CN104951756A

CN104951756A - Face recognition method based on compressed sensing

Info

Publication number: CN104951756A
Application number: CN201510309822.2A
Authority: CN
Inventors: 于爱华; 李刚; 常丽萍; 李胜; 白煌; 姜倩茹; 洪涛; 徐智星; 候北平
Original assignee: Zhejiang Lover Health Science and Technology Development Co Ltd
Current assignee: Zhejiang Lover Health Science and Technology Development Co Ltd
Priority date: 2015-06-08
Filing date: 2015-06-08
Publication date: 2015-09-30

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

Face recognition method based on compressed sensing

Technical Field

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

Background

The face recognition technology is receiving high attention from academia as one of the important research directions of machine vision and image processing technology. With the continuous and deep application of digital technology, the resolution of daily images is higher and higher, which puts high demands on hardware devices for image information acquisition, transmission, storage, processing and the like. To alleviate the pressure of information storage and transmission, the current solution is signal compression, such as the discrete cosine transform-based JPEG standard and the wavelet transform-based JPEG2000 standard.

The traditional mode identification process comprises image acquisition, image compression, image decompression, feature extraction and image identification, wherein the identification technology generally adopts high-speed sampling of image information, most redundant information is discarded according to the correlation among image data pixel points to obtain compressed data for transmission, a background receiving end reconstructs an image, and image features are extracted for identity identification.

Because the traditional face recognition technology needs to sample images at high speed and compress a large amount of data to transmit to a background for identity judgment, the traditional face recognition technology puts high requirements on channels and image processing hardware equipment, and the system recognition accuracy is not high in a complex environment.

Disclosure of Invention

The invention aims to provide a face recognition method and a face recognition system based on compressed sensing, and aims to solve the problems that the existing face recognition technology puts high requirements on channels and image processing hardware equipment and is low in recognition accuracy.

The invention is realized in such a way that a face recognition method based on compressed sensing comprises the following steps:

s1, constructing a dictionary base psi ═ psi according to the setting requirement according to the face sample₁,...,Ψ_p,...,Ψ_P]To test the face image x₀Preprocessing to form a column vector x;

s2, designing a projection matrix phi according to the construction dictionary library psi;

s3, inputting the projection value y of the column vector x under the projection matrix phi into a function

Solving forWhen P is traversed from 1 to P, allWherein P is the number of individual face samples, V_p、Σ_pAndthe projection matrix phi, the dictionary base psi and the input projection value y are used to obtain,is of any size ofThe vector of (a); passing function

<math> <mrow> <mover> <mi>p</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>arg</mi> <msub> <mi>min</mi> <mi>p</mi> </msub> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <mi>Φ</mi> <msub> <mi>ψ</mi> <mi>p</mi> </msub> <msub> <mover> <mi>s</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> <mo>,</mo> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mi>p</mi> <mo>&Element;</mo> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mi>P</mi> <mo>]</mo> </mrow> </math>

To pairPerforming discrimination and outputting discrimination typeWherein, thereinReferred to as the projection matrix.Is a sample set of the p-th person,sparse coefficients of the dictionary sub-block p;

s4, judging type according to the outputReconstructing the image data intoRearrangingA reconstructed image is obtained.

Preferably, the method further comprises the step of before step S1

S0, inputting initial conditions, wherein the initial conditions comprise face library samples formed by P personal face samples and test face images x₀。

Preferably, in step S1, the construction process of the dictionary library includes the following steps:

suppose that a face library stores P face samples, where each person has many samples with different angles, different expressions, and different illuminations, and the size of each sample is the same;

randomly selecting Q different samples for each person, forming a column vector by each sample image according to the same arrangement rule and respectively doing l₂Norm normalization processing, the size of which is set to be Nx 1, and the norm normalization processing is used as an atom in a dictionary library to form the dictionary library:

for any sub-block of dictionary with P being more than or equal to 1 and less than or equal to PIs a sample set of a pth person, where L ═ FQ; for 1 ═ L ≦ L,and | | | ψ_l||₂1 is a column vector of the dictionary.

