CN106203256A - A kind of low resolution face identification method based on sparse holding canonical correlation analysis - Google Patents

Abstract

The present invention provides a kind of low resolution face identification method based on sparse holding canonical correlation analysis.The present invention combines the sparse and thought of canonical correlation analysis, propose a kind of low resolution face identification method based on sparse holding canonical correlation analysis, the thought using canonical correlation analysis meets the maximum correlation requirement of the feature of extraction, achieve the fusion of high-resolution and low-resolution face characteristic authentication information, use sparse thought to keep structural information, improve the robustness of low resolution recognition of face.The present invention not only achieves the effective integration of high-resolution and low-resolution face characteristic collection authentication information, and enhances character representation and distinguishing ability, meets dependency and keeps structural information requirement.

Description

A kind of low resolution face identification method based on sparse holding canonical correlation analysis

Technical field

The present invention relates to a kind of low resolution face identification method based on sparse holding canonical correlation analysis, belong to calculating Machine vision and the technical field of pattern recognition.

Background technology

Face recognition technology obtains in recent decades and develops rapidly, especially under controlled scene, and recognition of face skill Art has begun to be applied.But, recognition of face is an extremely complex problem, and its difficulty is the transmutability of pattern, The face intrinsic factor such as major influence factors has age, the colour of skin, expression, illumination, the environmental factors such as block and video acquisition sets The standby changing factor brought.At present, in order to overcome the impact of face intrinsic factor and environmental factors, researcher has been devised by Various different algorithms, and achieve good effect；But, the always recognition of face of low resolution problem is difficult to overcome Difficult point.The difficulty of low resolution recognition of face problem essentially consists in data dimension between high-resolution human face and low resolution face Do not mate and diversity between data.

Under non-controllable scene, under the conditions of remote, testee is unconscious, facial image is caught by low quality photographic head Obtain.Owing to quality of human face image ratio is relatively low, lacking a large amount of discriminant information in low-resolution face image, this has challenged tradition significantly Face recognition algorithms.At present, face identification method based on low resolution is largely divided into two classes: one is by low resolution Facial image to identical size, then passes through principal component analysis, linear discriminant analysis with high-resolution human face image normalization And the conventional subspace dimension reduction method such as locality preserving projections carries out feature extraction.Although this kind of method overcomes high-resolution human face The unmatched problem of dimension between image and low-resolution face image, but the recognition effect that can not obtain.Two be based on The method of Coupling Metric study, its thought is by high-resolution human face image and low resolution face by coupling sub-space learning Image study one group mapping, and project to a common subspace, reduces the difference between face image data in class, increases class Between divergence between facial image.Based on this thought, Zhou et al. is inspired by linear discriminant analysis, proposes simultaneous differentiation point Analysis (Simultaneous Discriminant Analysis, SDA) algorithm, is incorporated into supervision message in sub-space learning； Similarly, Siena et al. is inspired and analyzes in big spacing Fisher, proposes a kind of coupling space Fisher and analyzes (Coupled Marginal Fisher Analysis, CMFA), CMFA to SDA has similar object function, but empty to low-dimensional after projection Interior data are made that different hypothesis；Ben et al. proposes a kind of coupling distance metric learning method, introduces similarity measurements Amount, not only achieves preferable effect in low resolution recognition of face and is also applied to cross-domain gait certification；It addition, canonical correlation divides Analysis is often used for weighing the similarity between two groups of data, obtains preferable effect in recent years in low resolution recognition of face, It addition, sparse thought is also widely used in recognition of face.

Low resolution recognition of face problem, owing to quality of human face image is low and dimension does not mates, has been challenged traditional significantly Face identification method.

Summary of the invention

For the problem existing for prior art, the present invention provides a kind of based on sparse holding canonical correlation analysis low point Resolution face identification method.The present invention combines the sparse and thought of canonical correlation analysis, it is proposed that a kind of based on sparse holding The low resolution face identification method of canonical correlation analysis, the thought of employing canonical correlation analysis meets the maximum of the feature of extraction Correlation requirement, it is achieved that the fusion of high-resolution and low-resolution face characteristic authentication information, uses sparse thought to keep structure letter Breath, improves the robustness of low resolution recognition of face.The present invention not only achieves high-resolution and low-resolution face characteristic collection authentication information Effective integration, and enhance character representation and distinguishing ability, meet dependency and keep structural information requirement.

