicate that corresponding set of circumstances, M are constant.
Sparse coefficient computing module 204 is specifically used for the sparse coefficient according to excessively complete dictionary DSolution formula is calculated
Cross the sparse coefficient of complete dictionary D
Denoising image module 205 is reconstructed to be specifically used for calculating reconstruct denoising image according to denoising image formula；
Cross the sparse coefficient of complete dictionary DSolution formula be：
Wherein,For the corresponding sparse coefficient of iteration j ith cluster, RijIndicate corresponding piece of extraction operator, X tables
Diagram indicates error parameter as signal matrix, T (σ).
Denoising image formula is：
Wherein,Indicate that the hot-tempered image that goes after iteration j, R are that image block extracts operator, λ1For Lagrangian constant, X
For noise image, D is updated dictionary,For the corresponding sparse coefficient of iteration j ith cluster, I is cell matrix.
The above, the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to before
Stating embodiment, invention is explained in detail, it will be understood by those of ordinary skill in the art that：It still can be to preceding
The technical solution recorded in each embodiment is stated to modify or equivalent replacement of some of the technical features；And these
Modification or replacement, the spirit and scope for various embodiments of the present invention technical solution that it does not separate the essence of the corresponding technical solution.
Claims (10)
1. a kind of image processing method based on k-means cluster and dictionary learning, which is characterized in that including：
Initialisation image parameter obtains waiting for the noise image of piecemeal, and the noise image for treating piecemeal carries out image block acquisition image
Block；
It runs k-means algorithms and K cluster of cluster calculation acquisition is carried out to image block, MOD-AK-SVD words are run to each cluster
Allusion quotation learning algorithm obtains training cluster dictionary { D1,D2,D3...Dk}；
By training cluster dictionary { D1,D2,D3…DkIt was polymerized to complete dictionary D={ D1,D2,D3…Dk}；
Operation OMP orthogonal matching pursuit algorithms solve the sparse coefficient of corresponding excessively complete dictionary D
According to sparse coefficientCalculate reconstruct denoising image；
Judge whether iterations reach preset targeted number, if so, output reconstruct denoising image, if it is not, then by iteration
Number adds the step of returning to initialisation image parameter together, and the initial value of the iterations is 1.
2. a kind of image processing method based on k-means cluster and dictionary learning according to claim 1, feature exist
In the initialisation image parameter obtains waiting for the noise image of piecemeal, and the noise image for treating piecemeal carries out image block acquisition
Image block specifically includes：
It enables
Be arranged image block size be n*n, dictionary size k, Lagrange multiplier λ1, cluster numbers K, be by image size
The fragmental image processing of N*N obtains (N-n+1)2A image block；
Wherein, y is pending noise image,To wait for the noise image of piecemeal,It is gone for the reconstruct after last iteration
It makes an uproar image, β is preset related coefficient, and j is iterations and initial value is 1.
3. a kind of image processing method based on k-means cluster and dictionary learning according to claim 1, feature exist
In the operation k-means algorithms carry out k cluster of cluster calculation acquisition to image block and specifically include：
Image block is divided into K classes by calculating the Euclidean distance between each segment, forms K cluster.
4. a kind of image processing method based on k-means cluster and dictionary learning according to claim 1, feature exist
In described to obtain training cluster dictionary { D to each cluster operation MOD-AK-SVD dictionary learning algorithms1,D2,D3…DkSpecific
Including：
Randomly build a dictionary Dk, to DkExecute normalized；
Main iterative process is executed according to k-th of cluster；
JudgeWhether preset minimum value is less than or equal to, if so, output dictionary Dk, if it is not, then returning to execution
Main iterative process；
Wherein, the main iterative process is：
Operation OMP orthogonal matching pursuit algorithms solve dictionary DkSparse coefficient；
It runs MOD and AK-AVD algorithms and updates dictionary, that is, calculate following equation：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
Dictionary atom d is updated according to following equationj0And sparse coefficient
dj0=Ej0xj0；
Wherein, Y indicates picture signal matrix, XKIndicate sparse coefficient matrix, dj0Represent DKIn jth 0 arrange,Represent XKIn
0 row of jth, Ωj0Indicate that corresponding set of circumstances, M are constant.
5. a kind of image processing method based on k-means cluster and dictionary learning according to claim 1, feature exist
In the operation OMP orthogonal matching pursuit algorithms solve the sparse coefficient of corresponding excessively complete dictionary DSpecially：
According to the sparse coefficient of excessively complete dictionary DThe sparse coefficient of complete dictionary D was calculated in solution formula
The sparse coefficient of the excessively complete dictionary DSolution formula be：
Wherein,For the corresponding sparse coefficient of iteration j ith cluster, RijIndicate that corresponding piece of extraction operator, X indicate figure
As signal matrix, T (σ) indicates error parameter.