Preferably, in step S2, the projection matrix Φ is functionally defined as:

wherein U is an orthogonal matrix of arbitrary size mxm; v₂₂Is of any size ofAn orthogonal matrix of (a); u shape_ΨIs the U matrix of the SVD decomposition for Ψ, for W₁₁Decomposition eigenvalue V₁₁。

Aiming at the characteristic that redundant information in an image is not needed in the traditional identification technology, the Compressed Sensing (CS) theory adopts a technology of directly compressing and sampling an image signal, thereby avoiding resource waste caused by high-speed sampling and information discarding processes. For an input high-dimensional signalLinearly projecting the projection value y on a matrix phi to obtain a projection value y, wherein the process is as follows:

wherein,referred to as the projection matrix. The theory of CS is that when M<<N, how to solve the original high-dimensional signal x for a given projection value y and projection matrix Φ. It is clear that equation (1) is an underdetermined problem, i.e., the number of equations is less than the number of unknowns, and there are countless multiple solutions. Therefore, x also needs to be limited in the solving process. The sparsity constraint is a key factor in CS theory, and this condition requires that the signal x can be composed of L basis vectors { psi_lLinearly means:

wherein,called a dictionary (matrix), s is a sparse vector with most elements zero, if s contains K non-zero elements, x is called K sparse at Ψ. Substituting the formula (2) into the formula (1)) to obtain:

wherein,referred to as an equivalent dictionary. If the projection value y is transmitted, the receiving end uses the sparse representation coefficient s of the projection value y under the equivalent dictionary D to perform image reconstruction and recognition classification, which is a Compressed Sensing based Classifier (CSC) to be researched herein, and includes three processes of Compressed sampling, sparse representation and recognition reconstruction.

When M < < N, the data volume of y is far less than x, which greatly reduces the pressure of transmitting data through a channel and storing and processing data in the background. However, in practical application, the projection matrix Φ has a large influence on image reconstruction and recognition effects, and therefore, the projection matrix optimization design is also one of the main contents to be studied herein. For the CS system, the projection matrix has the functions of compressing the input signal on one hand and extracting the characteristics of the signal on the other hand, and the projection matrix after the optimization design can greatly improve the accuracy of signal identification, classification and recovery.

Based on the theory, the invention overcomes the defects of the prior art, and provides a face recognition method and a face recognition system based on compressed sensing.

Drawings

FIG. 1 is a graph of the change of the recognition rate with the change of the face recognition method based on compressed sensing;

FIG. 2 is a curve of change of the recognition rate with M of the face recognition method based on compressed sensing;

FIG. 3 is a curve of change of the recognition rate of the face recognition method based on compressive sensing to the PIE library system along with M;

FIG. 4 is a curve of the face recognition method based on compressed sensing varying with M.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

A face recognition method based on compressed sensing is characterized by comprising the following steps:

s1, constructing a dictionary base psi ═ psi according to the setting requirement according to the face sample₁，...，Ψ_p，...，Ψ_P]To test the face image x₀The pre-processing forms a column vector x.

In step S1, assume that a face library stores P face samples, each of which has a plurality of samples with different angles, different expressions, and different illuminations, and each sample has the same size. Randomly selecting Q different samples for each person, forming a column vector by each sample image according to the same arrangement rule and respectively doing l₂Norm normalization, with size set to N × 1, as an atom in the dictionary library, thus forming the dictionary library:for any sub-block of dictionary with P being more than or equal to 1 and less than or equal to PIs the sample set of the pth individual, and is easy to see L ═ PQ. L is more than or equal to 1 and less than or equal to L,and | | | ψ_l||₂1 is one of a dictionaryColumn vectors, i.e., atoms.

Solving forWhen P is traversed from 1 to P, allWherein P is the number of individual face samples, V_p、Σ_pAndthe projection matrix phi, the dictionary base psi and the input projection value y are used to obtain,is of any size ofThe vector of (a); s4, pass function

<math> <mrow> <mover> <mi>p</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>arg</mi> <msubsup> <mrow> <munder> <mi>min</mi> <mi>p</mi> </munder> <mrow> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <mi>Φ</mi> <msub> <mi>ψ</mi> <mi>p</mi> </msub> <msub> <mover> <mi>s</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> <mo>,</mo> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mi>p</mi> <mo>&Element;</mo> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mi>P</mi> <mo>]</mo> </mrow> </math>

To pairPerforming discrimination and outputting discrimination typeWherein, inReferred to as a projection matrix;is a sample set of the p-th person,sparse coefficients of dictionary sub-block p.

