CN104951756A - Face recognition method based on compressed sensing - Google Patents

Abstract

The invention provides a face recognition method based on compressed sensing. The face recognition method includes constructing a dictionary database according to face samples and setting requirements and preprocessing tested facial images to column vector, designing projection matrix according to the constructed dictionary database; inputting projection value y of the column vector under the projection matrix into function to solve, when p traverses from 1 to P, solving to obtain all Sp, judging the Sp by the function, outputting judgement types; reconstructing image data according to the judgement types, and rearranging to obtain reconstruction images. On one hand, hardware requirements of high-speed sampling and big data transmission; on the other hand, system identification rate can be effectively improved, and effectiveness of the face recognition method is proved by experimental simulation.

Description

A kind of face identification method based on compressed sensing

Technical field

The invention belongs to technical field of face recognition, particularly relate to a kind of face identification method based on compressed sensing and system.

Background technology

Face recognition technology, as one of the important research direction of machine vision and image processing techniques, is more and more subject to showing great attention to of academia.Along with deepening continuously of digital technology application, the resolution of daily image is more and more higher, and this proposes very high request to hardware devices such as image information collecting, transmission, Storage and Processings.Store the pressure with transmission to alleviate information, current solution is signal compression, as the Joint Photographic Experts Group based on discrete cosine transform and the JPEG2000 standard etc. based on wavelet transformation.

Traditional pattern-recognition flow process, be respectively image acquisition, compression of images, image decompression, feature extraction and image recognition, this kind of recognition technology is generally by high-speed sampling image information, then most of redundant information is abandoned to obtain packed data for transmission according to the correlativity between image data pixel point, backstage receiving end rebuilds image, extracts characteristics of image and is used for identification.

Because traditional face recognition technology needs to carry out high-speed sampling to image, mass data compression is transferred to backstage and carries out identity differentiation, this proposes very high requirement to channel and image processing hardware equipment, and system identification accuracy is not high under complex environment.

Summary of the invention

The object of the present invention is to provide a kind of face identification method based on compressed sensing and system, be intended to solve existing face recognition technology and channel and image processing hardware equipment are proposed to very high requirement, identify the problem that accuracy is not high.

The present invention is achieved in that a kind of face identification method based on compressed sensing, comprises the following steps:

S1, according to face sample, require structure dictionary library Ψ=[Ψ according to setting ₁..., Ψ _p..., Ψ _p], facial image x will be tested ₀pre-service forms column vector x;

S2, design projection matrix Φ according to structure dictionary library Ψ;

S3, by the projection value y input function of column vector x under projection matrix Φ ${\hat{s}}_p=V_p\left[\begin{array}{c}{\mathrm{\Σ}}_p^{-1}{\tilde{y}}_1\\ {\tilde{s}}_2\end{array}\right]$ Solve after p traverses P from 1, try to achieve all wherein, P is the quantity of individual face sample, V _p, Σ _pwith tried to achieve by projection matrix Φ, dictionary library Ψ and input projection value y, for arbitrary dimension is vector; Pass through function $\hat{p}=\arg {\min }_p{\left|\right|y-\mathrm{\Φ}{\mathrm{\ψ}}_p{\hat{s}}_p\left|\right|}_2^2,s.t.p\∈[1,P]$ Right differentiate, export and differentiate type wherein, wherein be called projection matrix. the sample set of p people, the sparse coefficient of dictionary sub-block p;

S4, differentiate type according to described output reconstructed image data is permutatation obtains reconstructed image.

Preferably, also comprised before step S1

S0, input starting condition, described starting condition comprises face storehouse sample and the test facial image x of the composition of sample of P Ge Ren people face ₀.

Preferably, in step sl, the construction process that described dictionary library is comprises the following steps:

Suppose to store P Ge Ren face sample in a face database, wherein, everyone has again the sample of many different angles, different expression, different light, and the size of each sample is all identical;

Choose the individual different sample of its Q at random to everyone, each sample image forms a column vector according to same queueing discipline and is l respectively ₂norm normalized, size is set to N × 1, as the atom of in dictionary library, forms dictionary library:

To arbitrary 1≤p≤P, dictionary sub-block the sample set of p people, wherein, L=FQ; To 1=l≤L, and || ψ _l|| ₂=1 is a column vector of dictionary.

