CN109859123A - Image de-noising method and system based on Primal-dual - Google Patents
Image de-noising method and system based on Primal-dual Download PDFInfo
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Abstract
The invention discloses a kind of image de-noising method and system based on Primal-dual.The denoising method includes: the dual vector space of the training sample set for obtaining sample image, former vector space and the former vector space；Obtain in former vector space the second regularization term corresponding to dual variable in the first regularization term corresponding to former variable and dual vector space；Training matrix is constructed according to training sample set；Training sample set constant and iteration step length are determined according to training matrix；The objective function of Non-smooth surface is established according to the first regularization term, the second regularization term and training sample set constant；Using individual output form, former variable and dual variable are updated according to the objective function of Non-smooth surface and iteration step length, determine the former variable of individual output and the dual variable of individual output；Denoising is carried out to sample image according to the dual variable of the former variable of individual output and individual output.Image denoising efficiency can be improved using denoising method provided by the invention and system.
Description
Technical field
The present invention relates to image denoising field, more particularly to a kind of image de-noising method based on Primal-dual and
System.
Background technique
Traditional images denoising method is based only upon former variable or dual variable obtains sparsity and therefore can only select in feature
Take or number of samples on reach sparse, processing large-scale image data collection denoising effect on it is not excellent enough while traditional
Image de-noising method is only obtained in Non-smooth surface type functionRate of convergence；And Primal-dual method
Rate of convergence can be further promoted, but the solution of the Primal-dual methods for image application most of at present is most
It is exported with averaged version, individual exports relatively fewer, and is not added with regularization term, and generalization ability is poor, can not obtain good
Sparsity, it is thus impossible to it is suitable for the demand that high-precision denoises effect, the image so as to cause tradition based on Primal-dual
Denoising method image denoising low efficiency.
Summary of the invention
The object of the present invention is to provide a kind of image de-noising method and system based on Primal-dual, to solve tradition
The problem of image de-noising method image denoising low efficiency based on Primal-dual.
To achieve the above object, the present invention provides following schemes:
A kind of image de-noising method based on Primal-dual, comprising:
Obtain the training sample set of sample image, the dual vector space of former vector space and the former vector space；
The training sample set includes classification type corresponding to the feature vector and described eigenvector of sample image；
Initialize the first regularization term and the dual vector space corresponding to former variable in the former vector space
Second regularization term corresponding to interior dual variable；
Training matrix is constructed according to the training sample set；
Training sample set constant and iteration step length are determined according to the training matrix；
Non-smooth surface is established according to first regularization term, second regularization term and the training sample set constant
Objective function；
Using individual output form, the former change is updated according to the objective function of the Non-smooth surface and the iteration step length
Amount and the dual variable determine the former variable of individual output and the dual variable of individual output；
The sample image is carried out according to the dual variable of the former variable of the individual output and the individual output
Denoising.
Optionally, described that training sample set constant and iteration step length are determined according to the training matrix, it specifically includes:
The training sample set constant and the iteration step length are determined according to two norms of the training matrix.
Optionally, described normal according to first regularization term, second regularization term and the training sample set
Number establishes the objective function of Non-smooth surface, specifically includes:
According to formulaEstablish the target letter of Non-smooth surface
Number；Wherein, It is non-
Smooth loss function；X is the former vector space；Y is the dual vector space；W ∈ X, α ∈ Y, α are the antithesis based on w
Variable, w are for training sample set xiOptimization weight vectors；λ1R (w) is the first regularization term；λ2R (α) is the second regularization
?；wTFor the transposed matrix of w；αTFor the transposed matrix of α；H (S, y), a (S, y), b (S, y), d are based on the normal of training sample set S
Number.
Optionally, described using individual output form, according to the objective function of the Non-smooth surface and the iteration step length
The former variable and the dual variable are updated, determines the former variable of individual output and the dual variable of individual output, tool
Body includes:
Using individual output form, according to formulaFormulaAnd formulaDetermine individual output former variable with
And the dual variable of individual output；Wherein, Gα(wt-1, βt-1) bePartial derivative at α；Gw(wt-1, αt) bePartial derivative at w；β is to connect w, the vector of α in construction iteration；wt, αt, βt(t=0,1,2 ... ..., T) is w,
The output vector of α, β after t circulation； C=D2/ m, D are x in training sample set SiTwo norms
Maximum value.