Technical scheme is as follows:

A kind of low resolution face identification method based on sparse holding canonical correlation analysis includes training part and test Part；

Described training department divides and comprises the following steps that

First, effective spy of high-resolution human face image and low-resolution face image is extracted respectively by principal component analysis Levy and respectively obtain the principal component analysis projection matrix corresponding to high-resolution human face image and low-resolution face image；

Then, construct sparse reconstruction weights matrix, make sparse reconstructed error minimum, learn one group of matrix of a linear transformation, make Correlation maximum between the resolution that secures satisfactory grades facial image and low-resolution face image data, by low resolution training sample set and height Resolution training sample set projects in a common subspace；

Described part of detecting comprises the following steps that

First, the principal component analysis projection matrix corresponding to low-resolution face image using training department to get is treated The low-resolution face image sample surveyed carries out preliminary feature extraction；

Then, the throwing corresponding to low resolution training sample set then by sparse holding Canonical Correlation Analysis obtained The feature that upper step principal component analysis extracts is carried out Linear Mapping by shadow matrix；

Finally, by nearest neighbor classifier based on Euclidean distance, the sample after mapping is carried out Classification and Identification.

According to currently preferred, specifically comprising the following steps that of described training part

The high-resolution human face image training sample set making high-resolution human face image construction is H=[h₁,h₂,…,h_N]∈ R^M×N, the low-resolution face image training sample set that low-resolution face image is constituted is L=[l₁,l₂,…,l_N]∈R^m×N, Wherein, h_i∈R^M,l_i∈R^mRepresent respectively in high-resolution human face image training sample set and low-resolution face image training set I-th sample, M, m represent high-resolution human face image and the dimension of low-resolution face image sample respectively；

A. principal component analysis

As a example by high-resolution human face sample set, provide Principal Component Analysis Algorithm.Principal component analysis is a kind of effective special Levying linear transformation method, in essence, the data of higher-dimension are projected in lower dimensional space by linear transformation by PCA, maximize Variance, the data that projection obtains can represent initial data, eliminate noise and existence of redundant；

First the average facial image of N number of high-resolution human face image pattern is calculatedDivide according to main constituent Analysis principle, for N number of high-resolution human face image pattern object function be

$a=\arg \underset{u^{T}u=I}{max}{a}^T\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}(h_i-\stackrel{\‾}{h}){(h_i-\stackrel{\‾}{h})}^{T}a---\left(1\right)$

OrderThe most above-mentioned formula (1) is expressed asAccording to drawing Ge Lang function, formula (1) is converted into the following eigenvalue problem of solution

∑ a=λ a (2)

In formula (2), λ is the eigenvalue of ∑, and a is eigenvalue characteristic of correspondence vector；Covariance matrix is carried out eigenvalue Decompose, the front d obtained_hIndividual eigenvalue of maximum characteristic of correspondence vector is exactly optimal d_hReform feature, Therefore, sample set is mapped in lower dimensional space,

X=A^TH (3)

Similarly, the low-resolution face image training sample set constituted for low-resolution face image passes through above-mentioned master Component analysis procedure study projection matrixLow-resolution face image training sample is mapped to low-dimensional Space Y=B^TL；

The most sparse holding canonical correlation analysis

Assuming that after above-mentioned principal component analysis process high-resolution human face image training sample set and low resolution face figure As training sample set is each mapped toWithFor each high score Distinguish facial image sample x_i, all there is a corresponding subsample collectionBased on 1 model The target of number rarefaction representation finds one group of factor alpha exactly_i∈R^N-1, meet x_i=M_iα_i, and require α_iMiddle absolute coefficient sum The least, it is expressed as follows by mathematical form:

$\begin{array}{cc}\min & \left|\right|{\mathrm{\α}}_i|{|}_1\\ s.t.& x_i=M_i{\mathrm{\α}}_i\end{array}---\left(4\right)$

In actual applications, formula (4) condition is difficult to set up, and therefore considers the reconstruct of sample in above-mentioned Optimized model by mistake Difference, proposes a kind of stable rarefaction representation, is expressed as follows:

$\begin{array}{cc}\min & \left|\right|{\mathrm{\α}}_i;t_i\left|\right|\\ s.t.& x_i=\[\begin{array}{cc}{M}_i& I\end{array}\]\left[\begin{array}{c}{\mathrm{\α}}_i\\ t_i\end{array}\right]\end{array}---\left(5\right)$

Formula (5),Representing with intrinsic dimensionality with the unit matrix tieed up, above-mentioned Optimized model can be converted into convex programming Problem；

When obtaining sample x_iIn corresponding subset M_iOn rarefaction representation factor alpha_iAfter, construct current sparse reconstruct power accordingly Weight matrix S=[s₁,s₂,…,s_N], wherein, s_i=[α_i,1,…,α_i,i-1,0,α_i,i,…,α_i,N-1]^T, α_i,jRepresent α_iJth Coefficient；Rarefaction representation is owing to can give, in the case of instructing without supervision message, the weighted value that similar sample is bigger；Therefore, Sparse Remodeling between this sample can represent an important measurement index with distinguishing ability as measures characteristic；

Assume that high-resolution human face image training sample set and low-resolution face image training sample set are led respectively The eigenmatrix obtained after component analysis is respectively In employing State sparse reconstruction weights matrix method, construct the sparse reconstruction weights matrix R=[r of two feature sets respectively₁,r₂,…,r_N]∈ R^N×NWith S=[s₁,s₂,…,s_N]∈R^N×N；Sparse holding canonical correlation analysis is intended to find a pair projection vector w and u, makes to carry Not only there is between high-resolution human face characteristics of image and low-resolution face image feature after taking the correlation coefficient of maximum, with Time projection latter two feature set in sparse reconstructed error the least；To sum up, sparse holding canonical correlation analysis object function It is defined as

$\left\{\begin{array}{c}\underset{w,u}{max}{w}^T{S}_{xy}u\\ \underset{w\≠0}{\min }{w}^{T}X(I-R){(I-R)}^T{X}^{T}w\\ \underset{u\≠0}{\min }{u}^{T}Y(I-S){(I-S)}^T{Y}^{T}u\end{array}\right.---\left(6\right)$

In formula (6), S_xyRepresent the Cross-covariance of X and Y, describe the dependency between two groups of variablees；Due to formula (6) Cannot direct solution, use the multiplication and division in evaluation function method that formula (6) is converted into following single object optimization model herein:

$\underset{w,u\≠0}{\arg \max }\mathrm{\ρ}=\frac{w^T{S}_{xy}u}{\sqrt{w^T{\tilde{S}}_{xx}w}\sqrt{u^T{\tilde{S}}_{yy}u}}---\left(7\right)$

In formula (7),WithIt is respectively the sparse of feature set X and Y Keep Scatter Matrix；They need to meet matrix positive definition condition simultaneously, and otherwise denominator may be 0 to cause model degradation；Adopt With method of Lagrange multipliers commonly used in canonical correlation analysis model optimization, the optimization problem of formula (7) is converted into following two Individual generalized eigenvalue problem:

$\left\{\begin{array}{c}{S}_{xy}{\tilde{S}}_{yy}^{-1}{S}_{xy}^{T}w={\mathrm{\λ}}^2{\tilde{S}}_{xx}w\\ S_{xy}^T{\tilde{S}}_{xx}^{-1}{S}_{xy}u={\mathrm{\λ}}^2{\tilde{S}}_{yy}u\end{array}\right.---\left(8\right)$

And meet between w and u

$\{\begin{array}{c}{S}_{xy}u=\mathrm{\λ}{\tilde{S}}_{xx}w\\ S_{xy}^{T}w=\mathrm{\λ}{\tilde{S}}_{yy}u\end{array}---\left(9\right)$

For generalized eigenvalue problem in formula (8), (9), front d group eigenvalue of maximum characteristic of correspondence vector w_i,u_i(i= 1 ..., d) constitute the projection matrix W=on high-resolution human face image pattern collection and low-resolution face image sample set [w₁,…,w_d]∈R^m×dWith U=[u₁,…,u_d]∈R^n×d；Therefore, high-resolution human face image and low-resolution face image are thrown The feature of movie queen is

$\left\{\begin{array}{c}Z=W^{T}X\\ Q=U^{T}Y\end{array}\right.---\left(10\right).$

