CN110414530A - Image based on Riemann manifold optimization goes mixing impulse noise method and system - Google Patents
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Abstract
The present invention provides a kind of images based on Riemann manifold optimization to go mixing impulse noise method and system, include the following steps: step 1, based on structural sparse representation method, construct the distinctive structure sparse representation model with block orthogonality constraint, block orthogonality constraint is applied to objective function, improving model indicates ability to image detail；Step 2, alternating minimization frame is constructed, and starts iterative process；Step 3, image median filter is constructed, for removing part impulse noise, provides the image of the Gaussian noise containing part for next step；Step 4, the Riemann manifold optimization problem under block orthogonality constraint is solved, to update rarefaction representation dictionary；Step 5, it constructs rarefaction smooth function and carries out automatic rarefaction representation；Step 6, building updates classification function and is updated；Step 7, if not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition requires to set according to user；Step 8, reconstruction image.
Description
Technical field
The present invention relates to Riemann manifold optimisation technique fields, and in particular, to a kind of image based on Riemann manifold optimization
Go mixing impulse noise method and system.
Background technique
Since the 1980s, high spectrum resolution remote sensing technique is believed by the solar radiation that atural object can be obtained in imaging spectrometer
Breath, such as visible light, near-infrared, in infrared, short-wave infrared.Compared with multispectral image, high spectrum image can reflect atural object
Subtle spectral properties, therefore information content can increase by 10 times to 100 times.Currently, each big country carries out a large amount of scientific research project pair
Hyperspectral technique is studied, and develops different types of imaging spectrometer, and be applied to resource exploration, disaster investigation, target
The fields such as investigation and battlefield surroundings monitoring.It is quick excellent in a kind of Riemann manifold as disclosed in patent document CN105868162A
Change method comprising following steps: (1) composite objective function in a kind of Riemann manifold is given；(2) proximal end Riemann gradient is used
Method is approached by optimal value of the progressive alternate local optimum to composite objective function；(3) initial point X0 is provided, is utilized
Line search obtains X1；As k >=2, indicate that point Xk-1 is directed toward the vector of Xk-2 with lifting operator, and this vector is on one
Direction is risen, its negative direction is exactly a descent direction, from point Xk-1, walks a specified step-length (tk- along descent direction
1) then/tk+1 wherein t1=1 generates new point by retracting function point from being mapped in Riemann manifold, is denoted as Yk；Again from
Yk sets out, and new iteration point Xk is generated by line search；(4) when specified requirements is satisfied, iteration stopping.Wherein indicate Riemann's stream
Shape is that manifold cuts space at point Xk-1；Lifting operator indicates that the point Xk-2 in manifold is mapped to point or the table cut spatially
Show the vector that a little point Xk-1 is directed toward on cutting space；Function representation is retracted to be mapped in manifold the point for cutting spatially.
But the promotion of hyperspectral imager Spectral dimension and spectral resolution brought to the processing of high spectrum image it is huge
Big technological challenge.Therefore, these technical problems exacerbate the complexity of the preprocessing process of hyperspectral image data, reduce
Treatment effeciency.In addition, wherein the image local feature of excessive redundancy makes the precision of high spectrum image algorithm by unfavorable shadow
It rings.Therefore, the present invention goes mixing impulse noise problem for high spectrum image, in conjunction with existing convex optimization scheduling theory and method,
Foundation is provided for the excavation of subsequent spectral signature and image space and its processing of space geometry feature intelligentization.
Summary of the invention
For the defects in the prior art, the object of the present invention is to provide a kind of images based on Riemann manifold optimization to go to mix
Syzygies swashs Noise Method and system.
A kind of image based on Riemann manifold optimization provided according to the present invention goes mixing impulse noise method, including as follows
Step:
Step 1, it is based on structural sparse representation method, constructs the distinctive structure rarefaction representation with block orthogonality constraint
Model applies block orthogonality constraint to objective function, and improving model indicates ability to image detail；
Step 2, alternating minimization frame is constructed, and starts iterative process；
Step 3, image median filter is constructed, for removing part impulse noise, provides Gauss containing part for next step
The image of noise；
Step 4, the Riemann manifold optimization problem under block orthogonality constraint is solved, to update rarefaction representation dictionary；
Step 5, it constructs rarefaction smooth function and carries out automatic rarefaction representation；
Step 6, building updates classification function and is updated；
Step 7, if not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition requires to set according to user
It is fixed；
Step 8, reconstruction image.