A kind of image denoising system based on Primal-dual, comprising:
Sample image parameter acquisition module, for obtaining the training sample set of sample image, former vector space and described
The dual vector space of former vector space；The training sample set includes the feature vector and described eigenvector of sample image
Corresponding classification type；
Regularization term obtains module, for initializing the first regularization term corresponding to former variable in the former vector space
And the second regularization term corresponding to dual variable in the dual vector space；
Training matrix constructing module, for constructing training matrix according to the training sample set；
Training sample set constant and iteration step length determining module, for determining training sample set according to the training matrix
Constant and iteration step length；
The objective function determining module of Non-smooth surface, for according to first regularization term, second regularization term with
And the training sample set constant establishes the objective function of Non-smooth surface；
Output module, for using individual output form, according to the objective function of the Non-smooth surface and the iteration step
It is long to update the former variable and the dual variable, determine the former variable of individual output and the dual variable of individual output；
Denoising module, for according to the former variable of the individual output and the dual variable pair of the individual output
The sample image carries out denoising.
Optionally, the training sample set constant and iteration step length determining module specifically include:
Training sample set constant and iteration step length determination unit, for determining institute according to two norms of the training matrix
State training sample set constant and the iteration step length.
Optionally, the objective function of the Non-smooth surface is established module and is specifically included:
The objective function of Non-smooth surface establishes unit, for according to formulaEstablish the objective function of Non-smooth surface；Wherein, For the damage of Non-smooth surface
Lose function；X is the former vector space；Y is the dual vector space；W ∈ X, α ∈ Y, α are the dual variable based on w, and w is
For training sample set xiOptimization weight vectors；λ1R (w) is the first regularization term；λ2R (α) is the second regularization term；wTFor w
Transposed matrix；αTFor the transposed matrix of α；H (S, y), a (S, y), b (S, y), d are the constant based on training sample set S.
Optionally, the output module specifically includes:
Output unit, for using individual output form, according to formulaFormulaAnd formulaDetermine individual output former variable with
And the dual variable of individual output；Wherein, Gα(wt-1, βt-1) bePartial derivative at α；Gw(Wt-1, αt) bePartial derivative at w；β is to connect w, the vector of α in construction iteration；wt, αt, βt(t=0,1,2 ..., T) be
The output vector of w, α, β after t circulation； C=D2/ m, D are x in training sample set SiTwo
The maximum value of norm.
The specific embodiment provided according to the present invention, the invention discloses following technical effects: using provided by the present invention
A kind of image de-noising method and system based on Primal-dual, regularization term is added to former variable and dual variable, and
The way of output for taking individual output determines the former variable of individual output and the dual variable of individual output, is based on obtaining
And the dual sparsity of dual variable, it is ensured that the sparsity of understanding.
The quantity of non-zero dimension can be lacked as much as possible in the solution vector of individual output, to greatly reduce of supporting vector
Number, is of great significance for the feature selecting of high dimensional data, sparsity is obtained in Feature Selection or number of samples, handles
Large-scale data and high dimensional data have excellent effect, when can greatly reduce prediction for the image pattern with sparse model
Between, improve image denoising efficiency.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without any creative labor, can also be according to these attached drawings
Obtain other attached drawings.
Fig. 1 is the image de-noising method flow chart provided by the present invention based on Primal-dual；
Fig. 2 is the image de-noising method flow chart based on Primal-dual provided by the present invention by taking two classification as an example；
Fig. 3 is the image denoising system construction drawing provided by the present invention based on Primal-dual.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The object of the present invention is to provide a kind of image de-noising method and system based on Primal-dual, can be improved figure
As denoising efficiency.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real
Applying mode, the present invention is described in further detail.