In step S3, for any input test sample, it is first resized and formed into an N × 1 column vector x according to the above-mentioned rule for arranging images, and then the expression equation of x under the dictionary base Ψ is:

x＝Ψs+∈ (4)

wherein,is indicative of an error. The invention is based on CS face recognition, and the test sample x is compressed and projected to obtain a projection signal(M < N), the procedure is as follows:

<math> <mrow> <mi>y</mi> <mo>=</mo> <mi>Φx</mi> <mo>=</mo> <mi>ΦΨs</mi> <mo>+</mo> <mi>Φ</mi> <mo>&Element;</mo> <mover> <mo>=</mo> <mi>Δ</mi> </mover> <mi>Ds</mi> <mo>+</mo> <mi>e</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,to design a projection matrix with certain properties,in the form of an equivalent dictionary,is the projection domain error. CS theory requires that signal x is sparsely represented in dictionary Ψ, i.e., s contains many zero elements, so that s can be accurately reconstructed from the measurement y. For the face recognition method of the invention, the dictionary database is composed of samples of P different persons, so that the property of block sparsity is utilized when s is reconstructed.

Definition of

s = {[s_{1}^{T}, . . ., s_{p}^{T}, . . ., s_{P}^{T}]}^{T},

Any of the p is a group of p,rewrite (5) formula:

y＝Φ(Ψ₁s₁+…+Ψ_ps_p+…+Ψ_Ps_P)+e (6)

for all the selection cases of s, the requirement is that non-zero elements can only exist in a certain s_pAnd the other parts are all zero values. Resolving formula (6) into the following problem:

<math> <mrow> <msub> <mover> <mi>s</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <mi>arg</mi> <munder> <mi>min</mi> <msub> <mi>s</mi> <mi>p</mi> </msub> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <mi>Φ</mi> <msub> <mi>Ψ</mi> <mi>p</mi> </msub> <msub> <mi>s</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> <mo>,</mo> <mo>&ForAll;</mo> <mi>p</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>P</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

in obtainingThen, the result is applied to a face recognition method, and the following problems are formed:

<math> <mrow> <mover> <mi>p</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>arg</mi> <munder> <mi>min</mi> <mi>p</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <mi>Φ</mi> <msub> <mi>Ψ</mi> <mi>p</mi> </msub> <msub> <mover> <mi>s</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> <mo>,</mo> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mi>p</mi> <mo>&Element;</mo> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mi>P</mi> <mo>]</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

obtained at this timeIs the result of the method's discrimination of the input x.

Given a well-designed projection matrix Φ, the difficulty of the above problem is mainly focused on how to solve equation (7) accurately. For a certain p, let(7) The formula cost function translates into:

let D_pThe Singular Value Decomposition (SVD) of (1) is as follows:

wherein,

substituting the formula (10) into the formula (9) to obtain:

order to

\tilde{y} = [\begin{matrix} {\tilde{y}}_{1} \\ {\tilde{y}}_{2} \end{matrix}], \tilde{s} = [\begin{matrix} {\tilde{s}}_{1} \\ {\tilde{s}}_{2} \end{matrix}]

WhereinAndall sizes of(11) The formula is developed as follows:

note that the second term on the right of the equal sign of the above formula is associated with s_pIrrelevant, therefore when:

(12) the minimum value is obtained. In this case, the solution of the formula (7) is:

wherein, V_p、Σ_pAndis obtained from the projection matrix, the dictionary and the input projection value,is of any size ofThe vector of (2). When P is traversed from 1 to P, allIs obtained by the formula (8)The result of the input x is known.

S4, judging type according to the outputReconstructing the image data intoAnd rearranging to obtain a reconstructed image.

In step S4, since the method is to transmit the compressed projection value y to the background for determination, if it is required to reconstruct the input image at this time, it is possible to reconstruct the image data into image data based on the determination result

According to the CS-based face recognition method, the projection value is transmitted instead of the image itself, so that the working efficiency is improved, and the bandwidth pressure of a channel for transmitting a large amount of data is relieved.