According to currently preferred, described part of detecting specifically includes following steps:

Given low-resolution face image test sample l_test, through principal component analysis and sparse holding canonical correlation Analyze to be characterized as after linear transformation

q_test=U^TB^Tl_test (11)

Finally use the described low resolution face figure based on sparse holding canonical correlation analysis of nearest neighbor classifier checking As the effectiveness of recognition methods feature extraction, carry out by calculating the Euclidean distance between training sample and test sample eigenvalue Classification, if

$\begin{array}{c}Dis(l_i,l_{test})=\arg \underset{i}{min}Dis(q_i,q_{test})\\ =\left|\right|q_i-q_{test}|{|}_2\end{array}---\left(12\right)$

Then l_testBelong to l_iThe classification at place, otherwise, l_testIt is not belonging to l_iThe classification at place, wherein, | | | |₂Represent 2 models Number.The invention has the beneficial effects as follows:

1, the present invention proposes a kind of low resolution face identification method based on sparse holding canonical correlation analysis, by sparse Differentiate that thought incorporates in canonical correlation analysis model, not only maintain the dependency between two category features, and maintain data Structural information.

2, sparse holding canonical correlation analysis algorithm is applied to low resolution recognition of face by the present invention, it is to avoid high-resolution The unmatched problem of dimension between rate facial image and low-resolution face image.

3, the present invention provides a kind of effective low resolution face identification method, not only makes the high-resolution human face after projection Image and low-resolution face image have a correlation coefficient of maximum, and after making projection the reconstructed error in two feature sets is Little.

Accompanying drawing explanation

The flow chart of Fig. 1 present invention；

In Fig. 2 present invention, described high-resolution human face image and the comparison diagram of low resolution facial image；

Fig. 3 method proposed by the invention discrimination is with dimension situation of change.

Detailed description of the invention

With example, the present invention is described in detail below in conjunction with the accompanying drawings, but is not limited to this.

Embodiment,

A kind of low resolution face identification method based on sparse holding canonical correlation analysis, shown in accompanying drawing 1, including training Part and part of detecting；

Described training department divides and comprises the following steps that

First, effective spy of high-resolution human face image and low-resolution face image is extracted respectively by principal component analysis Levy and respectively obtain the principal component analysis projection matrix corresponding to high-resolution human face image and low-resolution face image；

Then, construct sparse reconstruction weights matrix, make sparse reconstructed error minimum, learn one group of matrix of a linear transformation, make Correlation maximum between the resolution that secures satisfactory grades facial image and low-resolution face image data, by low resolution training sample set and height Resolution training sample set projects in a common subspace；

Described part of detecting comprises the following steps that

First, the principal component analysis projection matrix corresponding to low-resolution face image using training department to get is treated The low-resolution face image sample surveyed carries out preliminary feature extraction；

Then, the throwing corresponding to low resolution training sample set then by sparse holding Canonical Correlation Analysis obtained The feature that upper step principal component analysis extracts is carried out Linear Mapping by shadow matrix；

Finally, by nearest neighbor classifier based on Euclidean distance, the sample after mapping is carried out Classification and Identification.

Specifically comprising the following steps that of described training part

The high-resolution human face image training sample set making high-resolution human face image construction is H=[h₁,h₂,…,h_N]∈ R^M×N, the low-resolution face image training sample set that low-resolution face image is constituted is L=[l₁,l₂,…,l_N]∈R^m×N, Wherein, h_i∈R^M,l_i∈R^mRepresent respectively in high-resolution human face image training sample set and low-resolution face image training set I-th sample, M, m represent high-resolution human face image and the dimension of low-resolution face image sample respectively；

High-resolution human face image contrasts as shown in Figure 2 with low-resolution face image, and low-resolution face image is relatively For high-resolution human face image, lacking substantial amounts of identification information, image visual effect the most drastically declines.

