CN111104868A - Cross-quality face recognition method based on convolutional neural network characteristics - Google Patents

Cross-quality face recognition method based on convolutional neural network characteristics Download PDF

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CN111104868A
CN111104868A CN201911164077.1A CN201911164077A CN111104868A CN 111104868 A CN111104868 A CN 111104868A CN 201911164077 A CN201911164077 A CN 201911164077A CN 111104868 A CN111104868 A CN 111104868A
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汪焰南
高广谓
吴松松
邓松
张皖
岳东
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides a cross-quality face recognition method based on convolutional neural network characteristics, which comprises the steps of firstly obtaining image blocks of each characteristic point of a high-quality training sample image, a low-quality measurement sample image and a high-low quality training dictionary sample image; secondly, designing a deep convolutional neural network, and obtaining a feature vector for each feature point image block through learning of the neural network; performing linear representation on the feature vector of the test image block and the feature vector of the training image block again; then, similarity measurement is carried out on the feature representation of the low-quality measurement image block and the feature representation of the high-resolution training image block, and the category of each test image block is output; and finally, for an image block set of which the face image is divided into S key points of the face, voting the classification result of the image block at each key point position, distributing the image to the class with the largest number of votes, and outputting the class of the final low-quality test image.

Description

Cross-quality face recognition method based on convolutional neural network characteristics
Technical Field
The invention relates to an image recognition method, in particular to a cross-quality face recognition method based on convolutional neural network characteristics, and belongs to the technical field of pattern recognition and biological characteristic recognition.
Background
The face recognition technology is a popular research topic based on computer, image processing and pattern recognition. In the past, with the wide application of face recognition in various social fields, such as criminal case identification, public security system, monitoring and the like, face recognition technology has gained more and more attention.
In the process of face recognition, the problem of low recognition accuracy caused by inconsistent face image quality exists, and the recognition work is sometimes difficult to complete. The existing face detection method comprises the following steps:
[1]X.Cao,Y.Wei,F.Wen,J.Sun,“Face alignment by explicit shaperegression”Int.J.Computer.Vis.107(2)(2014),pp.177–190.
the existing optimization solving method comprises the following steps:
[2]E.Hale,W.Yin,Y.Zhang,“Fixed-point contiuation for l1-minimization:methodology and convergence”,SIAM J.Optim.19(3)(2008)1107–1130.
the existing method has the defects that the identification between images with different qualities cannot be processed in time, and the identification efficiency is greatly reduced due to factors such as illumination, shielding and the like.
Disclosure of Invention
The invention aims to solve the technical problem of providing a cross-quality face recognition method based on convolutional neural network characteristics to overcome the defects of the prior art.
The invention provides a cross-quality face recognition method based on convolutional neural network characteristics, which comprises the following steps:
s1, sampling the low-quality face image to the resolution as high-quality image, and obtaining image blocks of each feature point of the high-quality training sample image, the low-quality measurement sample image and the high-low quality training dictionary sample image by the face feature point detection technology [1 ]; go to step S2;
s2, designing a deep convolution neural network, and obtaining a feature vector for each feature point image block through learning of the neural network; go to step S3;
s3, performing linear representation on the feature vector of the low-quality measurement trial image block and the feature vector of the high-quality training image block by using a weighted sparse coding regular regression representation method; go to step S4;
s4, carrying out similarity measurement on the linear representation of the feature vector of the low-quality measurement attempt image block and the linear representation of the feature vector of the high-quality training image block, and outputting the category of each low-quality measurement attempt image block; go to step S5;
and S5, for a face image which is divided into image block sets of S face key points, voting the image block classification result of each key point position, distributing the image to the class with the largest number of votes, and outputting the class of the final low-quality test image.
By the method, the image is partitioned by the human face characteristic point detection technology, and the image blocks of the key parts of the human face are extracted, so that the influence of unnecessary part information on the recognition result is avoided, and the calculation complexity is reduced. The vector is obtained by learning based on the feature expression convolutional neural network, the direct extraction of pixel point features is replaced, and then linear feature expression is carried out, so that the low-quality face images can be identified.