Fig. 1 is the image de-noising method flow chart provided by the present invention based on Primal-dual, as shown in Figure 1, a kind of
Image de-noising method based on Primal-dual, comprising:
Step 101: obtain the antithesis of the training sample set of sample image, former vector space and the former vector space to
Quantity space；The training sample set includes classification type corresponding to the feature vector and described eigenvector of sample image.
Step 102: the first regularization term and the antithesis corresponding to former variable in the initialization former vector space
Second regularization term corresponding to dual variable in vector space.
Step 103: training matrix is constructed according to the training sample set.
The matrix P based on picture training sample set S is constructed, parameter c (c=D is solved2/ m, D are x in training sample set Si's
The maximum value of two norms)；And determine step-length γtValue range constructs and connects w, the vector β of α in iteration, initializes α0=0, β0
=0.
Step 104: training sample set constant and iteration step length are determined according to the training matrix.
Step 105: being built according to first regularization term, second regularization term and the training sample set constant
The objective function of vertical Non-smooth surface.
As indicated with 2, by taking two classification as an example, for independent identically distributed picture training sample setxiFor the feature vector based on picture sample, yiFor needle
To sample xiClassification type (+1, -1), RnFor Hilbert space.Its optimization Non-smooth surface based on image denoising application problem
Objective function may be expressed as:
Wherein, For
The loss function of Non-smooth surface；X is the former vector space；Y is the dual vector space；W ∈ X, α ∈ Y, α are pair based on w
Mutation amount, w are for training sample set xiOptimization weight vectors；λ1R (w) is the first regularization term；λ2R (α) is the second canonical
Change item, the first regularization term and the second regularization term are L1 regularization term；wTFor the transposed matrix of w；αTFor the transposition square of α
Battle array；H (S, y), a (S, y), b (S, y), d are the constant based on training sample set S；The Hinge loss function of the Non-smooth surface.
Step 106: using individual output form, being updated according to the objective function of the Non-smooth surface and the iteration step length
The original variable and the dual variable determine the former variable of individual output and the dual variable of individual output.
Initialize regularization parameter λ1、λ2And step-length γt, T circulation is executed in the following way:
i)
ii)
iii)
Wherein, Gα(wt-1, βt-1) bePartial derivative at α；Gw(wt-1, αt) beLocal derviation at w
Number；β is to connect w, the vector of α in construction iteration；wt, αt, βt(t=0,1,2 ..., T) it is w, α, β are after t circulation
Output vector；C=D2/ m, D are x in training sample set SiTwo norms maximum value.
α is exported after T circulationT, wT, be respectively individual output dual variable and former variable, if image denoising effect or
Classifying quality (i.e. function error value) reaches desired value, then terminates；Otherwise redjustment and modification step-length γt, regularization parameter λ1And
λ2。
By updating solution vector w every time, so that it is approached to theoretical optimal solution, so that the loss function of Non-smooth surface
It gradually becomes smaller, and then gets a desired effect by recycling every time.
Step 107: according to the former variable of the individual output and the dual variable of the individual output to the sample
Image carries out denoising.
The present invention is taken by adding L1 regularization term to the required former variable for denoising image data and dual variable
The form of individual output, it is ensured that the sparsity of understanding；The quantity of non-zero dimension can be lacked as much as possible in the solution vector of individual output, from
And the number of supporting vector is greatly reduced, it is of great significance for the feature selecting of high dimensional data, for sparse model
Image pattern can greatly reduce predicted time, the application strong for timeliness have extremely important application value.
Fig. 3 is the image denoising system construction drawing provided by the present invention based on Primal-dual, as shown in figure 3, a kind of
Image denoising system based on Primal-dual, comprising:
Sample image parameter acquisition module 301, for obtaining training sample set, former vector space and the institute of sample image
State the dual vector space of former vector space；The training sample set include sample image feature vector and the feature to
The corresponding classification type of amount.
Regularization term obtains module 302, for initializing the first canonical corresponding to former variable in the former vector space
Change the second regularization term corresponding to dual variable in item and the dual vector space.
Training matrix constructing module 303, for constructing training matrix according to the training sample set.
Training sample set constant and iteration step length determining module 304, for determining training sample according to the training matrix
This collection constant and iteration step length.