Preferably, in step s 2, described projection matrix Φ function is defined as:

$\widehat{\mathrm{\Φ}}=U\left[\begin{array}{cc}{\mathrm{\Σ}}_{11}& 0\end{array}\right]{\left[\begin{array}{cc}{V}_{11}& 0\\ 0& V_{22}\end{array}\right]}^T{U}_{\mathrm{\Ψ}}^T;$ Wherein, the orthogonal matrix of U to be arbitrary dimension be M × M; V ₂₂being arbitrary dimension is orthogonal matrix; U _Ψthe U matrix that the SVD of Ψ is decomposed, to W ₁₁characteristics of decomposition value V ₁₁.

For the feature not needing redundant information in image in conventional identification techniques, compressed sensing (Compressed Sensing, CS) theoretical what adopt is directly carry out compression sampling technology to picture signal, and then avoids high-speed sampling and the wasting of resources abandoning information process and cause.For the high dimensional signal of an input it is obtained projection value y in the projection of matrix Φ lower linear, and process is as follows:

Wherein, be called projection matrix.CS theoretical research be exactly work as M<<N, for given projection value y and projection matrix Φ, how to solve former high dimensional signal x.Obviously, equation (1) is a underdetermined problem, and namely equation number is less than unknown number number, there is countless multiple solution.Therefore, also need to be limited x in solution procedure.Sparsity constraints is exactly a key factor in CS theory, and this conditional request signal x can by L base vector { ψ _llinear expression:

$x=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{s}_1{\mathrm{\&psi;}}_1\stackrel{\mathrm{\&Delta;}}{=}\mathrm{\&Psi;s}---\left(2\right)$

Wherein, be called dictionary (matrix), s is a most elements is the sparse vector of zero, if s contains K nonzero element, then x is called that K is sparse under Ψ.(2) formula is substituted into (1)) formula obtains:

$y=\mathrm{\&Phi;x}=\mathrm{\&Phi;\&Psi;s}\stackrel{\mathrm{\&Delta;}}{=}\mathrm{Ds}---\left(3\right)$

Wherein, be called equivalent dictionary.If that transmission is projection value y, receiving end utilizes its rarefaction representation coefficient s under equivalent dictionary D to carry out image reconstruction and discriminator, (the Compressed Sensing based Classifier of the sorter based on compressed sensing that Here it is will study herein, CSC), comprise compression sampling, rarefaction representation and identify reconstruction three processes.

As M<<N, the data volume of y is far fewer than x, and this greatly reduces channel transmission data and backstage stores, the pressure of process data.But in practical application, projection matrix Φ affects comparatively large on image reconstruction and recognition effect, therefore projection matrix optimal design is also one of main contents will studied herein.For C/S system, the effect of projection matrix is the compression to input signal on the one hand, is also the characteristic extraction procedure to signal on the other hand, through the precision that the projection matrix of optimal design greatly can improve Signal analysis classification and recover.

Based on above-mentioned theory, the present invention overcomes the deficiencies in the prior art, a kind of face identification method based on compressed sensing and system are provided, first face training sample optimal design calculation matrix is utilized, then the calculation matrix of optimization is utilized to carry out the compressed sensing classification of facial image, avoid the hardware requirement of high-speed sampling and the transmission of large data on the one hand, effectively can improve system recognition rate on the other hand, experiment simulation confirms the validity worked herein.

Accompanying drawing explanation

Fig. 1 be the present invention is based on compressed sensing face identification method discrimination with change curve;

Fig. 2 be the present invention is based on compressed sensing face identification method discrimination with M change curve;

Fig. 3 be the present invention is based on compressed sensing face identification method to PIE storehouse system recognition rate with M change curve;

Fig. 4 be the present invention is based on compressed sensing face identification method with M change curve.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

Based on a face identification method for compressed sensing, it is characterized in that, comprise the following steps:

S1, according to face sample, require structure dictionary library Ψ=[Ψ according to setting ₁..., Ψ _p..., Ψ _p], facial image x will be tested ₀pre-service forms column vector x.

In step sl, suppose the face's sample storing P people in a face database, wherein everyone has again the sample of many different angles, different expression, different light, and the size of each sample is all identical.Choose the individual different sample of its Q at random to everyone, each sample image forms a column vector according to same queueing discipline and is l respectively ₂norm normalized, size is set to N × 1, as the atom of in dictionary library, forms dictionary library like this: to arbitrary 1≤p≤P, dictionary sub-block be the sample set of p people, easily see L=PQ.To 1≤l≤L, and || ψ _l|| ₂=1 is column vector, i.e. an atom of dictionary.