As a further technical solution of the present invention, the specific method of step S2 is as follows:
designing a deep convolutional neural network, wherein the neural network consists of 10 convolutional layers, 10 normalization layers and 9 activation layers;
for each feature point image block, the block size is 32 × 32, and learning by the convolutional neural network results in a feature vector of 1 × 128.
The specific method of step S3 is as follows:
s301, for a low-quality measurement attempt image block feature vector y, the low-quality measurement attempt image block is linearly represented by using the image block feature vector of the corresponding position on the low-quality training dictionary sample image as follows,
y＝x1A1+x2A2+...xiAi+...+xNAN+E
wherein A isiRepresenting the image block feature vector of the corresponding position on the ith low-quality training dictionary sample image, wherein i is {1,2iRepresenting a coefficient corresponding to the ith element in the coefficient vector x, and E represents a residual error item; go to step S302;
s302, linear representation of the image block set of the high-quality training image block at the corresponding position on the high-quality training dictionary sample image is obtained by using a weighted sparse coding regular regression representation method.
In step S301, the method of solving the low-quality-measurement-attempt-block-representative vector is as follows:
first, define
Figure BDA0002286940980000031
For each low-quality measurement image block, a weighted sparse coding canonical regression representation method is used to obtain a linear representation of the low-quality training sample image block, a regression model of the linear representation is expressed as,
Figure BDA0002286940980000032
wherein
Figure BDA0002286940980000033
Denotes the L2 norm, λ is positiveQuantizing the parameters, wherein W is a given local similarity matrix, and x represents a coefficient vector of the low-quality measurement attempt image block;
secondly, for the convenience of solving, an auxiliary variable z is required to be introduced to express the above model as,
Figure BDA0002286940980000034
finally, by introducing two auxiliary variables P and P, the augmented lagrange function of the above equation is expressed as,
Figure BDA0002286940980000041
where μ is a penalty parameter and μ >0, P, p is the lagrange multiplier, tr (·) is the trace operation, T is the transition rank of the matrix, and F is the Frobenius norm of the matrix.
The specific optimization process of parameters in the augmented Lagrange function is as follows:
< a > optimization of z
Figure BDA0002286940980000042
zk+1Can be solved by a soft threshold method [2 ]]Obtaining, wherein k represents the iteration of the k step;
< b > optimization of x
Figure BDA0002286940980000043
Wherein H ═ vec (A)1),vec(A2),...,vec(AN)]，
Figure BDA0002286940980000044
Figure BDA0002286940980000045
k denotes the iteration of the k-th step, resulting in a solution,
xk+1＝(HTH+WTW)-1(HTek+1+WTbk+1)；
< c > select proper ε, check convergence condition
max(||y-A(xk+1)||∞,||zk+1-Wxk+1||∞)<ε
If the maximum iteration times are reached or the termination condition is met, outputting xk+1As x, otherwise, returning to step<a>。
The specific method of step S302 is as follows:
for each high quality training image block feature vector y1Performing linear representation by using image block feature vectors at corresponding positions on the high-quality training dictionary sample image,
y1＝c1G1+c2G2+...ciGi+...+cNGN+E2
wherein G isiRepresenting image block feature vectors of corresponding positions on the ith low-quality training dictionary sample image, wherein i is {1,2iRepresenting the coefficient corresponding to the ith element in the coefficient vector x, E2Representing the residual terms.
In step S302, the solving method for the representative coefficients of the high-quality training image block is as follows:
first, define
Figure BDA0002286940980000051
For each high-quality training image block feature vector, a weighted sparse coding regular regression representation method is used to obtain the linear representation of each high-quality training image block in the low-quality training sample image block, a regression model of each high-quality training image block is expressed as,
Figure BDA0002286940980000052
wherein
Figure BDA0002286940980000053
Denotes the L2 norm, λ is the regularization parameter, W1C represents the representation coefficient of the high-quality training image block;
secondly, for solving conveniently, an auxiliary variable z needs to be introduced1The above model is represented as,
Figure BDA0002286940980000054
wherein, by introducing two auxiliary variables M and M, the augmented Lagrangian function of the above formula is expressed as,
Figure BDA0002286940980000055
where μ is a penalty parameter and μ >0, M, M is the Lagrangian multiplier, tr (-) is the trace operation.