A. principal component analysis

As a example by high-resolution human face sample set, provide Principal Component Analysis Algorithm.Principal component analysis is a kind of effective special Levying linear transformation method, in essence, the data of higher-dimension are projected in lower dimensional space by linear transformation by PCA, maximize Variance, the data that projection obtains can represent initial data, eliminate noise and existence of redundant；

First the average facial image of N number of high-resolution human face image pattern is calculatedDivide according to main constituent Analysis principle, for N number of high-resolution human face image pattern object function be

$a=\arg \underset{u^{T}u=I}{max}{a}^T\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}(h_i-\stackrel{\‾}{h}){(h_i-\stackrel{\‾}{h})}^{T}a---\left(1\right)$

OrderThe most above-mentioned formula (1) is expressed asAccording to drawing Ge Lang function, formula (1) is converted into the following eigenvalue problem of solution

∑ a=λ a (2)

In formula (2), λ is the eigenvalue of ∑, and a is eigenvalue characteristic of correspondence vector；Covariance matrix is carried out eigenvalue Decompose, the front d obtained_hIndividual eigenvalue of maximum characteristic of correspondence vector is exactly optimal d_hReform feature, Therefore, sample set is mapped in lower dimensional space,

X=A^TH (3)

Similarly, the low-resolution face image training sample set constituted for low-resolution face image passes through above-mentioned master Component analysis procedure study projection matrixLow-resolution face image training sample is mapped to low-dimensional Space Y=B^TL；

The most sparse holding canonical correlation analysis

Assuming that after above-mentioned principal component analysis process high-resolution human face image training sample set and low resolution face figure As training sample set is each mapped toWithFor each high score Distinguish facial image sample x_i, all there is a corresponding subsample collectionBased on 1 model The target of number rarefaction representation finds one group of factor alpha exactly_i∈R^N-1, meet x_i=M_iα_i, and require α_iMiddle absolute coefficient sum The least, it is expressed as follows by mathematical form:

$\begin{array}{cc}\min & \left|\right|{\mathrm{\α}}_i|{|}_1\\ s.t.& x_i=M_i{\mathrm{\α}}_i\end{array}---\left(4\right)$

In actual applications, formula (4) condition is difficult to set up, and therefore considers the reconstruct of sample in above-mentioned Optimized model by mistake Difference, proposes a kind of stable rarefaction representation, is expressed as follows:

$\begin{array}{cc}\min & \left|\right|{\mathrm{\α}}_i;t_i\left|\right|\\ s.t.& x_i=\[\begin{array}{cc}{M}_i& I\end{array}\]\left[\begin{array}{c}{\mathrm{\α}}_i\\ t_i\end{array}\right]\end{array}---\left(5\right)$

Formula (5),Representing with intrinsic dimensionality with the unit matrix tieed up, above-mentioned Optimized model can be converted into convex programming Problem；

When obtaining sample x_iIn corresponding subset M_iOn rarefaction representation factor alpha_iAfter, construct current sparse reconstruct power accordingly Weight matrix S=[s₁,s₂,…,s_N], wherein, s_i=[α_i,1,…,α_i,i-1,0,α_i,i,…,α_i,N-1]^T, α_i,jRepresent α_iJth Coefficient；Rarefaction representation is owing to can give, in the case of instructing without supervision message, the weighted value that similar sample is bigger；Therefore, Sparse Remodeling between this sample can represent an important measurement index with distinguishing ability as measures characteristic；

Assume that high-resolution human face image training sample set and low-resolution face image training sample set are led respectively The eigenmatrix obtained after component analysis is respectively In employing State sparse reconstruction weights matrix method, construct the sparse reconstruction weights matrix R=[r of two feature sets respectively₁,r₂,…,r_N]∈ R^N×NWith S=[s₁,s₂,…,s_N]∈R^N×N；Sparse holding canonical correlation analysis is intended to find a pair projection vector w and u, makes to carry Not only there is between high-resolution human face characteristics of image and low-resolution face image feature after taking the correlation coefficient of maximum, with Time projection latter two feature set in sparse reconstructed error the least；To sum up, sparse holding canonical correlation analysis object function It is defined as

$\left\{\begin{array}{c}\underset{w,u}{max}{w}^T{S}_{xy}u\\ \underset{w\≠0}{\min }{w}^{T}X(I-R){(I-R)}^T{X}^{T}w\\ \underset{u\≠0}{\min }{u}^{T}Y(I-S){(I-S)}^T{Y}^{T}u\end{array}\right.---\left(6\right)$

In formula (6), S_xyRepresent the Cross-covariance of X and Y, describe the dependency between two groups of variablees；Due to formula (6) Cannot direct solution, use the multiplication and division in evaluation function method that formula (6) is converted into following single object optimization model herein:

$\underset{w,u\≠0}{\arg \max }\mathrm{\ρ}=\frac{w^T{S}_{xy}u}{\sqrt{w^T{\tilde{S}}_{xx}w}\sqrt{u^T{\tilde{S}}_{yy}u}}---\left(7\right)$

In formula (7),WithIt is respectively the sparse of feature set X and Y Keep Scatter Matrix；They need to meet matrix positive definition condition simultaneously, and otherwise denominator may be 0 to cause model degradation；Adopt With method of Lagrange multipliers commonly used in canonical correlation analysis model optimization, the optimization problem of formula (7) is converted into following two Individual generalized eigenvalue problem:

$\left\{\begin{array}{c}{S}_{xy}{\tilde{S}}_{yy}^{-1}{S}_{xy}^{T}w={\mathrm{\λ}}^2{\tilde{S}}_{xx}w\\ S_{xy}^T{\tilde{S}}_{xx}^{-1}{S}_{xy}u={\mathrm{\λ}}^2{\tilde{S}}_{yy}u\end{array}\right.---\left(8\right)$

And meet between w and u

$\{\begin{array}{c}{S}_{xy}u=\mathrm{\λ}{\tilde{S}}_{xx}w\\ S_{xy}^{T}w=\mathrm{\λ}{\tilde{S}}_{yy}u\end{array}---\left(9\right)$

For generalized eigenvalue problem in formula (8), (9), front d group eigenvalue of maximum characteristic of correspondence vector w_i,u_i(i= 1 ..., d) constitute the projection matrix W=on high-resolution human face image pattern collection and low-resolution face image sample set [w₁,…,w_d]∈R^m×dWith U=[u₁,…,u_d]∈R^n×d；Therefore, high-resolution human face image and low-resolution face image are thrown The feature of movie queen is

$\left\{\begin{array}{c}Z=W^{T}X\\ Q=U^{T}Y\end{array}\right.---\left(10\right).$

Described part of detecting specifically includes following steps:

Given low-resolution face image test sample l_test, through principal component analysis and sparse holding canonical correlation Analyze to be characterized as after linear transformation

q_test=U^TB^Tl_test (11)

Finally use the described low resolution face figure based on sparse holding canonical correlation analysis of nearest neighbor classifier checking As the effectiveness of recognition methods feature extraction, carry out by calculating the Euclidean distance between training sample and test sample eigenvalue Classification, if

$\begin{array}{c}Dis(l_i,l_{test})=\arg \underset{i}{min}Dis(q_i,q_{test})\\ =\left|\right|q_i-q_{test}|{|}_2\end{array}---\left(12\right)$

Then l_testBelong to l_iThe classification at place, otherwise, l_testIt is not belonging to l_iThe classification at place, wherein, | | | |₂Represent 2 models Number.

Checking test:

On Extend YaleB face database, 38 people are carried out low resolution face recognition experiment.Wherein, each person 10 facial images also sample into high-resolution human face image that size is 24 × 21 as training sample, similarly, and 10 people Face image sampling becomes the low-resolution face image of 8 × 7 as test sample, and remaining 11 facial images are sampled into size and are The low-resolution face image of 8 × 7 is tested, and the method for the invention is under difference retains dimension, and discrimination change is as attached Shown in Fig. 3.Test respectively Selective principal component analysis (PCA), linear discriminant analysis (LDA), locality preserving projections (LPP), multi-thread Property dimensional analysis (MDS) and canonical correlation analysis (CCA) carry out contrast experiment, the highest discrimination comparing result under various methods As shown in table 1 below.

Table 1: the highest discrimination of various methods contrasts

Method	PCA	LDA	LPP	MDS	CCA	SPCCA
							Discrimination	0.42	0.67	0.66	0.76	0.70	0.88

By accompanying drawing 3 it can be seen that the present invention propose low resolution based on sparse holding canonical correlation analysis (SPCCA) People's image-recognizing method discrimination is affected by dimension, and its highest discrimination is 0.88, by table 1 comparing result it can be seen that Method proposed by the invention has best recognition effect.