S2, design projection matrix Φ according to structure dictionary library Ψ;

S3, by the projection value y input function of column vector x under projection matrix Φ ${\hat{s}}_p=V_p\left[\begin{array}{c}{\mathrm{\&Sigma;}}_p^{-1}{\tilde{y}}_1\\ {\tilde{s}}_2\end{array}\right]$ Solve after p traverses P from 1, try to achieve all wherein, P is the quantity of individual face sample, V _p, Σ _pwith tried to achieve by projection matrix Φ, dictionary library Ψ and input projection value y, for arbitrary dimension is vector; S4, pass through function $\hat{p}=\arg {\underset{p}{\min }\left|\right|y-\mathrm{\&Phi;}{\mathrm{\&psi;}}_p{\hat{s}}_p\left|\right|}_2^2,s.t.p\&Element;[1,P]$ Right differentiate, export and differentiate type wherein, in be called projection matrix; the sample set of p people, the sparse coefficient of dictionary sub-block p.

In step s3, for the test sample book of arbitrarily input, first adjust size and formed the column vector x of N × 1 according to the rule of above-mentioned Pareto diagram picture, then the expression equation of x under dictionary library Ψ is:

x＝Ψs+∈ (4)

Wherein, represent error.The present invention is based on the recognition of face of CS, test sample book x is carried out compression projection and obtains projection signal (M < N), process is as follows:

$y=\mathrm{\&Phi;x}=\mathrm{\&Phi;\&Psi;s}+\mathrm{\&Phi;}\&Element;\stackrel{\mathrm{\&Delta;}}{=}\mathrm{Ds}+e---\left(5\right)$

Wherein, for the projection matrix with certain character designed, for equivalent dictionary, for projection domain error.CS theory calls signal x can rarefaction representation under dictionary Ψ, namely in s containing a lot of neutral elements, just from measured value y, accurately can reconstruct s.For the face identification method of invention, dictionary library is made up of the sample of P different people, the character therefore utilizing block sparse when reconstructing s.

Definition $s={[s_1^T,...,s_p^T,...,s_P^T]}^T,$ Any p, (5) formula of rewriting is:

y＝Φ(Ψ ₁s ₁+…+Ψ _ps _p+…+Ψ _Ps _P)+e (6)

Situation is chosen for all s, requires that nonzero element can only be present in some s _pin, and other parts are null value.(6) formula is disassembled into following formula problem:

${\hat{s}}_p=\arg \underset{s_p}{\min }{\left|\right|y-\mathrm{\&Phi;}{\mathrm{\&Psi;}}_p{s}_p\left|\right|}_2^2,\&ForAll;p=\mathrm{1,2},...,P---\left(7\right)$

Try to achieve after, this result is applied to face identification method, forms problem as follows:

$\hat{p}=\arg \underset{p}{\min }{\left|\right|y-\mathrm{\&Phi;}{\mathrm{\&Psi;}}_p{\hat{s}}_p\left|\right|}_2^2,s.t.p\&Element;[1,P]---\left(8\right)$

Now try to achieve it is exactly the result that method differentiates input x.

When the projection matrix Φ designed at given, the problems referred to above difficult point mainly concentrates on how accurately to solve (7) formula.For some p, order (7) formula cost function is converted into:

If D _psvd (Singular Value De-composition, SVD) as follows:

$D_p=U_p\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_p& 0\\ 0& 0\end{array}\right]V_p^T---\left(10\right)$

Wherein,

(10) formula is substituted into (9) formula obtain:

$\begin{array}{c}F(s_p)={||\begin{array}{c}y-U_p\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_p& 0\\ 0& 0\end{array}\right]V_p^T{s}_p\end{array}||}_2^2\\ ={||\begin{array}{c}{U}_p^{T}y-\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_p& 0\\ 0& 0\end{array}\right]V_p^T{s}_p\end{array}||}_2^2\\ \stackrel{\mathrm{\&Delta;}}{=}{||\begin{array}{c}\tilde{y}\end{array}-\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_p& 0\\ 0& 0\end{array}\right]\tilde{s}||}_2^2\end{array};---\left(11\right)$