In a further implementation process, in order to achieve greater improvement in the accuracy of the input value determination, in the embodiment of the present invention, in step S2, the designing the projection matrix Φ according to the constructed dictionary library Ψ is defined as:

wherein U is an orthogonal matrix of arbitrary size mxm; v₂₂Is of any size ofAn orthogonal matrix of (a); wherein U is an orthogonal matrix of arbitrary size mxm; v₂₂Is of any size ofAn orthogonal matrix of (a); u shape_ΨIs the U matrix of the SVD decomposition for Ψ, for W₁₁Decomposition eigenvalue V₁₁。

In the embodiment of the present invention, the design process of the projection matrix Φ is specifically as follows:

using said marks, dictionary sub-blocksDictionary libraryEquivalent dictionaryProjection matrixWherein

The projection matrix optimization in the CS system is based on the following equation:

wherein, | | - | F is defined as the Frobenius norm, G is the Gram matrix of the equivalent dictionary D, G is only related to the projection matrix phi for a given dictionary Ψ, G_tIs a target Gram matrix. (14) The purpose of the formula is to enable the Gram matrix corresponding to the equivalent dictionary to approximate a given target Gram matrix with certain properties by designing a projection matrix.

For signals which cannot be completely sparsely represented under a dictionary, such as image signals, if the projection matrix phi is designed to enable the equivalent dictionary D to have the property of the dictionary psi, the CS system has very good performance, and the target Gram matrix is selected asFor the face image sample of the invention, the sparse representation equation under the dictionary Ψ is as formula (4), and in general, ∈ is not all-zero vector, so that G can be considered_ΨThe projection matrix Φ is designed as the target Gram matrix.

In the embodiment of the present invention, the dictionary library Ψ is composed of P face samples of different persons, and even a sample of the same person may have a poor correlation due to differences in angle, expression, illumination, and the like, that is, the same sub-block Ψ_pThe inner product between each two atoms is small. On the other hand, for two different people, i.e., different dictionary sub-blocks, we want the correlation between atoms as small as possible. Order:

the target Gram matrix is modified as follows:

G_t＝Ψ^τΨ+Δ (15)

wherein the correction matrixCan be expressed as:

for any 1 ≤ i ≤ P, 1 ≤ j ≤ P, and Δ_ijAll of which are equal to Ψ_ijThe same; m is more than or equal to 1 and less than or equal to L, n is more than or equal to 1 and less than or equal to L_mnIs the element of the corresponding position in Δ and:

<math> <mrow> <msub> <mi>δ</mi> <mi>mn</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mo>-</mo> <mi>η</mi> <mo>,</mo> </mtd> <mtd> <mi>i</mi> <mo>&NotEqual;</mo> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mi>η</mi> <mo>,</mo> </mtd> <mtd> <mi>i</mi> <mo>=</mo> <mi>j</mi> <mo>,</mo> <mi>m</mi> <mo>&NotEqual;</mo> <mi>n</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>i</mi> <mo>=</mo> <mi>j</mi> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mi>n</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>

where η is a small constant greater than zero, called the correction constant. G constructed by the formula (15)_tThe method not only reduces the correlation among atoms of different dictionary sub-blocks, but also properly strengthens the correlation among atoms in the same dictionary sub-block. It should be noted that each atom in the dictionary library is normalized, i.e. 1 ≦ L, | | ψ is arbitrary_l||₂1, the largest interatomic product is therefore 1, i.e. G_ΨDiagonal elements of (a). In order to update G_tThe physical significance is more clear, and the invention forces G_tThe value of the medium element is at most 1, so that the diagonal elements do not change their size, while the non-diagonal elements are not allowed to exceed 1 and be larger than zero after correction, which imposes certain requirements on the selection of the correction constant η.

Thus, the problem of forming the projection matrix design herein is as follows:

wherein G is_tIs defined by the formula (15).

