CN105260995B - A kind of image repair and denoising method and system - Google Patents
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Abstract
The invention discloses a kind of image repairs and denoising method and system, for given original training image, this method comprises: passing through the thought for introducing joint low-rank and sparse matrix decomposition, utilize convex optimisation technique, given training sample image data matrix is decomposed into joint low-rank and sparse principal component feature coding matrix and sparse Error Matrix, according to the low-rank and sparse characteristic of the training image sample data, determine the joint low-rank and sparse principal component feature and Error Matrix of the training image sample data, realize that the image for including mistake to the original possibility carries out reparation and denoising, it obtains by repairing and the image after denoising.Image repair provided by the present invention and denoising method and system, in the robust low-rank and sparse characteristic for carrying out having fully considered data while feature describes to image data, with overcome the deficiencies in the prior art, the performance of image repair and denoising and the robustness of model are improved.
Description
Technical Field
The invention relates to the technical field of computer vision and image processing, in particular to an image restoration and denoising method and system.
Background
In a large number of practical applications, real-world data can be represented by high-dimensional attributes or features, such as visual images, but the high-dimensional data often contains much redundant information or noise. Therefore, in recent years, there has been a great deal of attention paid to efficient image restoration and efficient description of images by feature learning or low-rank, sparse coding techniques.
The feature extraction aims to obtain compact features with strong descriptive property by a mapping or transformation method, and realize transformation from high dimension to low dimension. Pca (principal Component analysis) is one of the most representative unsupervised feature learning models. The specific operation is as follows: for a given data matrix(where N is the sample dimension and N is the number of samples), PCA optimizes to a potential projection matrix by maximizing the covariance structure of the data
Where I is an identity matrix, d represents the dimension to which | · |. the calculation of the calculation is performed2Is a2The norm of the number of the first-order-of-arrival,is the average of all samples. PCA can effectively reveal linear relationships between data, but PCA models based on the L2 norm have proven to be very sensitive to noisy data, outliers, or pixel corruptions, and thus in practice it may not be possible to accurately reveal the subspace structure of the data.
In order to make up for the deficiency of PCA and enhance the robustness of the model to noise data and error data, some robust Principal Component feature extraction models have been proposed in recent years, wherein rpca (robust Principal Component analysis) is a novel and effective method. The RPCA technique performs data repair and feature extraction by the following kernel norm minimization problem:
<L,E>＝arg minL,E||L||*+γ||E||1,s.t.X＝L+E
where γ > 0 is a trade-off parameter, E ═ X-L represents sparse error data, and the optimal solution L to the above problem*The "lowest rank description" of the original data also corresponds to the best principal component features of the original data.
When the data error degree is low, the RPCA can effectively recover the original data. However, the RPCA technique only considers the low-rank robust characteristic of the data and does not consider the sparse robust characteristic in the data description process, so that a certain negative influence may be caused on the image restoration result when the principal component feature extraction is performed.
Disclosure of Invention
The invention aims to provide a method and a system for image restoration and denoising, and aims to solve the problem that the robust low rank and the sparse characteristic of data are not considered simultaneously in the prior art.
In order to solve the above technical problem, the present invention provides an image repairing and denoising method, comprising:
preprocessing the training image sample data and initializing and setting model parameters;
decomposing a given training image sample data matrix into a combined low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing the idea of combining low-rank and sparse matrix decomposition and utilizing a convex optimization technology;
and repairing and denoising the original image to obtain a repaired and denoised image.
Optionally, decomposing a given training image sample data matrix into a joint low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing a concept of joint low-rank and sparse matrix decomposition and using a convex optimization technique includes:
for vector setsDecomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
wherein, λ > 0 is a trade-off parameter, α ∈ [0,1 ]]For trade-off parameters between low-rank and sparse coding terms, | · | | luminance*Is the kernel norm of the matrix, | ·| luminance1Is 11The norm of the number of the first-order-of-arrival,optimal solution L obtained by optimizationS*Coding a matrix, x, for joint low rank and sparse principal component features of the training image sample dataiFor one sample in the training image sample data, N is the dimension of the image sample, and N is the total number of image samples.
Optionally, decomposing a given training image sample data matrix into a joint low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing a concept of joint low-rank and sparse matrix decomposition and using a convex optimization technique includes:
decomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
defining an augmented Lagrangian function:
wherein, Y1,Y2,Y3Is a Lagrange multiplier, mu is a weight parameter, and the Lagrange function is augmented by the weight parameterTo alternately update the variables in turn:
and (3) sequentially updating variable values to complete solution by iteratively optimizing the convex sub problem:
j is solved by a singular value contraction operation, and F and E are solved by a scalar contraction operation.