6. a kind of image processing method based on k-means cluster and dictionary learning according to claim 1, feature exist
In described according to sparse coefficientCalculating reconstruct denoising image is specially：
Reconstruct denoising image is calculated according to denoising image formula；
The denoising image formula is：
Wherein,Indicate that the hot-tempered image that goes after iteration j, R are that image block extracts operator, λ1For Lagrangian constant, X is to make an uproar
Acoustic image, D are updated dictionary,For the corresponding sparse coefficient of iteration j ith cluster, I is cell matrix.
7. a kind of image processing apparatus based on k-means cluster and dictionary learning, which is characterized in that including：
Image block module obtains waiting for the noise image of piecemeal for initialisation image parameter, treat the noise image of piecemeal into
Row image block obtains image block；
Cluster and dictionary learning module carry out K cluster of cluster calculation acquisition for running k-means algorithms to image block, right
Each cluster operation MOD-AK-SVD dictionary learning algorithms obtain training cluster dictionary { D1,D2,D3...Dk}；
Dictionary aggregation module, for cluster dictionary { D will to be trained1,D2,D3…DkIt was polymerized to complete dictionary D={ D1,D2,D3…
Dk}；
Sparse coefficient computing module solves the sparse of corresponding excessively complete dictionary D for running OMP orthogonal matching pursuit algorithms
Coefficient
Denoising image module is reconstructed, for according to sparse coefficientCalculate reconstruct denoising image；
Loop iteration module, for judging whether iterations reach preset targeted number, if so, output reconstruct denoising figure
Picture executes image block module if it is not, then adding iterations to return together, and the initial value of the iterations is 1.
8. a kind of image processing apparatus based on k-means cluster and dictionary learning according to claim 7, feature exist
In described image piecemeal module specifically includes：
Image initial unit, for enabling
Image block unit for image block size to be arranged is n*n, dictionary size k, Lagrange multiplier λ1, cluster numbers
For K, the fragmental image processing that image size is N*N is obtained (N-n+1)2A image block；
Wherein, y is pending noise image,To wait for the noise image of piecemeal,It is gone for the reconstruct after last iteration
It makes an uproar image, β is preset related coefficient, and j is iterations and initial value is 1.
9. a kind of image processing apparatus based on k-means cluster and dictionary learning according to claim 7, feature exist
In the cluster and dictionary learning module specifically include：
Cluster cell forms K cluster for image block to be divided into K classes by calculating the Euclidean distance between each segment；
Normalization unit, for randomly building a dictionary Dk, to DkExecute normalized；
Main iteration unit, for executing main iterative process according to k-th of cluster；
Judging unit, for judgingWhether preset minimum value is less than or equal to, if so, output dictionary DkIf
It is no, then it returns and executes main iterative process；
Wherein, the main iterative process is：
Operation OMP orthogonal matching pursuit algorithms solve dictionary DkSparse coefficient；
It runs MOD and AK-AVD algorithms and updates dictionary, that is, calculate following equation：
Ωj0=i | 1≤i≤M, X(k)(j0,i)≠0}；
Calculate residual matrix：
Dictionary atom d is updated according to following equationj0And sparse coefficient
dj0=Ej0xj0；
Wherein, Y indicates picture signal matrix, XKIndicate sparse coefficient matrix, dj0Represent DKIn jth 0 arrange,Represent XKIn
0 row of jth, Ωj0Indicate that corresponding set of circumstances, M are constant.
10. a kind of image processing apparatus based on k-means cluster and dictionary learning according to claim 7, feature
It is,
The sparse coefficient computing module is specifically used for the sparse coefficient according to excessively complete dictionary DSolution formula was calculated
The sparse coefficient of complete dictionary D
The reconstruct denoising image module is specifically used for calculating reconstruct denoising image according to denoising image formula；
The sparse coefficient of the excessively complete dictionary DSolution formula be：
Wherein,For the corresponding sparse coefficient of iteration j ith cluster, RijIndicate that corresponding piece of extraction operator, X indicate figure
As signal matrix, T (σ) indicates error parameter；
The denoising image formula is：
Wherein,Indicate that the hot-tempered image that goes after iteration j, R are that image block extracts operator, λ1For Lagrangian constant, X is to make an uproar
Acoustic image, D are updated dictionary,For the corresponding sparse coefficient of iteration j ith cluster, I is cell matrix.
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