Order

$\tilde{y}=\left[\begin{array}{c}{\tilde{y}}_1\\ {\tilde{y}}_2\end{array}\right],\tilde{s}=\left[\begin{array}{c}{\tilde{s}}_1\\ {\tilde{s}}_2\end{array}\right]$

Wherein with size be (11) formula expands into:

$F\left(s_p\right)={\left|\right|{\tilde{y}}_1-{\mathrm{\&Sigma;}}_p{\tilde{s}}_1\left|\right|}_2^2+{\left|\right|{\tilde{y}}_2\left|\right|}_2^2---\left(12\right)$

Notice Section 2 and s on the right of above formula equal sign _pirrelevant, therefore when getting:

(12) formula obtains minimum value.Now, the solution of (7) formula is:

${\hat{s}}_p=V_p\left[\begin{array}{c}{\mathrm{\&Sigma;}}_p^{-1}{\tilde{y}}_1\\ {\tilde{s}}_2\end{array}\right]---\left(13\right)$

Wherein, V _p, Σ _pwith tried to achieve by projection matrix, dictionary and input projection value, for arbitrary dimension is vector.After p traverses P from 1, try to achieve all tried to achieve by (8) formula namely known the inventive method is to the differentiation result of input x.

S4, differentiate type according to described output reconstructed image data is permutatation obtains reconstructed image.

In step s 4 which, because the method compression projection value y is flowed to backstage differentiate, if now require the image of reconstruct input, can be according to differentiation result reconstructed image data

The above-mentioned face identification method based on CS, by transmission projection value, instead of test pattern itself, increase work efficiency, alleviate the bandwidth pressure of transmission mass data.

In further implementation process, for reaching the larger raising of accuracy differentiated input value, in embodiments of the present invention, in above-mentioned steps S2, describedly designing projection matrix φ function according to structure dictionary library Ψ and be defined as:

$\widehat{\mathrm{\&Phi;}}=U\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{11}& 0\end{array}\right]{\left[\begin{array}{cc}{V}_{11}& 0\\ 0& V_{22}\end{array}\right]}^T{U}_{\mathrm{\&Psi;}}^T;$ Wherein, the orthogonal matrix of U to be arbitrary dimension be M × M; V ₂₂being arbitrary dimension is orthogonal matrix; Wherein, the orthogonal matrix of U to be arbitrary dimension be M × M; V ₂₂being arbitrary dimension is orthogonal matrix; U _Ψthe U matrix that the SVD of Ψ is decomposed, to W ₁₁characteristics of decomposition value V ₁₁.

In embodiments of the present invention, the design process of above-mentioned projection matrix Φ is specific as follows:

Adopt aforementioned mark, dictionary sub-block dictionary library equivalence dictionary projection matrix wherein

In C/S system, projection matrix optimization is based on following formula:

$\underset{\mathrm{\&Phi;}}{\min }{\left|\right|G-G_t\left|\right|}_F^{2}s.t.G=D^{\mathrm{\&tau;}}D---\left(14\right)$

Wherein, || || F is defined as Frobenius norm, and G is the Gram matrix of equivalent dictionary D, only relevant with projection matrix Φ for given dictionary Ψ, G, G _tit is a target Gram matrix.(14) object of formula is exactly by the given target Gram matrix with certain character of the design projection matrix Gram matrix approximation one that makes equivalent dictionary corresponding.

For can not under dictionary the signal of complete rarefaction representation, such as picture signal, if make equivalent dictionary D have the similar character of dictionary Ψ by design projection matrix Φ, so such C/S system will possess extraordinary performance, now, the target Gram matrix chosen is for facial image sample of the present invention, its rarefaction representation equation under dictionary Ψ is such as formula (4), and generally ∈ can not be full null vector, therefore can consider G _Ψprojection matrix Φ is designed as target Gram matrix.