Optionally, after obtaining the repaired and denoised image, the method further includes:
and evaluating the repairing effect of the image by performing visual observation and index quantification on the repaired and denoised image.
The invention also provides an image restoration and denoising system, which comprises:
the preprocessing module is used for preprocessing the training image sample data and carrying out initialization setting on model parameters;
the decomposition module is used for decomposing a given training image sample data matrix into a combined low-rank and sparse principal component characteristic coding matrix and a sparse error matrix by introducing the idea of combined low-rank and sparse matrix decomposition and utilizing a convex optimization technology;
and the restoration module is used for restoring and denoising the original image to obtain the restored and denoised image.
Optionally, the decomposition module is specifically configured to:
for vector setsDecomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
wherein, λ > 0 is a trade-off parameter, α ∈ [0,1 ]]For low rank and between sparse coding termsThe balance parameter, | · | | non-calculation*Is the kernel norm of the matrix, | ·| luminance1Is 11The norm of the number of the first-order-of-arrival,optimal solution L obtained by optimizationS*Coding a matrix, x, for joint low rank and sparse principal component features of the training image sample dataiFor one sample in the training image sample data, N is the dimension of the image sample, and N is the total number of image samples.
Optionally, the decomposition module is specifically configured to:
decomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
defining an augmented Lagrangian function:
wherein, Y1,Y2,Y3Is a Lagrange multiplier, mu is a weight parameter, and the Lagrange function is augmented by the weight parameterTo alternately update the variables in turn:
and (3) sequentially updating variable values to complete solution by iteratively optimizing the convex sub problem:
j is solved by a singular value contraction operation, and F and E are solved by a scalar contraction operation.
Optionally, the method further comprises:
and the evaluation module is used for evaluating the restoration effect of the image by performing visual observation and index quantification on the restored and denoised image after the restored and denoised image is obtained.
The image restoration and denoising method and the system thereof provided by the invention carry out preprocessing operation on the training image sample data and carry out initialization setting on the model parameters; decomposing a given training image sample data matrix into a combined low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing the idea of combining low-rank and sparse matrix decomposition and utilizing a convex optimization technology; and repairing and denoising the original image to obtain a repaired and denoised image. . Therefore, the image repairing and denoising method and the image repairing and denoising system provided by the invention fully consider the robust low rank and the sparse characteristic of the data while performing feature description on the image data, so as to overcome the defects of the prior art and improve the performance of image repairing and denoising and the robustness of the model.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flowchart illustrating an embodiment of an image repairing and denoising method according to the present invention;
FIG. 2 is a flowchart illustrating an image restoration and denoising method according to another embodiment of the present invention;
FIG. 3 is a schematic diagram showing a comparison of the results of a description of handwritten image data of the MNIST dataset;
FIG. 4 is a schematic diagram showing the comparison of the results of the descriptions of the facial image data in the JAFFE data set, the AR data set, the Yale data set, and the Yale-B data set;
FIG. 5 is a diagram illustrating a result of a quantitative evaluation of image restoration and denoising effects provided by the present invention;
FIGS. 6(a) -6(f) are graphs showing results for the original image, 10% pixel failure, 30% pixel failure, 50% pixel failure, 70% pixel failure, and 90% pixel failure levels, respectively;
fig. 7 is a block diagram of a structure of an image repairing and denoising system according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the disclosure, the invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A flowchart of a specific embodiment of the image restoration and denoising method provided by the present invention is shown in fig. 1, and the method includes:
step S101: preprocessing the training image sample data and initializing and setting model parameters;
because the original image is limited by various conditions and random interference, the original image cannot be directly used in a visual system, and therefore in this step, the original image can be used as the training image sample data after image preprocessing operation is performed on the original image, and initialization setting is performed on each parameter in the model.
Step S102: decomposing a given training image sample data matrix into a combined low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing the idea of combining low-rank and sparse matrix decomposition and utilizing a convex optimization technology;
step S103: and repairing and denoising the original image to obtain a repaired and denoised image.
The image restoration and denoising method provided by the invention carries out preprocessing operation on training image sample data and carries out initialization setting on model parameters; decomposing a given training image sample data matrix into a combined low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing the idea of combining low-rank and sparse matrix decomposition and utilizing a convex optimization technology; and repairing and denoising the original image to obtain a repaired and denoised image. . Therefore, the image restoration and denoising method provided by the invention fully considers the low robustness rank and the sparse characteristic of the data while performing feature description on the image data, so as to overcome the defects of the prior art and improve the performance of image restoration and denoising and the robustness of the model.