Claims (3)

1. a low resolution face identification method based on sparse holding canonical correlation analysis, it is characterised in that the method bag Include training part and part of detecting；

Described training department divides and comprises the following steps that

First, the validity feature of high-resolution human face image and low-resolution face image is extracted respectively by principal component analysis also Respectively obtain the principal component analysis projection matrix corresponding to high-resolution human face image and low-resolution face image；

Then, construct sparse reconstruction weights matrix, make sparse reconstructed error minimum, learn one group of matrix of a linear transformation so that be high Correlation maximum between resolution facial image and low-resolution face image data, by low resolution training sample set and high-resolution Rate training sample set projects in a common subspace；

Described part of detecting comprises the following steps that

First, use the principal component analysis projection matrix corresponding to low-resolution face image that training department gets to be measured Low-resolution face image sample carries out preliminary feature extraction；

Then, the projection square corresponding to low resolution training sample set then by sparse holding Canonical Correlation Analysis obtained The feature that upper step principal component analysis extracts is carried out Linear Mapping by battle array；

Finally, by nearest neighbor classifier based on Euclidean distance, the sample after mapping is carried out Classification and Identification.

A kind of low resolution face identification method based on sparse holding canonical correlation analysis the most according to claim 1, It is characterized in that, specifically comprising the following steps that of described training part

The high-resolution human face image training sample set making high-resolution human face image construction is H=[h₁,h₂,…,h_N]∈R^M×N, The low-resolution face image training sample set that low-resolution face image is constituted is L=[l₁,l₂,…,l_N]∈R^m×N, wherein, h_i∈R^M,l_i∈R^mRepresent i-th in high-resolution human face image training sample set and low-resolution face image training set respectively Sample, M, m represent high-resolution human face image and the dimension of low-resolution face image sample respectively；

A. principal component analysis

First the average facial image of N number of high-resolution human face image pattern is calculatedFor N number of high-resolution human Face image pattern object function is

$a=\arg \underset{u^{T}u=I}{max}{a}^T\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}\left(h_i-\stackrel{\‾}{h}\right){\left(h_i-\stackrel{\‾}{h}\right)}^{T}a---\left(1\right)$

OrderThe most above-mentioned formula (1) is expressed asBright according to glug Day function, formula (1) is converted into the following eigenvalue problem of solution

∑ a=λ a (2)

In formula (2), λ is the eigenvalue of ∑, and a is eigenvalue characteristic of correspondence vector；Covariance matrix is carried out eigenvalue divide Solve, the front d obtained_hIndividual eigenvalue of maximum characteristic of correspondence vector is exactly optimal d_hReform feature, Therefore, sample set is mapped in lower dimensional space,

X=A^TH (3)

For low-resolution face image constitute low-resolution face image training sample set by above-mentioned principal component analysis mistake Journey study projection matrixLow-resolution face image training sample is mapped to lower dimensional space Y=B^TL；

The most sparse holding canonical correlation analysis

Assuming that high-resolution human face image training sample set and low-resolution face image are instructed after above-mentioned principal component analysis process Practice sample set to be each mapped toWithFor each high-resolution people Face image pattern x_i, all there is a corresponding subsample collectionDilute based on 1 norm The target that relieving the exterior syndrome shows finds one group of factor alpha exactly_i∈R^N-1, meet x_i=M_iα_i, and require α_iMiddle absolute coefficient sum to the greatest extent may be used Can be little, it is expressed as follows by mathematical form:

$\begin{array}{cc}\min & \left|\right|{\mathrm{\α}}_i|{|}_1\\ s.t.& x_i=M_i{\mathrm{\α}}_i\end{array}---\left(4\right)$

Propose a kind of stable rarefaction representation, be expressed as follows:

$\begin{array}{cc}\min & \left|\right|{\mathrm{\α}}_i;t_i\left|\right|\\ s.t.& x_i=\left[\begin{array}{cc}{M}_i& I\end{array}\right]\left[\begin{array}{c}{\mathrm{\α}}_i\\ t_i\end{array}\right]\end{array}---\left(5\right)$

Formula (5),Represent with intrinsic dimensionality with the unit matrix tieed up；

When obtaining sample x_iIn corresponding subset M_iOn rarefaction representation factor alpha_iAfter, construct current sparse reconstruction weights square accordingly Battle array S=[s₁,s₂,…,s_N], wherein, s_i=[α_i,1,…,α_i,i-1,0,α_i,i,…,α_i,N-1]^T, α_i,jRepresent α_iJth coefficient；