In the embodiment of the present invention, dictionary library Ψ is made up of face's sample of P different people, even the sample of same person also can make correlativity be deteriorated because of the difference of the aspects such as angle, expression, illumination, i.e. and same sub-block Ψ _pin atom inner product is less between any two.On the other hand, for different two people, between namely different dictionary sub-blocks, we wish that atom correlativity between any two should be little as much as possible.Order:

Following improvement is done to target Gram matrix:

G _t＝Ψ ^τΨ+Δ (15)

Wherein, correction matrix can be expressed as:

To any 1≤i≤P, 1≤j≤P, Δ _ijsize all and Ψ _ijidentical; 1≤m≤L, 1≤n≤L, { δ _mnfor correspondence position in Δ element and:

${\mathrm{\&delta;}}_{\mathrm{mn}}=\left\{\begin{array}{cc}-\mathrm{\&eta;},& i\&NotEqual;j\\ \mathrm{\&eta;},& i=j,m\&NotEqual;n\\ 0,& i=j,m=n\end{array}\right.---\left(16\right)$

Wherein, η is a little constant being greater than zero, is called correction constant.By the G of (15) formula structure _tboth reduce the interatomic correlativity of different dictionary sub-blocks, have again suitable reinforcement to interatomic correlativity in same dictionary sub-block.It should be noted that, each atom of aforementioned dictionary library has carried out normalized, i.e. any 1≤l≤L, || ψ _l|| ₂=1, therefore between atom, inner product is maximum is exactly 1, i.e. G _Ψdiagonal entry.In order to make the G of renewal _tphysical significance is clearer and more definite, and the present invention forces G _tmiddle element value is 1 to the maximum, therefore its diagonal entry is not changed to their size, and off-diagonal element does not allow it more than 1 yet and is greater than zero after correction, and this has just had certain requirement to revising choosing of constant η.

Thus, this paper projection matrix design problem is formed as follows:

$\widehat{\mathrm{\&Phi;}}=\arg \underset{\mathrm{\&Phi;}}{\min }{\left|\right|G-G_t\left|\right|}_F^{2}s.t.G={\mathrm{\&Psi;}}^{\mathrm{\&tau;}}{\mathrm{\&Phi;}}^{\mathrm{\&tau;}}\mathrm{\&Phi;\&Psi;}---\left(17\right)$

Wherein, G _tdefined by (15) formula.

If the SVD of dictionary Ψ decomposes as follows:

$\mathrm{\&Psi;}=U_{\mathrm{\&Psi;}}\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}& 0\\ .0& 0\end{array}\right]V_{\mathrm{\&Psi;}}^T$

Wherein, be easy to get:

$G=V_{\mathrm{\&Psi;}}\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}& 0\\ 0& 0\end{array}\right]W\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}& 0\\ 0& 0\end{array}\right]V_{\mathrm{\&Psi;}}^T;$

Wherein $W\stackrel{\mathrm{\&Delta;}}{=}{U}_{\mathrm{\&Psi;}}^{\mathrm{\&tau;}}{\mathrm{\&Phi;}}^{\mathrm{\&tau;}}\mathrm{\&Phi;}{U}_{\mathrm{\&Psi;}}.$

Order the representing matrix W upper left corner is of a size of submatrix, then (17) formula cost function is deployable is:

$\begin{array}{c}{\left|\right|G-G_t\left|\right|}_F^2\\ ={||\begin{array}{c}{V}_{\mathrm{\&Psi;}}\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}& 0\\ 0& 0\end{array}\right]W\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}& 0\\ 0& 0\end{array}\right]V_{\mathrm{\&Psi;}}^{\mathrm{\&tau;}}-G_t\end{array}||}_F^2\\ ={||\begin{array}{c}\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}{W}_{11}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}& 0\\ 0& 0\end{array}\right]\end{array}{V}_{\mathrm{\&Psi;}}^{\mathrm{\&tau;}}{G}_t{V}_{\mathrm{\&Psi;}}||]}_F^2\end{array}---\left(18\right)$

Order ${\tilde{G}}_t\stackrel{\mathrm{\&Delta;}}{=}{V}_{\mathrm{\&Psi;}}^{\mathrm{\&tau;}}{G}_t{V}_{\mathrm{\&Psi;}},{\tilde{G}}_t^{11}={\tilde{G}}_t(1:\tilde{N},1:\tilde{N})$ Be the upper left corner is of a size of submatrix, then (18) formula is converted into:

${\left|\right|G-G_t\left|\right|}_F^2={\left|\right|{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}{W}_{11}{\mathrm{\&Sigma;}}_{\mathrm{\&Psi;}}-{\tilde{G}}_t^{11}\left|\right|}_F^2+{\left|\right|{\tilde{G}}_t\left|\right|}_F^2-{\left|\right|{\tilde{G}}_t^{11}\left|\right|}_F^2$