In another specific embodiment of the image restoration and denoising method provided by the present invention, a specific process for determining the joint low-rank and sparse principal component characteristics and the error matrix of the training image sample data is described in detail.
For any given set of vectors that may contain erroneous data:wherein x isiRepresents one sample, i.e. a vectorized description of the original image, N is the dimension of the image sample, and N is the total number of image samples.
The present embodiment decomposes a given data matrix X into a joint low rank and sparse principal component feature L by optimizing the minimization problemSAnd a sparse error term E:
where the trade-off parameter λ > 0 depends on the noise level of the data set, α ∈ [0,1 ∈]A trade-off parameter between low rank and sparse coding terms. I | · | purple wind*Representing the nuclear norm of a matrix, i.e. the sum of singular values in this matrix, | · |. survival1Is 11Norm, defined as follows:
wherein A is a matrix.
By optimizing the above problem, the optimal solution L is obtainedS*The feature called the joint minimum rank and sparsest principal component of the original data also corresponds to the optimal low rank and sparse recovery of the original data.
The above problems can be specifically solved by various solutions. In order to improve efficiency, the present embodiment adopts an inaccurate augmented lagrange multiplier method. The method specifically comprises the following steps:
the original problem is first transformed into an equivalent problem as follows:
if l is performed on the sparse error term E1Norm regularization, the corresponding augmented Lagrangian function can be defined as follows:
wherein, Y1,Y2,Y3For lagrange multipliers, μ is a positive weight parameter.
By solving the Lagrange's function augmented byTo update the variables alternately in turns:
since the variables are all interdependent, the above problem cannot be solved directly. In this embodiment, when a certain variable is calculated, other variables are all fixed, and the solution is completed by iteratively optimizing the following convex sub-problems and sequentially updating the variable values:
where J may be solved by a singular value contraction operation and F and E may be solved by a scalar contraction operation. The problem to be optimized in each step in the method is a convex problem, so that the problem can be effectively solved.
The specific algorithm of the direct-push combined low rank and sparse principal component feature coding algorithm adopted in the embodiment is as follows:
inputting: matrix of raw dataControl parameter α, λ.
And (3) outputting: joint low rank and sparse principal component featuresSparse noise or error matrix (E)*←Ek+1)。
Initialization:
do when while has not converged
The other variables are fixed to update the low rank matrix J:
fix other variables and update sparse matrix F:
fixing other variables and updating principal component characteristics LS：
Fixing other variables and updating the sparse error matrix E:
to fix otherVariable, update lagrange multiplier Y1、Y2、Y3：
Updating the parameter mu:
μk+1＝min(ημk,maxμ)；
checking whether convergence occurs:
if it isStopping the operation;
otherwise k is k +1
end while.
Fig. 2 shows a flowchart of another specific implementation of the image repairing and denoising method provided by the present invention, and on the basis of any of the above embodiments, after obtaining the repaired and denoised image, the present embodiment may further include:
step S104: and evaluating the repairing effect of the image by performing visual observation and index quantification on the repaired and denoised image.
Specifically, after the image is repaired and denoised, the repairing effect can be visually displayed through an image visualization technology, and the repairing effect can be visually compared with the results of other related methods.
In addition, a quantitative evaluation index based on reconstruction accuracy can be adopted, and the reconstruction accuracy is defined as follows:
wherein,indicating the result of the restoration for the original given data,indicating the effect of image inpainting with different degrees of image pixel damage. From the above definition, the result of the repair in the presence of noiseAnd the repair result of the original dataWhen relatively close, reconstruction accuracyWill be a larger number; on the contrary, the method can be used for carrying out the following steps,to a lesser value. That is to say that the position of the first electrode,the larger the size, the better the effect of image pixel error correction or image denoising.
According to the image restoration and denoising method provided by the invention, the ideas of low-rank matrix restoration and sparse matrix description which are popular at present are introduced, and the low rank and sparse characteristics of the robustness of data are considered when the robust principal component characteristics are extracted, so that the robust principal component characteristics with stronger descriptive performance can be extracted, the image restoration and denoising performance and the model robustness can be further improved, and a better image restoration effect can be obtained.
The method can be used for testing the handwriting repairing effect, and particularly can be carried out in a database of MNIST handwriting numbers. The MNIST database has 60000 training samples and 10000 testing samples, and 24 digital '0' samples are extracted from the training samples and tested. The face description, restoration and denoising effect test is carried out in the following four face databases: a japanese female facial expression database (JAFFE), an AR face database, an extended Yale-B face database, and a Yale face database. The JAFFE face database holds 213 emoticons of 7 expressions made by 10 japanese women. Images in the Yale face database have differences in light, facial expressions, whether glasses are worn or not and the like. The extended Yale-B face database contains about 64 pictures of each person under different lighting and different expressions. The AR face database has more variations, such as different lighting, different expressions, and whether it is obscured by a scarf or sunglasses. This embodiment selects 24 face images from each database to form a data matrix of 128 × 192 size.