The specific optimization process of parameters in the augmented Lagrange function is as follows:
<a>z1is optimized
Figure BDA0002286940980000061
Figure BDA0002286940980000062
Can be solved by a soft threshold method [2 ]]Obtaining;
< b > c optimization
Figure BDA0002286940980000063
Wherein H ═ vec (G)1),vec(G2),...,vec(GN)]，
Figure BDA0002286940980000064
Figure BDA0002286940980000065
So as to obtain the following solution,
ck+1＝(HTH+W1 TW1)-1(HTek+1+W1 Tbk+1)；
<c>selecting an appropriate ε1Checking the convergence condition
Figure BDA0002286940980000066
Wherein | · | | is a given norm, and if the maximum iteration number is reached or the above termination condition is satisfied, c is outputk+1As c, otherwise, returning to step<a>。
The specific method of step S4 is as follows:
for a low quality training image block feature vector y, the linear representation x of the low quality training dictionary image block feature vector is obtained through step S3, and for a high quality training image block set, the linear representation c ═ c of the high quality training dictionary image block is obtained1,c2,…cL]And L represents the number of high-quality training dictionary images, the combination coefficient w can be obtained by the following formula,
Figure BDA0002286940980000067
where η is a balance parameter, then the reconstruction error e for each classi(x) It is calculated that,
Figure BDA0002286940980000071
wherein, ciLinear representation of class i low-quality metric attempt blocks on high-quality training dictionary image blocks, function deltaiRepresenting the weight associated with the i-th class, w*Representing the combining coefficient.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: the invention solves the identification difficulty caused by different image quality between images, and improves the identification rate compared with the prior art; the technical scheme solves the identification difficulty caused by factors such as shielding, illumination and the like, and effectively solves the problem by extracting and blocking the characteristic points of the face image.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection authority of the present invention is not limited to the following embodiments.
The embodiment provides a cross-quality face recognition method based on convolutional neural network characteristics, which is characterized by comprising the following steps of:
s1, the low-quality face image is up-sampled to the resolution same as that of the high-quality image, and image blocks of each feature point of the high-quality training sample image, the low-quality measurement sample image and the high-low quality training dictionary sample image are obtained through the face feature point detection technology [1 ].
The high-quality image and the low-quality image have different resolutions, and the low-quality test image and the low-quality training dictionary sample image are up-sampled to the resolution same as the high-quality image through an up-sampling technology; effective information of the recognizable parts of the human face is less, and characteristic points of low-quality measurement sample images, high-quality training sample images and high-quality training dictionary sample images are extracted by adopting a human face characteristic point detection technology, such as effective parts of eyes, nose, mouth and the like; then the effective parts are divided into blocks.
S2, designing a deep convolution neural network, and obtaining a feature vector for each feature point image block through learning of the neural network.
The specific method of step S2 is as follows:
designing a deep convolutional neural network, as shown in table 1 below, the neural network is composed of 10 convolutional layers, 10 normalization layers and 9 activation layers;
for each feature point image block, the block size is 32 × 32, and learning by the convolutional neural network results in a feature vector of 1 × 128.
TABLE 1
Figure BDA0002286940980000081
Figure BDA0002286940980000091
And S3, performing linear representation on the feature vector of the low-quality measurement trial image block and the feature vector of the high-quality training image block by using a weighted sparse coding regular regression representation method.
The specific method of step S3 is as follows:
s301, for a low-quality measurement attempt image block feature vector y, the low-quality measurement attempt image block is linearly represented by using the image block feature vector of the corresponding position on the low-quality training dictionary sample image as follows,
y＝x1A1+x2A2+...xiAi+...+xNAN+E
wherein A isiAnd representing image block feature vectors of corresponding positions on the ith low-quality training dictionary sample image, wherein i is {1, 2., N }, N represents the number of the low-quality training dictionary sample images, xi represents a coefficient corresponding to the ith element in the coefficient vector x, and E represents a residual error term.