On the right of above formula equal sign, latter two have nothing to do with projection matrix, definition (17) formula is equivalent to:

$\widehat{\mathrm{\&Phi;}}=\arg \underset{\mathrm{\&Phi;}}{\min }{\left|\right|{\tilde{W}}_{11}-{\tilde{G}}_t^{11}\left|\right|}_F^2---\left(19\right)$

If: ${\tilde{W}}_{11}=V_W{\mathrm{\&Lambda;}}_W{V}_W^{\mathrm{\&tau;}},{\tilde{G}}_t^{11}=V_t{\mathrm{\&Lambda;}}_t{V}_t^{\mathrm{\&tau;}}$ Be respectively and a kind of Eigenvalues Decomposition form, require Λ _wand Λ _tin eigenwert all with descending sort, 468 pages of Corollary 7.4.9.3 by document " R.A.Horn and C.R.Johnson, Matrix Analysis, Cambridge University Press, 2nd edition, 2012 ") known:

${\left|\right|{\tilde{W}}_{11}-{\tilde{G}}_t^{11}\left|\right|}_F^2\&GreaterEqual;{\left|\right|{\mathrm{\&Lambda;}}_W--{\mathrm{\&Lambda;}}_t\left|\right|}_F^2---\left(20\right)$

When getting V _w=V _t, above formula equal sign is set up.Due to the restriction of projection matrix Φ, order can not more than M, therefore Λ _wnonzero element mostly be M most, when this M nonzero element equals Λ _tduring M element of middle maximum absolute value, (20)) obtain minimum value on the right of the formula sign of inequality, note eigenvalue matrix is now therefore, when getting:

${\tilde{W}}_{11}=V_t{\widetilde{\mathrm{\&Lambda;}}}_W{V}_t^{\mathrm{\&tau;}};$

(20) formula equal sign is set up and is obtained minimum value.And then can try to achieve by W ₁₁carry out SVD to divide and solve: $W_{11}=V_{11}\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{11}^2& 0\\ 0& 0\end{array}\right]V_{11}^{\mathrm{\&tau;}};$

Can choose thus: $W=\left[\begin{array}{cc}{V}_{11}& 0\\ 0& V_{22}\end{array}\right]\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{11}^2& 0\\ 0& 0\end{array}\right]{\left[\begin{array}{cc}{V}_{11}& 0\\ 0& V_{22}\end{array}\right]}^{\mathrm{\&tau;}};$

Wherein, V ₂₂the orthogonal matrix of to be arbitrary dimension be (N-N) × (N-N).Because the solution obtaining (17) formula is to sum up discussed is:

$\widehat{\mathrm{\&Phi;}}=U\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{11}& 0\end{array}\right]{\left[\begin{array}{cc}{V}_{11}& 0\\ 0& V_{22}\end{array}\right]}^{\mathrm{\&tau;}}{U}_{\mathrm{\&Psi;}}^{\mathrm{\&tau;}}---\left(21\right)$

Wherein, the orthogonal matrix of U to be arbitrary dimension be M × M.

From above-mentioned discussion, the present invention about the optimal design of projection matrix Φ only with dictionary Ψ with to revise constant η relevant, therefore for fixing Ψ and η, as long as try to achieve Φ under system line, without the need to carrying out projection matrix design procedure to each input test image, and (21) formula is analytic solution results, calculation cost is also little.In addition, also there are two degree of freedom U and V in this result ₂₂, this provides possibility for improving system performance further.

For verifying actual effect of the present invention, in embodiments of the present invention, by experiment the performance of the face identification method based on CS that proposes of simulating, verifying the present invention and projection matrix optimization to the improvement situation of system performance.Face Sample Storehouse used in experiment comprises ORL storehouse, Yale storehouse, Yale-EXTENDED storehouse (being designated as Yale-E) and CMU PIE storehouse (being designated as PIE).