Fig. 3 and fig. 4 show effect diagrams of the image restoration and denoising method provided by the present invention. Wherein, fig. 3 is a result display for describing the handwriting image data of the MNIST dataset, which respectively shows the comparison result of the present invention method with the RPCA and SR, and the first row picture is the handwriting restoration effect of the RPCA method; the second row of pictures is the handwriting restoration effect of the SR, the third row is the handwriting restoration effect of the invention, and the pictures are the original picture, the restored picture and the error in sequence from left to right. Fig. 4 is a result display of description of face image data in the JAFFE data set, the AR data set, the Yale data set, and the Yale-B data set, where the first row to the fourth row respectively represent the face image restoration results of the JAFFE, the AR, the Yale-B, and the Yale data set, and the pictures sequentially represent the original picture, the restored picture, and the error from left to right. The result shows that the method can be effectively used for image description and automatic error detection by simultaneously considering the low-rank and sparse characteristics of the data, and obtains better image restoration and denoising effects.
Fig. 5 and fig. 6(a) -6(f) are schematic diagrams illustrating quantitative evaluation results of image restoration and denoising effects provided by the present invention, where fig. 5 is a quantitative evaluation result, fig. 6(a) -6(f) are exemplary illustrations of an original image and several different pixel destruction degrees, where 6(a) -6(f) respectively correspond to the original image, 10% pixel destruction, 30% pixel destruction, 50% pixel destruction, 70% pixel destruction, and 90% pixel destruction. In this embodiment, several images in the AR face data set are used for experiments, the method of the present invention and other related methods are further used for repairing and denoising by destroying pixels of the face image to different degrees, and the effect of image denoising by the method of the present invention and other related methods is measured quantitatively by reconstruction accuracy, wherein the destroyed pixel gray value is replaced by the inverse pixel gray value, that is, any destroyed pixel gray value g is replaced by 255-g. It can be seen that the reconstruction accuracy of each method decreases as the pixel corruption increases. But the method of the invention shows the property of being more robust to the damaged pixel, and obtains better repairing and denoising effects.
The method is described in detail in the embodiment disclosed by the invention, and the method can be realized by adopting systems in various forms, so that the invention also discloses a system. In the following, the image repairing and denoising system provided by the embodiment of the present invention is introduced, and the image repairing and denoising system described below and the image repairing and denoising method described above may be referred to correspondingly. Fig. 7 is a block diagram of a structure of an image repairing and denoising system according to an embodiment of the present invention, where, referring to fig. 7, the image repairing and denoising system may include:
the preprocessing module 100 is configured to perform preprocessing operation on the training image sample data and perform initialization setting on model parameters;
the decomposition module 200 is configured to decompose a given training image sample data matrix into a joint low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing a concept of joint low-rank and sparse matrix decomposition and using a convex optimization technology;
the restoration module 300 is configured to restore and denoise an original image to obtain a restored and denoised image.
As a specific implementation manner, the image repairing and denoising system provided by the present invention may specifically use the decomposition module 200 to:
for vector setsDecomposing a data matrix X into joint low-rank and sparse principal component features LSAnd sparse error matrix E:
wherein, λ > 0 is a trade-off parameter, α ∈ [0,1 ]]For trade-off parameters between low-rank and sparse coding terms, | · | | luminance*Represents the kernel norm, | ·| non-woven phosphor of the matrix1Is 11The norm of the number of the first-order-of-arrival,optimal solution L obtained by optimizationS*For joint low rank and sparse principal component features, x, of the training image sample dataiFor one sample in the training image sample data, N is the dimension of the image sample, and N is the total number of image samples.
As a specific implementation manner, in the image repairing and denoising system provided by the present invention, the decomposition module 200 is specifically configured to:
decomposing a data matrix X into joint low-rank and sparse principal component features LSAnd sparse error matrix E:
defining an augmented Lagrangian function:
wherein, Y1,Y2,Y3Is a Lagrange multiplier, mu is a weight parameter, and the Lagrange function is augmented by the weight parameterTo alternately update the variables in turn:
and (3) sequentially updating variable values to complete solution by iteratively optimizing the convex sub problem:
j is solved by a singular value contraction operation, and F and E are solved by a scalar contraction operation.