The training sample set constant and iteration step length determining module 304 specifically include: training sample set constant and
Iteration step length determination unit, for two norms according to the training matrix determine the training sample set constant and it is described repeatedly
It rides instead of walk length.
The objective function determining module 305 of Non-smooth surface, for according to first regularization term, second regularization term
And the training sample set constant establishes the objective function of Non-smooth surface.
The objective function of the Non-smooth surface is established module 305 and specifically included: the objective function of Non-smooth surface establishes unit, is used for
According to formulaEstablish the target letter of Non-smooth surface
Number；Wherein, It is non-
Smooth loss function；X is the former vector space；Y is the dual vector space；W ∈ X, α ∈ Y, α are the antithesis based on w
Variable, w are for training sample set xiOptimization weight vectors；λ1R (w) is the first regularization term；λ2R (α) is the second regularization
?；wTFor the transposed matrix of w；αTFor the transposed matrix of α；H (S, y), a (S, y), b (S, y), d are based on the normal of training sample set S
Number.
Output module 306, for using individual output form, according to the objective function of the Non-smooth surface and the iteration
Step-length updates the former variable and the dual variable, determine individual output former variable and individual output to mutation
Amount.
The output module 306 specifically includes: output unit, for using individual output form, according to formulaFormulaAnd formulaDetermine the former variable of individual output
And the dual variable of individual output；Wherein, Gα(wt-1, βt-1) bePartial derivative at α；Gw(wt-1, αt) bePartial derivative at w；β is to connect w, the vector of α in construction iteration；wt, αt, βt(t=0,1,2 ..., T) be
The output vector of w, α, β after t circulation； C=D2/ m, D are x in training sample set SiTwo models
Several maximum values.
Denoising module 307, for according to it is described individual output former variable and it is described individual output to mutation
Amount carries out denoising to the sample image.
Only in former variable, perhaps dual variable acquirement sparsity can only be in Feature Selection or number of samples for conventional method
Reach sparse；The present invention by adding L1 regularization term to former variable and dual variable, with obtain based on dual variable
Dual sparsity can obtain sparsity in Feature Selection or number of samples simultaneously, in processing large-scale data and higher-dimension
Data have excellent effect.
The present invention defeated is individual solution vector, and demonstrates it by skills such as transformation, scaling, recurrence and can obtain individual receipts
Rate is held back, and can preferably be promoted suitable for all kinds of machine learning application.
The present invention can obtain O (1/ for the special nature (such as bilinear function) of special class functions certain in smooth perturbation problem
T average rate of convergence (T is expressed as the number of iterations)), more traditional first order gradient algorithm faster an order of magnitude
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with other
The difference of embodiment, the same or similar parts in each embodiment may refer to each other.For system disclosed in embodiment
For, since it is corresponded to the methods disclosed in the examples, so being described relatively simple, related place is said referring to method part
It is bright.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said
It is bright to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, foundation
Thought of the invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not
It is interpreted as limitation of the present invention.
Claims (8)
1. a kind of image de-noising method based on Primal-dual characterized by comprising
Obtain the training sample set of sample image, the dual vector space of former vector space and the former vector space；It is described
Training sample set includes classification type corresponding to the feature vector and described eigenvector of sample image；
It is right in the first regularization term corresponding to former variable and the dual vector space to initialize in the former vector space
Second regularization term corresponding to mutation amount；
Training matrix is constructed according to the training sample set；
Training sample set constant and iteration step length are determined according to the training matrix；
The mesh of Non-smooth surface is established according to first regularization term, second regularization term and the training sample set constant
Scalar functions；
Using individual output form, according to the objective function of the Non-smooth surface and the iteration step length update the former variable with
And the dual variable, determine the former variable of individual output and the dual variable of individual output；
The sample image is denoised according to the dual variable of the former variable of the individual output and the individual output
Processing.
2. the image de-noising method according to claim 1 based on Primal-dual, which is characterized in that described according to institute
It states training matrix and determines training sample set constant and iteration step length, specifically include:
The training sample set constant and the iteration step length are determined according to two norms of the training matrix.