The solution for the low quality measurement attempt block's representative vector is as follows:
first, define
Figure BDA0002286940980000092
For each low-quality measurement image block, a weighted sparse coding canonical regression representation method is used to obtain a linear representation of the low-quality training sample image block, a regression model of the linear representation is expressed as,
Figure BDA0002286940980000093
wherein
Figure BDA0002286940980000094
A representative vector representing the L2 norm, λ is the regularization parameter, W is the given local similarity matrix, x represents the low quality measurement attempt patch;
secondly, for the convenience of solving, an auxiliary variable z is required to be introduced to express the above model as,
Figure BDA0002286940980000095
finally, by introducing two auxiliary variables P and P, the augmented lagrange function of the above equation is expressed as,
Figure BDA0002286940980000101
where μ is a penalty parameter and μ >0, P, p is the lagrange multiplier, tr (·) is the trace operation, T is the transition rank of the matrix, and F is the Frobenius norm of the matrix.
The specific optimization process of the parameters in the augmented lagrangian function is as follows:
< a > optimization of z
Figure BDA0002286940980000102
zk+1Can be solved by a soft threshold method [2 ]]Obtaining, wherein k represents the iteration of the k step; (ii) a
< b > optimization of x
Figure BDA0002286940980000103
Wherein H ═ vec (A)1),vec(A2),...,vec(AN)]，
Figure BDA0002286940980000104
Figure BDA0002286940980000105
k denotes the iteration of the k-th step, resulting in a solution,
xk+1＝(HTH+WTW)-1(HTek+1+WTbk+1)；
< c > select proper ε, check convergence condition
max(||y-A(xk+1)||∞,||zk+1-Wxk+1||∞)<ε
If the maximum iteration times are reached or the termination condition is met, outputting xk+1As x, otherwise, returning to step<a>。
S302, after the expression coefficient vector of the low-quality image block feature vector is obtained, further, a weighted sparse coding regular regression expression method is used for obtaining linear expression of the image block set of the high-quality training image block at the corresponding position on the high-quality training dictionary sample image.
For each high quality training image block feature vector y1Performing linear representation by using image block feature vectors at corresponding positions on the high-quality training dictionary sample image,
y1＝c1G1+c2G2+...ciGi+...+cNGN+E2
wherein G isiRepresenting image block feature vectors of corresponding positions on the ith low-quality training dictionary sample image, wherein i is {1,2iRepresenting the coefficient corresponding to the ith element in the coefficient vector x, E2Representing the residual terms.
The solving method of the representation coefficients of the high-quality training image block is as follows:
first, define
Figure BDA0002286940980000111
For each high-quality training image block feature vector, applying weighted sparse codingThe canonical regression representation method obtains its linear representation in the low-quality training sample image patch, expresses its regression model as,
Figure BDA0002286940980000112
wherein
Figure BDA0002286940980000113
Denotes the L2 norm, λ is the regularization parameter, W1C represents the representation coefficient of the high-quality training image block;
secondly, for solving conveniently, an auxiliary variable z needs to be introduced1The above model is represented as,
Figure BDA0002286940980000114
wherein, by introducing two auxiliary variables M and M, the augmented Lagrangian function of the above formula is expressed as,
Figure BDA0002286940980000115
where μ is a penalty parameter and μ >0, M, M is the Lagrangian multiplier, tr (-) is the trace operation.
The specific optimization process of the parameters in the augmented lagrangian function is as follows:
<a>z1is optimized
Figure BDA0002286940980000121
Figure BDA0002286940980000122
Can be solved by a soft threshold method [2 ]]Obtaining;
< b > c optimization
Figure BDA0002286940980000123
Wherein H ═ vec (G)1),vec(G2),...,vec(GN)]，
Figure BDA0002286940980000124
Figure BDA0002286940980000125
So as to obtain the following solution,
ck+1＝(HTH+W1 TW1)-1(HTek+1+W1 Tbk+1)；
<c>selecting an appropriate ε1Checking the convergence condition
Figure BDA0002286940980000126
Wherein | · | | is a given norm, and if the maximum iteration number is reached or the above termination condition is satisfied, c is outputk+1As c, otherwise, returning to step<a>。
S4, similarity measures the linear representation of the feature vector of the low quality training image block and the linear representation of the feature vector of the high quality training image block, and outputs a class for each test image block.