As a specific implementation manner, the image repairing and denoising system provided by the present invention may further include:
and the evaluation module is used for evaluating the restoration effect of the image by performing visual observation and index quantification on the restored and denoised image after the restored and denoised image is obtained.
The image restoration and denoising system provided by the invention carries out preprocessing operation on training image sample data and carries out initialization setting on model parameters; decomposing a given training image sample data matrix into a combined low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing the idea of combining low-rank and sparse matrix decomposition and utilizing a convex optimization technology; and repairing and denoising the original image to obtain a repaired and denoised image. . Therefore, the image repairing and denoising system provided by the invention fully considers the low robustness rank and the sparse characteristic of the data while performing feature description on the image data, so as to overcome the defects of the prior art and improve the performance of image repairing and denoising and the robustness of the model.
The embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same or similar parts among the embodiments are referred to each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. An image restoration and denoising method is characterized by comprising the following steps:
preprocessing the training image sample data and initializing and setting model parameters;
decomposing a given training image sample data matrix into a combined low-rank and sparse principal component feature coding matrix and a sparse error matrix by introducing the idea of combining low-rank and sparse matrix decomposition and utilizing a convex optimization technology;
repairing and denoising the original image to obtain a repaired and denoised image;
the method for decomposing the given training image sample data matrix into the joint low-rank and sparse principal component feature coding matrix and the sparse error matrix by introducing the idea of joint low-rank and sparse matrix decomposition and utilizing the convex optimization technology comprises the following steps of:
for vector setsDecomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
wherein, λ > 0 is a trade-off parameter, α ∈ [0,1 ]]For trade-off parameters between low-rank and sparse coding terms, | · | | luminance*Is the kernel norm of the matrix, | ·| luminance1Is 11The norm of the number of the first-order-of-arrival,σi(A) singular values in the matrix A; optimal solution L obtained by optimizationS*Coding a matrix, x, for joint low rank and sparse principal component features of the training image sample dataiFor one sample in the training image sample data, N is the dimension of the image sample, and N is the total number of the image samples;
the method for decomposing the given training image sample data matrix into the joint low-rank and sparse principal component feature coding matrix and the sparse error matrix by introducing the idea of joint low-rank and sparse matrix decomposition and utilizing the convex optimization technology comprises the following steps of:
decomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
defining an augmented Lagrangian function:
wherein, Y1,Y2,Y3Is a Lagrange multiplier, mu is a weight parameter, and the Lagrange function is augmented by the weight parameterTo alternately update the variables in turn:
and (3) sequentially updating variable values to complete solution by iteratively optimizing the convex sub problem:
j is solved by a singular value contraction operation, and F and E are solved by a scalar contraction operation.
2. The method for restoring and denoising an image according to claim 1, wherein after obtaining the restored and denoised image, the method further comprises:
and evaluating the repairing effect of the image by performing visual observation and index quantification on the repaired and denoised image.
3. An image inpainting and denoising system, comprising:
the preprocessing module is used for preprocessing the training image sample data and carrying out initialization setting on model parameters;
the decomposition module is used for decomposing a given training image sample data matrix into a combined low-rank and sparse principal component characteristic coding matrix and a sparse error matrix by introducing the idea of combined low-rank and sparse matrix decomposition and utilizing a convex optimization technology;
the restoration module is used for restoring and denoising the original image to obtain a restored and denoised image;
the decomposition module is specifically configured to:
for vector setsDecomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
wherein, λ > 0 is a trade-off parameter, α ∈ [0,1 ]]For trade-off parameters between low-rank and sparse coding terms, | · | | luminance*Is the kernel norm of the matrix, | ·| luminance1Is 11The norm of the number of the first-order-of-arrival,σi(A) singular values in the matrix A; optimal solution L obtained by optimizationS*Coding a matrix, x, for joint low rank and sparse principal component features of the training image sample dataiFor one sample in the training image sample data, N is the dimension of the image sample, and N is the total number of the image samples;
the decomposition module is specifically configured to:
decomposing a data matrix X into a joint low-rank and sparse principal component feature coding matrix LSAnd sparse error matrix E:
defining an augmented Lagrangian function:
wherein, Y1,Y2,Y3Is a Lagrange multiplier, mu is a weight parameter, and the Lagrange function is augmented by the weight parameterTo alternately update the variables in turn:
and (3) sequentially updating variable values to complete solution by iteratively optimizing the convex sub problem:
j is solved by a singular value contraction operation, and F and E are solved by a scalar contraction operation.
4. The image inpainting and denoising system of claim 3, further comprising:
and the evaluation module is used for evaluating the restoration effect of the image by performing visual observation and index quantification on the restored and denoised image after the restored and denoised image is obtained.
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