3. the image de-noising method according to claim 1 based on Primal-dual, which is characterized in that described according to institute
The objective function that the first regularization term, second regularization term and the training sample set constant establish Non-smooth surface is stated, is had
Body includes:
According to formulaEstablish the target letter of Non-smooth surface
Number；Wherein, For non-light
Sliding loss function；X is the former vector space；Y is the dual vector space；W ∈ X, α ∈ Y, α are based on w to mutation
Amount, w are for training sample set xiOptimization weight vectors；λ1R (w) is the first regularization term；λ2R (α) is the second regularization
?；wTFor the transposed matrix of w；αTFor the transposed matrix of α；H (S, y), a (S, y), b (S, y), d are based on the normal of training sample set S
Number.
4. the image de-noising method according to claim 1 based on Primal-dual, which is characterized in that described using a
Body output form updates the former variable and the antithesis according to the objective function of the Non-smooth surface and the iteration step length
Variable determines the former variable of individual output and the dual variable of individual output, specifically includes:
Using individual output form, according to formula
FormulaAnd formulaDetermine individual output former variable and
The dual variable of individual output；Wherein, Gα(wt-1, βt-1) bePartial derivative at α；Gw(wt-1, αt) be
Partial derivative at w；β is to connect w, the vector of α in construction iteration；wt, αt, βt(t=0,1,2 ..., T) it is w, α, β is in t
Output vector after secondary circulation； C=D2/ m, D are x in training sample set SiTwo norms maximum
Value.
5. a kind of image denoising system based on Primal-dual characterized by comprising
Sample image parameter acquisition module, for obtain the training sample set of sample image, former vector space and it is described it is former to
The dual vector space of quantity space；The training sample set include sample image feature vector and described eigenvector institute it is right
The classification type answered；
Regularization term obtains module, for initialize in the former vector space the first regularization term corresponding to former variable and
Second regularization term corresponding to dual variable in the dual vector space；
Training matrix constructing module, for constructing training matrix according to the training sample set；
Training sample set constant and iteration step length determining module, for determining training sample set constant according to the training matrix
And iteration step length；
The objective function determining module of Non-smooth surface, for according to first regularization term, second regularization term and institute
State the objective function that training sample set constant establishes Non-smooth surface；
Output module, for using individual output form, more according to the objective function of the Non-smooth surface and the iteration step length
The new former variable and the dual variable determine the former variable of individual output and the dual variable of individual output；
Denoising module, for the former variable and the individual dual variable exported according to the individual output to described
Sample image carries out denoising.
6. the image denoising system according to claim 5 based on Primal-dual, which is characterized in that the trained sample
This collection constant and iteration step length determining module specifically include:
Training sample set constant and iteration step length determination unit, for determining the instruction according to two norms of the training matrix
Practice sample set constant and the iteration step length.
7. the image denoising system according to claim 5 based on Primal-dual, which is characterized in that the Non-smooth surface
Objective function establish module and specifically include:
The objective function of Non-smooth surface establishes unit, for according to formulaEstablish the objective function of Non-smooth surface；Wherein, For the damage of Non-smooth surface
Lose function；X is the former vector space；Y is the dual vector space；W ∈ X, α ∈ Y, α are the dual variable based on w, and w is
For training sample set xiOptimization weight vectors；λ1R (w) is the first regularization term；λ2R (α) is the second regularization term；wTFor w
Transposed matrix；αTFor the transposed matrix of α；H (S, y), a (S, y), b (S, y), d are the constant based on training sample set S.
8. the image denoising system according to claim 5 based on Primal-dual, which is characterized in that the output mould
Block specifically includes:
Output unit, for using individual output form, according to formulaFormulaAnd formulaDetermine individual output former variable and
The dual variable of individual output；Wherein, Gα(wt-1, βt-1) bePartial derivative at α；Gw(wt-1, αt) be
Partial derivative at w；β is to connect w, the vector of α in construction iteration；wt, αt, βt(t=0,1,2 ..., T) it is w, α, β is in t
Output vector after secondary circulation； C=D2/ m, D are x in training sample set SiTwo norms maximum
Value.
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