In emulation, respectively dictionary is constructed to each face database wherein to p=1,2 ... P, each dictionary sub-block the present invention designs projection matrix by dictionary to each face sample standard deviation in each storehouse according to 32 × 32 size carry out pre-service and it formed respectively the column vector of 1024 × 1, i.e. N=1024.To 40 people in ORL storehouse, everyone random selecting 5 face's samples are totally 200 atom compositions dictionary library, now P=40, Q=5; To 15, Yale storehouse different people, everyone random selecting 8 face's samples are totally 120 atom compositions dictionary library, now P=15, Q=8; To 38, Yale-E storehouse different people, everyone random selecting 50 face's samples are totally 1900 atom compositions dictionary library, now P=38, Q=50; The people different to 68, PIE storehouse, everyone random selecting 40 face's samples are totally 2720 atom compositions dictionary library, now P=68, Q=40.To each face database residue sample, random selecting 5 samples are as test signal as far as possible, and each identification all repeats 10 experiments, 10 experimental results is got arithmetic mean and carries out discrimination analysis as net result.

(1) projection matrix Optimal Parameters is arranged

Choosing of A, η value:

First test revises constant η to the impact of system performance.Setting compression projection value M=80, compressibility is 1024/80, to different η values, by this paper Optimization Algorithm projection matrix Φ.What Fig. 1 described is with η change curve for different face database system recognition rate.From Fig. 1 analysis, for Yale storehouse and Yale-E storehouse, revise constant η and system recognition rate is not played a role in improving, even also can reduce discrimination when η is too large, see η > 0.06 black line variation tendency in figure; And for ORL storehouse and PIE storehouse, the η suitably chosen improves system recognition rate really.Consider, fixing correction constant η=0.03 in subsequent simulation, for these four face databases, Yan Junke obtains good recognition effect.

Choosing of B, M value:

From CS theoretical analysis, when compressing projection value M and being larger, the precision of system reconstructing image is also relatively higher, but the pressure of corresponding now channel transmission data and background process data is also larger.Therefore for different application scenarioss, weigh the advantages and disadvantages.Mainly verify the impact chosen system recognition rate of M value herein, for different M values, respectively by Optimization Algorithm projection matrix Φ, Fig. 2 description of the present invention is with M change curve for different face database system recognition rate.From Fig. 2 analysis, system recognition rate is not along with compression projection value M monotone variation.Different M value, Yale storehouse discrimination is substantially constant; For ORL storehouse and Yale-E storehouse, as M=80, system recognition rate is stabilized in a more satisfactory position; And although PIE storehouse discrimination is not increase along with M value dullness, still also has the trend risen on the whole.Consider validity problem, fix M=80 in subsequent simulation, namely compressibility is 1024/80.

(2) CSC performance test

Test signal is carried out projection compression according to the above-mentioned projection matrix designed, then carries out discriminator to projection value, sorting technique adopts KNN, SVM, NNSRC and CSC herein respectively, adds up as following table 1 discrimination of four face databases:

The different sorter discrimination of table 1 compares

From table 1, for ORL, Yale and Yale-E tri-face databases, CSC all obtains maximum system recognition rate, but when being applied to PIE storehouse, effect is slightly worse than NNSRC system.

(3) projection matrix optimized algorithm performance test

Test signal is carried out projection compression according to the above-mentioned projection matrix designed, then carries out discriminator to projection value, sorting technique adopts different compression algorithm respectively, adds up as following table 2 discrimination of four face databases:

The different compression method discrimination of table 2 compares

Table 2 data show, projection matrix method for designing of the present invention all reaches maximal value relative to stochastic sampling and PCA on system recognition rate, especially to the improvement situation in Yale storehouse and PIE storehouse; But relative to the situation without compression, PIE storehouse discrimination is still lower.The selected part emulation indication of 4.1 joint M values is to PIE storehouse, and system recognition rate increases the trend be also improved with M, therefore attempt continuing to increase M, to PIE storehouse system recognition rate change curve as shown in Figure 3.As seen from Figure 3, to PIE face database, when M value gets 120, system recognition rate has exceeded the situation without compression in table 2, and works as M=240, and system recognition rate reaches 98.24% especially, and now compressibility is 1024/240.