The specific method of step S4 is as follows:
for a low quality training image block feature vector y, the linear representation x of the low quality training dictionary image block feature vector is obtained through step S3, and for a high quality training image block set, the linear representation c ═ c of the high quality training dictionary image block is obtained1,c2,…cL]And L represents the number of high-quality training dictionary images, the combination coefficient w can be obtained by the following formula,
Figure BDA0002286940980000131
where η are balance parameters, then the reconstruction error for each class is calculated as,
Figure BDA0002286940980000132
wherein, ciLinear representation of class i low-quality metric attempt blocks on high-quality training dictionary image blocks, function deltaiRepresenting the weight associated with the i-th class, w*Representing the combining coefficient.
And S5, for a face image which is divided into image block sets of S face key points, voting the image block classification result of each key point position, distributing the image to the class with the largest number of votes, and outputting the class of the final low-quality test image.
For each low-quality test image, dividing the low-quality test image into an image block set of key points of S human faces, wherein for each low-quality image block, the class with the minimum reconstruction error is a classification result, and each low-quality test image tries to generate S classification results; and then voting decision is carried out on the S same or different classification results, and the classification result which is classified into the class with the largest number of image blocks is the final classification result of the low-quality test image.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (9)

1. A cross-quality face recognition method based on convolutional neural network features is characterized by comprising the following steps:
s1, sampling the low-quality face image to the resolution as high-quality image, and obtaining image blocks of each feature point of the high-quality training sample image, the low-quality measurement sample image and the high-low-quality training dictionary sample image by the face feature point detection technology; go to step S2;
s2, designing a deep convolution neural network, and obtaining a feature vector for each feature point image block through learning of the neural network; go to step S3;
s3, performing linear representation on the feature vector of the low-quality measurement trial image block and the feature vector of the high-quality training image block by using a weighted sparse coding regular regression representation method; go to step S4;
s4, carrying out similarity measurement on the linear representation of the feature vector of the low-quality measurement attempt image block and the linear representation of the feature vector of the high-quality training image block, and outputting the category of each low-quality measurement attempt image block; go to step S5;
and S5, for a face image which is divided into image block sets of S face key points, voting the image block classification result of each key point position, distributing the image to the class with the largest number of votes, and outputting the class of the final low-quality test image.
2. The cross-quality face recognition method based on the convolutional neural network feature of claim 1, wherein the specific method of step S2 is as follows:
designing a deep convolutional neural network, wherein the neural network consists of 10 convolutional layers, 10 normalization layers and 9 activation layers;
for each feature point image block, the block size is 32 × 32, and learning by the convolutional neural network results in a feature vector of 1 × 128.
3. The cross-quality face recognition method based on the convolutional neural network feature as claimed in claim 2, wherein the specific method of step S3 is as follows:
s301, for a low-quality measurement attempt image block feature vector y, the low-quality measurement attempt image block is linearly represented by using the image block feature vector of the corresponding position on the low-quality training dictionary sample image as follows,
y＝x1A1+x2A2+...xiAi+...+xNAN+E
wherein A isiRepresenting the image block feature vector of the corresponding position on the ith low-quality training dictionary sample image, wherein i is {1,2iRepresenting a coefficient corresponding to the ith element in the coefficient vector x, and E represents a residual error item; go to step S302;
s302, linear representation of the image block set of the high-quality training image block at the corresponding position on the high-quality training dictionary sample image is obtained by using a weighted sparse coding regular regression representation method.
4. The cross-quality face recognition method based on convolutional neural network features as claimed in claim 3, wherein in step S301, the method for solving the low-quality vector representation of the image block is as follows:
first, define
Figure FDA0002286940970000021
For each low-quality measurement image block, a weighted sparse coding canonical regression representation method is used to obtain a linear representation of the low-quality training sample image block, a regression model of the linear representation is expressed as,
Figure FDA0002286940970000022
wherein
Figure FDA0002286940970000023
Represents the L2 norm, λ is the regularization parameter, W is the given local similarity matrix, x represents the coefficient vector of the low quality measurement attempt patch;
secondly, for the convenience of solving, an auxiliary variable z is required to be introduced to express the above model as,
Figure FDA0002286940970000024
s.t.z＝Wx；
finally, by introducing two auxiliary variables P and P, the augmented lagrange function of the above equation is expressed as,
Figure FDA0002286940970000031
where μ is a penalty parameter and μ >0, P, p are both lagrange multipliers, tr (·) is a trace operation, T is the transition rank of the matrix, and F is the Frobenius norm of the matrix.