Preferably, step 1 building has the distinctive structure sparse representation model of block orthogonality constraint；Wherein, for
Fixed widthImage platform is divided into data matrix Y；Wherein, each piece of size isStructure sparse table
Representation model are as follows:
D represents dictionary, and A represents coefficient matrix corresponding with dictionary；Distinctive structure based on block orthogonality constraint
Sparse representation model are as follows:
BgIndicate the sub- dictionary in structural sparse expression；
AiRepresent coefficient matrix corresponding with sub- dictionary；
ωkIndicate the category set in structural sparse expression；
G indicates the index value [1 ..., G] of sub- dictionary；
G indicates ωkTotal classification number；
The index value of subscript i expression classification；
The index value of subscript k expression classification；
F indicates Frobenius norm；
Bg TIndicate the transposed matrix of sub- dictionary；
s0Zero norm of representing matrix A；
IdIndicate the unit matrix of d*d；
AiIndicate coefficient matrix corresponding with sub- dictionary；
YiThe submatrix of Y is represent, and has njA data point belongs to classification ω (j)=g, and set omega represents from data point
The mapping of (1 ..., n) to (1 ..., G)；The concrete form of Ω has:
ωjJ-th of classification is indicated, wherein including multiple sub- dictionaries；
N indicates there are n sub- dictionaries in classification；
ωiI-th of classification is indicated, wherein including multiple sub- dictionaries；
It indicates arbitrary classification, but is not equal to k-th of classification；
K indicates k-th of classification, wherein including multiple sub- dictionaries.
Preferably, the step 2 constructs alternating minimization frame, wherein the frame comprises the following steps:
Step 2.1, the dictionary updating based on Riemann manifold optimization；
Step 2.2, sparse coding；
Step 2.3, classification updates.
Preferably, the step 3 constructs image median filter, and structure is
Based on above-mentioned template, the selected image space for needing operation is ascending to the pixel of template to be ranked up, then uses
The intermediate value of template substitutes the value of original pixel.
Preferably, the step 4 solves the Riemann manifold optimization problem under block orthogonality constraint, to update rarefaction representation
Dictionary；By block condition of orthogonal constraints Bg TBgIt is embedded in search space Gg；Riemann manifold optimization problem under block orthogonality constraint
Form has:
Wherein, Gr represents Grassmann manifold；hεIt is customized rarefaction smooth function, hεForm have
Or
Wherein, ε > 0 is a smoothing parameter；The coefficient of representing matrix Y.
Preferably, the step 5 constructs rarefaction smooth function and carries out automatic rarefaction representation；Solve sparse coding variable
The equation of A are as follows:
Wherein, smooth function hεRarefaction effect ratio l1Norm is good.
Preferably, step 6 building updates classification function and is updated；For class variable ωk, construct target letter
Number
It indicates to carry out derivation to a in above formula；Wherein a is an element of matrix A；
λ is positive regularization parameter, yiThe column of data Y are represent, φ represents function that can be micro-, use classes variable ω
With analytic solutions.
Preferably, step 8 reconstruction image is carried out based on standard testing image barbara.
A kind of image based on Riemann manifold optimization provided according to the present invention goes mixing impulse noise system, including as follows
Module:
Module 1, the distinctive structure sparse representation model with block orthogonality constraint construct module；
Module 2, alternating minimization framework establishment module, and start iterative process；
Module 3, image median filter device constructs module, for removing part impulse noise, provides for next step containing part
The image module of Gaussian noise；
Module 4 solves the Riemann manifold optimization problem module under block orthogonality constraint, to update rarefaction representation dictionary；
Module 5, rarefaction smooth function simultaneously carry out automatic rarefaction representation module；
Module 6 updates classification function and constructs module；
Module 7, transfer module；If not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition according to
User requires setting；
Module 8, image reconstruction module.
Compared with prior art, the present invention have it is following the utility model has the advantages that
1, it is based on Riemann manifold optimum theory and method, proposes that mixing is gone to rush based on the high spectrum image that Riemann manifold optimizes
Swash Noise Method, complete the preprocessing tasks of high spectrum image, lays the foundation for subsequent classification hyperspectral imagery, identification.