(4) image reconstruction measure of merit

Projection matrix optimized algorithm of the present invention is applied to CSC, on backstage, image reconstruction is carried out to classification results.If test signal is reconstruction signal is the square error (Mean Square Error, MSE) of the two is defined as:

${\mathrm{\&sigma;}}_{\mathrm{mse}}\stackrel{\mathrm{\&Delta;}}{=}\frac{1}{N}{\left|\right|\hat{x}-x\left|\right|}_2^2---\left(22\right)$

Signal reconstruction performance adopts Y-PSNR (Peak Signal to Noise Ratio, PSNR) to weigh, and is defined as follows:

${\mathrm{\&sigma;}}_{\mathrm{psnr}}\stackrel{\mathrm{\&Delta;}}{=}10\&times;\log 10\left[\frac{{(2^r-1)}^2}{{\mathrm{\&sigma;}}_{\mathrm{mse}}}\right]---\left(23\right)$

Wherein, r=8 represents the number of coded bits of each pixel.Fig. 4 depicts σ _psnralong with the change curve of compression projection value M.Each face database σ in Fig. 4 _psnrsubstantially identical with the trend of system recognition rate in the variation tendency of M and Fig. 4, all do not increase with M value dullness, but general trend is in rising.

Compared to the shortcoming and defect of prior art, the present invention has following beneficial effect: the sorter that the present invention is based on compressed sensing, carry out projection compression to input signal, transmission projection value, backstage utilizes the rarefaction representation error of projection value to carry out discriminator to input signal; In addition, the projection matrix that the present invention is directed to system is optimized design, defines new estimating and makes the Gram matrix approximation one of equivalent dictionary pass through the dictionary Gram matrix of correction and utilize matrix decomposition to try to achieve the analytic solution of corresponding best projection matrix by design projection matrix.Simulation result confirms suitable projection matrix, and such recognition methods can reduce the pressure of system processes data on the one hand, effectively can improve system recognition rate on the other hand.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (4)

1. based on a face identification method for compressed sensing, it is characterized in that, comprise the following steps:

S1, according to face sample, require structure dictionary library Ψ=[Ψ according to setting ₁..., Ψ _p..., Ψ _p], facial image x will be tested ₀pre-service forms column vector x;

S2, design projection matrix Φ according to structure dictionary library Ψ;

S3, by the projection value y input function of column vector x under projection matrix Φ ${\hat{s}}_p=V_p\left[\begin{array}{c}{\mathrm{\&Sigma;}}_p^{-1}{\tilde{y}}_1\\ {\tilde{s}}_2\end{array}\right]$ Solve after p traverses P from 1, try to achieve all wherein, P is the quantity of individual face sample, V _p, Σ _pwith tried to achieve by projection matrix Φ, dictionary library Ψ and input projection value y, for arbitrary dimension is vector; Pass through function $\hat{p}=\arg {\min }_p{\left|\right|y-\mathrm{\&Phi;}{\mathrm{\&psi;}}_p{\hat{s}}_p\left|\right|}_2^2,s.t.p\&Element;[1,P]$ Right differentiate, export and differentiate type wherein, wherein be called projection matrix; the sample set of p people, it is the sparse coefficient of dictionary sub-block p;

S4, differentiate type according to described output reconstructed image data is permutatation obtains reconstructed image.

2., as claimed in claim 1 based on the face identification method of compressed sensing, it is characterized in that, also comprised before step S1

S0, input starting condition, described starting condition comprises face storehouse sample and the test facial image x of the composition of sample of P Ge Ren people face ₀.

3., as claimed in claim 1 based on the face identification method of compressed sensing, it is characterized in that, in step sl, the construction process that described dictionary library is comprises the following steps:

Suppose to store P Ge Ren face sample in a face database, wherein, everyone has again the sample of many different angles, different expression, different light, and the size of each sample is all identical;

Choose the individual different sample of its Q at random to everyone, each sample image forms a column vector according to same queueing discipline and is l respectively ₂norm normalized, size is set to N × 1, as the atom of in dictionary library, forms dictionary library:

To arbitrary 1≤p≤P, dictionary sub-block the sample set of p people, wherein, L=PQ; To 1≤1≤L, and || ψ _l|| ₂=1 is a column vector of dictionary.

4., as claimed in claim 2 based on the face identification method of compressed sensing, it is characterized in that, in step s 2, described projection matrix Φ function is defined as:

$\widehat{\mathrm{\&Phi;}}=U\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{11}& 0\end{array}\right]{\left[\begin{array}{cc}{V}_{11}& 0\\ 0& V_{22}\end{array}\right]}^T{U}_{\mathrm{\&Psi;}}^T;$ Wherein, the orthogonal matrix of U to be arbitrary dimension be M × M; V ₂₂being arbitrary dimension is orthogonal matrix; U _Ψthe U matrix that the SVD of Ψ is decomposed, to W ₁₁characteristics of decomposition value V ₁₁.