Assume that high-resolution human face image training sample set and low-resolution face image training sample set carry out main constituent respectively The eigenmatrix obtained after analysis is respectively Use above-mentioned dilute Dredge reconstruction weights matrix method, construct the sparse reconstruction weights matrix R=[r of two feature sets respectively₁,r₂,…,r_N]∈R^N×NWith S=[s₁,s₂,…,s_N]∈R^N×N；Sparse holding canonical correlation analysis is intended to find a pair projection vector w and u, after making extraction Not only there is between high-resolution human face characteristics of image and low-resolution face image feature the correlation coefficient of maximum, project simultaneously Sparse reconstructed error in latter two feature set is the least；To sum up, sparse holding canonical correlation analysis object function is defined as

$\left\{\begin{array}{cc}\underset{w,u}{max}& w^T{S}_{xy}u\\ \underset{w\≠0}{\min }& w^{T}X(I-R){(I-R)}^T{X}^{T}w\\ \underset{u\≠0}{\min }& u^{T}Y(I-S){(I-S)}^T{Y}^{T}u\end{array}\right.---\left(6\right)$

In formula (6), S_xyRepresent the Cross-covariance of X and Y, describe the dependency between two groups of variablees；Owing to formula (6) cannot Direct solution, uses the multiplication and division in evaluation function method that formula (6) is converted into following single object optimization model herein:

$\begin{array}{cc}\underset{w,u\≠0}{\arg \max }& \mathrm{\ρ}=\frac{w^T{S}_{xy}u}{\sqrt{w^T{\tilde{S}}_{xx}w}\sqrt{u^T{\tilde{S}}_{yy}u}}\end{array}---\left(7\right)$

In formula (7),WithIt is respectively feature set X and the sparse holding of Y Scatter Matrix；Using method of Lagrange multipliers commonly used in canonical correlation analysis model optimization, the optimization problem of formula (7) turns Turn to following two generalized eigenvalue problems:

$\left\{\begin{array}{c}{S}_{xy}{\tilde{S}}_{yy}^{-1}{S}_{xy}^{T}w={\mathrm{\λ}}^2{\tilde{S}}_{xx}w\\ S_{xy}^T{\tilde{S}}_{xx}^{-1}{S}_{xy}u={\mathrm{\λ}}^2{\tilde{S}}_{yy}u\end{array}\right.---\left(8\right)$

And meet between w and u

$\left\{\begin{array}{c}{S}_{xy}u=\mathrm{\λ}{\tilde{S}}_{xx}w\\ S_{xy}^{T}w=\mathrm{\λ}{\tilde{S}}_{yy}u\end{array}\right.---\left(9\right)$

For generalized eigenvalue problem in formula (8), (9), front d group eigenvalue of maximum characteristic of correspondence vector w_i, u_i(i=1 ..., D) the projection matrix W=[w on high-resolution human face image pattern collection and low-resolution face image sample set is constituted₁..., w_d] ∈R^m×dWith U=[u₁..., u_d]∈R^n×d；Therefore, the feature after high-resolution human face image and low-resolution face image project For

$\left\{\begin{array}{c}Z=W^{T}X\\ Q=U^{T}Y\end{array}\right.---\left(10\right).$

A kind of low resolution face identification method based on sparse holding canonical correlation analysis the most according to claim 1, It is characterized in that, described part of detecting specifically includes following steps:

Given low-resolution face image test sample l_test, through principal component analysis and sparse holding canonical correlation analysis It is characterized as after obtaining linear transformation

q_test=U^TB^Tl_test (11)

The described low-resolution face image based on sparse holding canonical correlation analysis of nearest neighbor classifier checking is finally used to know The effectiveness that other method feature extracts, is carried out point by calculating the Euclidean distance between training sample and test sample eigenvalue Class, if

$\begin{array}{c}Dis(l_i,l_{test})=\arg \underset{i}{min}Dis(q_i,q_{test})\\ =\left|\right|q_i-q_{test}|{|}_2\end{array}---\left(12\right)$

Then l_testBelong to l_iThe classification at place, otherwise, l_testIt is not belonging to l_iThe classification at place, wherein, | | | |₂Represent 2 norms.