2, the technical costs proposed by the present invention for going mixing impulse noise method that can reduce existing Hyperspectral imager,
It improves efficiency, there is high application value.
Detailed description of the invention
Upon reading the detailed description of non-limiting embodiments with reference to the following drawings, other feature of the invention,
Objects and advantages will become more apparent upon:
Fig. 1 is the distinctive structural sparse representation method and model schematic constructed required for the present invention.
Fig. 2 is the correlated results that the present invention carries out 5 iteration under standard testing image, and compares and analyzes signal
Figure.
Fig. 3 is the results of performance analysis that the present invention carries out 5 iteration under standard testing image, that is, PSNR, RMSE
Schematic diagram.
Specific embodiment
The present invention is described in detail combined with specific embodiments below.Following embodiment will be helpful to the technology of this field
Personnel further understand the present invention, but the invention is not limited in any way.It should be pointed out that the ordinary skill of this field
For personnel, without departing from the inventive concept of the premise, several changes and improvements can also be made.These belong to the present invention
Protection scope.
As shown in Figure 1 to Figure 3, a kind of image based on Riemann manifold optimization provided according to the present invention goes mixing impulse to make an uproar
Method for acoustic includes the following steps:
Step 1, it is based on structural sparse representation method, constructs the distinctive structure rarefaction representation with block orthogonality constraint
Model applies block orthogonality constraint to objective function, and improving model indicates ability to image detail；
Step 2, alternating minimization frame is constructed, and starts iterative process；
Step 3, image median filter is constructed, for removing part impulse noise, provides Gauss containing part for next step
The image of noise；
Step 4, the Riemann manifold optimization problem under block orthogonality constraint is solved, to update rarefaction representation dictionary；
Step 5, it constructs rarefaction smooth function and carries out automatic rarefaction representation；
Step 6, building updates classification function and is updated；
Step 7, if not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition requires to set according to user
It is fixed；
Step 8, reconstruction image.
Further, step 1 building has the distinctive structure sparse representation model of block orthogonality constraint；For structure
Change sparse representation model existing for subspace can not robust tracking outstanding problem, the present invention propose have block orthogonality constraint mirror
Other property structure sparse representation model, as shown in Figure 1.Wherein, for fixed widthImage platform is divided into data matrix
Y；Wherein, each piece of size isStructure sparse representation model are as follows:
D represents dictionary, and A represents coefficient matrix corresponding with dictionary；Distinctive structure based on block orthogonality constraint
Sparse representation model are as follows:
BgIndicate the sub- dictionary in structural sparse expression；
AiRepresent coefficient matrix corresponding with sub- dictionary；
ωkIndicate the category set in structural sparse expression；
G indicates the index value [1 ..., G] of sub- dictionary；
G indicates ωkTotal classification number；
The index value of subscript i expression classification；
The index value of subscript k expression classification；
F indicates Frobenius norm；
Bg TIndicate the transposed matrix of sub- dictionary；
s0Zero norm of representing matrix A；
IdIndicate the unit matrix of d*d；
AiIndicate coefficient matrix corresponding with sub- dictionary；
YiThe submatrix of Y is represent, and has njA data point belongs to classification ω (j)=g, and set omega represents from data point
The mapping of (1 ..., n) to (1 ..., G)；The concrete form of Ω has:
ωjJ-th of classification is indicated, wherein including multiple sub- dictionaries；
N indicates there are n sub- dictionaries in classification；
ωiI-th of classification is indicated, wherein including multiple sub- dictionaries；
It indicates arbitrary classification, but is not equal to k-th of classification；
K indicates k-th of classification, wherein including multiple sub- dictionaries.
Further, in order to solve above-mentioned equation, the present invention provides the alternating minimization frame based on Riemann manifold optimization,
The step 2 constructs alternating minimization frame, wherein the frame comprises the following steps:
Step 2.1, the dictionary updating based on Riemann manifold optimization；
Step 2.2, sparse coding；
Step 2.3, classification updates.
Further, the step 3 constructs image median filter, and structure is
Based on above-mentioned template, the selected image space for needing operation is ascending to the pixel of template to be ranked up, then uses
The intermediate value of template substitutes the value of original pixel.The impulse noise in observed image is removed using specific image median filter device,
Then the intermediate image for having Gaussian noise is generated.