5. The cross-quality face recognition method based on the convolutional neural network characteristics as claimed in claim 4, wherein the specific optimization process of parameters in the augmented Lagrangian function is as follows:
< a > optimization of z
Figure FDA0002286940970000032
zk+1Can be obtained by a soft threshold method, wherein k represents the iteration of the kth step;
< b > optimization of x
Figure FDA0002286940970000033
Wherein H ═ vec (A)1),vec(A2),...,vec(AN)]，
Figure FDA0002286940970000034
Figure FDA0002286940970000035
k denotes the iteration of the k-th step, resulting in a solution,
xk+1＝(HTH+WTW)-1(HTek+1+WTbk+1)；
< c > select proper ε, check convergence condition
max(||y-A(xk+1)||∞,||zk+1-Wxk+1||∞)<ε
If the maximum iteration times are reached or the termination condition is met, outputting xk+1As x, otherwise, returning to step<a>。
6. The cross-quality face recognition method based on the convolutional neural network feature as claimed in claim 5, wherein the specific method in step S302 is as follows:
for each high quality training image block feature vector y1Performing linear representation by using image block feature vectors at corresponding positions on the high-quality training dictionary sample image,
y1＝c1G1+c2G2+...ciGi+...+cNGN+E2
wherein G isiRepresenting image block feature vectors of corresponding positions on the ith low-quality training dictionary sample image, wherein i is {1,2iRepresenting the coefficient corresponding to the ith element in the coefficient vector x, E2Representing the residual terms.
7. The cross-quality face recognition method based on the convolutional neural network feature as claimed in claim 6, wherein in step S302, the method for solving the representation coefficients of the high-quality training image block is as follows:
first, define
Figure FDA0002286940970000041
For each high-quality training image block feature vector, a weighted sparse coding regular regression representation method is used to obtain the linear representation of each high-quality training image block in the low-quality training sample image block, a regression model of each high-quality training image block is expressed as,
Figure FDA0002286940970000042
wherein
Figure FDA0002286940970000045
Denotes the L2 norm, λ is the regularization parameter, W1C represents the representation coefficient of the high-quality training image block;
secondly, for solving conveniently, an auxiliary variable z needs to be introduced1The above model is represented as,
Figure FDA0002286940970000043
s.t.z1＝W1c；
wherein, by introducing two auxiliary variables M and M, the augmented Lagrangian function of the above formula is expressed as,
Figure FDA0002286940970000044
where μ is a penalty parameter and μ >0, M, M is the Lagrangian multiplier, tr (-) is the trace operation.
8. The cross-quality face recognition method based on the convolutional neural network characteristics as claimed in claim 7, wherein the specific optimization process of parameters in the augmented Lagrangian function is as follows:
<a>z1is optimized
Figure FDA0002286940970000051
Figure FDA0002286940970000052
The solution of (c) can be obtained by a soft threshold method;
< b > c optimization
Figure FDA0002286940970000053
Wherein H ═ vec (G)1),vec(G2),...,vec(GN)]，
Figure FDA0002286940970000054
Figure FDA0002286940970000055
So as to obtain the following solution,
ck+1＝(HTH+W1 TW1)-1(HTek+1+W1 Tbk+1)；
<c>selecting an appropriate ε1Checking the convergence condition
Figure FDA0002286940970000056
Wherein | · | | is a given norm, and if the maximum iteration number is reached or the above termination condition is satisfied, c is outputk+1As c, otherwise, returning to step<a>。
9. The cross-quality face recognition method based on the convolutional neural network feature of claim 8, wherein the specific method of step S4 is as follows:
for a low quality training image block feature vector y, the linear representation x of the low quality training dictionary image block feature vector is obtained through step S3, and for a high quality training image block set, the linear representation c ═ c of the high quality training dictionary image block is obtained1,c2,…cL]And L represents the number of high-quality training dictionary images, the combination coefficient w can be obtained by the following formula,
Figure FDA0002286940970000061
where η is a balance parameter, then the reconstruction error e for each classi(x) It is calculated that,
Figure FDA0002286940970000062
wherein, ciLinear representation of class i low-quality metric attempt blocks on high-quality training dictionary image blocks, function deltaiRepresenting the weight associated with the i-th class, w*Representing the combining coefficient.
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