Further, the step 4 solves the Riemann manifold optimization problem under block orthogonality constraint, to update sparse table
Show dictionary；The central idea of the step is by block condition of orthogonal constraints Bg TBgIt is embedded in search space Gg；Under block orthogonality constraint
The form of Riemann manifold optimization problem has:
Wherein, Gr represents Grassmann manifold；hεIt is customized rarefaction smooth function, hεForm have
Or
Wherein, ε > 0 is a smoothing parameter；The coefficient of representing matrix Y.For the rapid solving equation, the present invention
It is solved using Riemann manifold optimum theory, and constructs Riemann's conjugate gradient method for solving based on contractile mechanism.Wherein, it asks
The core of the solution equation is the vector transmission method of contractile mechanism, Riemann manifold gradient and specific structure.
Further, the step 5 constructs rarefaction smooth function and carries out automatic rarefaction representation；Solve sparse coding
The equation of variables A are as follows:
Wherein, pertinent literature thinks smooth function hεRarefaction effect compared with l1Norm will be got well.To improve the automatic dilute of algorithm
Thinization effect, the present invention use two kinds of relatively good smoothing objective functions.
Further, present invention introduces smooth regular terms, building updates the objective function of classification information, and carries out classification
It updates, improves the descriptive power of image authentication information, as shown in Figures 2 and 3；Step 6 building updates classification function simultaneously
It is updated；For class variable ωk, construct objective function
It indicates to carry out derivation to a in above formula；Wherein a is an element of matrix A；
λ is positive regularization parameter, yiThe column of data Y are represent, φ represents function that can be micro-, use classes variable ω
With analytic solutions.
Further, step 8 reconstruction image, be based on standard testing image barbara, 5 times of entire step 1-6
Iterative process is as shown in Figure 2；Wherein, the process of mixed Gaussian and impulse noise is removed, as shown in Figure 3.
A kind of image based on Riemann manifold optimization provided according to the present invention goes mixing impulse noise system, including as follows
Module:
Module 1, the distinctive structure sparse representation model with block orthogonality constraint construct module；
Module 2, alternating minimization framework establishment module, and start iterative process；
Module 3, image median filter device constructs module, for removing part impulse noise, provides for next step containing part
The image module of Gaussian noise；
Module 4 solves the Riemann manifold optimization problem module under block orthogonality constraint, to update rarefaction representation dictionary；
Module 5, rarefaction smooth function simultaneously carry out automatic rarefaction representation module；
Module 6 updates classification function and constructs module；
Module 7, transfer module；If not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition according to
User requires setting；
Module 8, image reconstruction module.
One skilled in the art will appreciate that in addition to realizing system provided by the invention in a manner of pure computer readable program code
It, completely can be by the way that method and step be carried out programming in logic come so that the present invention provides and its other than each device, module, unit
System and its each device, module, unit with logic gate, switch, specific integrated circuit, programmable logic controller (PLC) and embedding
Enter the form of the controller that declines etc. to realize identical function.So system provided by the invention and its every device, module, list
Member is considered a kind of hardware component, and to include in it can also for realizing the device of various functions, module, unit
To be considered as the structure in hardware component；It can also will be considered as realizing the device of various functions, module, unit either real
The software module of existing method can be the structure in hardware component again.
In the description of the present application, it is to be understood that term " on ", "front", "rear", "left", "right", " is erected at "lower"
Directly ", the orientation or positional relationship of the instructions such as "horizontal", "top", "bottom", "inner", "outside" is orientation based on the figure or position
Relationship is set, description the application is merely for convenience of and simplifies description, rather than the device or element of indication or suggestion meaning are necessary
It with specific orientation, is constructed and operated in a specific orientation, therefore should not be understood as the limitation to the application.
Specific embodiments of the present invention are described above.It is to be appreciated that the invention is not limited to above-mentioned
Particular implementation, those skilled in the art can make a variety of changes or modify within the scope of the claims, this not shadow
Ring substantive content of the invention.In the absence of conflict, the feature in embodiments herein and embodiment can any phase
Mutually combination.
Claims (9)
1. a kind of image based on Riemann manifold optimization goes mixing impulse noise method, which comprises the steps of:
Step 1, it is based on structural sparse representation method, constructs the distinctive structure rarefaction representation mould with block orthogonality constraint
Type applies block orthogonality constraint to objective function, and improving model indicates ability to image detail；
Step 2, alternating minimization frame is constructed, and starts iterative process；
Step 3, image median filter is constructed, for removing part impulse noise, provides Gaussian noise containing part for next step
Image；
Step 4, the Riemann manifold optimization problem under block orthogonality constraint is solved, to update rarefaction representation dictionary；
Step 5, it constructs rarefaction smooth function and carries out automatic rarefaction representation；
Step 6, building updates classification function and is updated；
Step 7, if not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition requires to set according to user；
Step 8, reconstruction image.
2. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
Step 1 building has the distinctive structure sparse representation model of block orthogonality constraint；Wherein, for fixed widthIt will
Image platform is divided into data matrix Y；Wherein, each piece of size isStructure sparse representation model are as follows:
D represents dictionary, and A represents coefficient matrix corresponding with dictionary；Distinctive structure based on block orthogonality constraint is sparse
Indicate model are as follows:
BgIndicate the sub- dictionary in structural sparse expression；
AiRepresent coefficient matrix corresponding with sub- dictionary；
ωkIndicate the category set in structural sparse expression；
G indicates the index value [1 ..., G] of sub- dictionary；
G indicates ωkTotal classification number；
The index value of subscript i expression classification；
The index value of subscript k expression classification；
F indicates Frobenius norm；
Bg TIndicate the transposed matrix of sub- dictionary；
s0Zero norm of representing matrix A；
IdIndicate the unit matrix of d*d；
AiIndicate coefficient matrix corresponding with sub- dictionary；
YiThe submatrix of Y is represent, and has njA data point belongs to classification ω (j)=g, and set omega represents from data point
The mapping of (1 ..., n) to (1 ..., G)；The concrete form of Ω has:
ωjJ-th of classification is indicated, wherein including multiple sub- dictionaries；
N indicates there are n sub- dictionaries in classification；
ωiI-th of classification is indicated, wherein including multiple sub- dictionaries；
It indicates arbitrary classification, but is not equal to k-th of classification；
K indicates k-th of classification, wherein including multiple sub- dictionaries.
3. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
The step 2 constructs alternating minimization frame, wherein the frame comprises the following steps:
Step 2.1, the dictionary updating based on Riemann manifold optimization；
Step 2.2, sparse coding；
Step 2.3, classification updates.
4. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
The step 3 constructs image median filter, and structure is
Based on above-mentioned template, the selected image space for needing operation is ascending to the pixel of template to be ranked up, then uses template
Intermediate value substitute the value of original pixel.
5. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
The step 4 solves the Riemann manifold optimization problem under block orthogonality constraint, to update rarefaction representation dictionary；Block is orthogonal about
Beam condition Bg TBgIt is embedded in search space Gg；The form of Riemann manifold optimization problem under block orthogonality constraint has:
Wherein, Gr represents Grassmann manifold；hεIt is customized rarefaction smooth function, hεForm have
Or
Wherein, ε > 0 is a smoothing parameter；The coefficient of representing matrix Y.
6. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
The step 5 constructs rarefaction smooth function and carries out automatic rarefaction representation；Solve the equation of sparse coding variables A are as follows:
7. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
Step 6 building updates classification function and is updated；For class variable ωk, construct objective function
It indicates to carry out derivation to a in above formula；Wherein a is an element of matrix A；
λ is positive regularization parameter, yiThe column of data Y are represent, φ represents function that can be micro-, and use classes variable ω has
Analytic solutions.
8. the image according to claim 1 based on Riemann manifold optimization goes mixing impulse noise method, which is characterized in that
Step 8 reconstruction image is carried out based on standard testing image barbara.
9. a kind of image based on Riemann manifold optimization goes mixing impulse noise system, which is characterized in that including following module:
Module 1, the distinctive structure sparse representation model with block orthogonality constraint construct module；
Module 2, alternating minimization framework establishment module, and start iterative process；
Module 3, image median filter device constructs module, for removing part impulse noise, provides Gauss containing part for next step
The image module of noise；
Module 4 solves the Riemann manifold optimization problem module under block orthogonality constraint, to update rarefaction representation dictionary；
Module 5, rarefaction smooth function simultaneously carry out automatic rarefaction representation module；
Module 6 updates classification function and constructs module；
Module 7, transfer module；If not meeting iteration stopping condition, step 3 is gone to；Wherein iteration stopping condition is according to user
It is required that setting；
Module 8, image reconstruction module.
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