The SVD decomposition for the dictionary Ψ is as follows:

wherein,easy obtaining:

wherein

Order toThe size of the upper left corner of the representation matrix W isThen the cost function of equation (17) can be expanded as:

order to

Is thatThe size of the upper left corner isThen (18) is converted into:

the last two items on the right side of the equal sign of the above formula are independent of the projection matrix and are defined(17) The formula is equivalent to:

setting:

are respectively asAnda form of eigenvalue decomposition, requirement Λ_WAnd Λ_tAll in descending order, as known from the document "r.a. horns and c.r.johnson, Matrix Analysis, Cambridge University Press,2nd edition, 2012", Corollary 7.4.9.3 on page 468):

<math> <mrow> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mover> <mi>W</mi> <mo>~</mo> </mover> <mn>11</mn> </msub> <mo>-</mo> <msubsup> <mover> <mi>G</mi> <mo>~</mo> </mover> <mi>t</mi> <mn>11</mn> </msubsup> <mo>|</mo> <mo>|</mo> </mrow> <mi>F</mi> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>Λ</mi> <mi>W</mi> </msub> <mo>-</mo> <mo>-</mo> <msub> <mi>Λ</mi> <mi>t</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mi>F</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow> </math>

when getting V_w＝V_tThe above formula is true. Due to the limitations of the projection matrix phi,does not exceed M, so Λ_WIs at most M, when the M non-zero elements are equal to Λ_tWhen M elements with the maximum absolute value are included, (20)) the right side of the equation inequality sign takes the minimum value, and the eigenvalue matrix at this time is recorded asTherefore, when:

(20) the equation equals and the minimum value is obtained. Further can obtainW is to be₁₁Carrying out SVD decomposition to obtain:

from this, one can choose:

wherein, V₂₂Is an orthogonal matrix of arbitrary size (N-N) x (N-N). Because of the fact thatThe above discussion yields a solution of equation (17):

where U is an orthogonal matrix of arbitrary size M × M.

From the above discussion, it can be seen that the present invention is directed to a projection matrix ΦThe optimization design is only related to the dictionary Ψ and the correction constant η, so for fixed Ψ and η, the system only needs to obtain Φ offline, a projection matrix design step is not needed for each input test image, and the formula (21) is an analytic solution result, so that the calculation cost is not high. In addition, there are two degrees of freedom U and V in this result₂₂This provides the possibility to further improve the system performance.

In order to verify the actual effect of the invention, in the embodiment of the invention, the performance of the CS-based face recognition method and the improvement condition of the projection matrix optimization on the system performance are verified through experimental simulation. The face sample library used in the experiment comprises ORL library, Yale-EXTENDED library (recorded as Yale-E) and CMU PIE library (recorded as PIE).

Dictionary is respectively constructed for each face library in simulationP, each dictionary sub-blockThe invention designs a projection matrix through a dictionaryEach face sample in each bank is preprocessed in a size of 32 × 32 and formed into a 1024 × 1 column vector, i.e., N — 1024. For 40 persons in the ORL library, randomly selecting 200 atoms of 5 face samples from each person to form a dictionary library, wherein P is 40, and Q is 5; for 15 different Yale library people, each person randomly selects 8 face samples and 120 atoms to form a dictionary library, wherein P is 15, and Q is 8; for 38 different Yale-E library people, each person randomly selects 50 face samples, and 1900 atoms form a dictionary library, wherein P is 38, and Q is 50; for 68 different people in the PIE library, 2720 face samples are randomly selected from each person to form a dictionary library, wherein P is 68, and Q is 40. For the rest samples in each face library, 5 samples are randomly selected as test signals as much as possible, and 10 experiments are repeated for each identificationAnd taking the arithmetic mean of the 10 experimental results as a final result to carry out recognition rate analysis.

(1) Projection matrix optimization parameter setting

A. Selecting the eta value:

the influence of the correction constant η on the system performance is firstly tested. And setting the compressed projection value M to be 80, wherein the compression ratio is 1024/80, taking values of different eta, and designing a projection matrix phi through a text optimization algorithm. Figure 1 depicts the system recognition rate versus η for different face libraries. From the analysis of FIG. 1, for Yale library and Yale-E library, the correction constant eta has no improvement effect on the system recognition rate, and even when eta is too large, the recognition rate can be reduced, wherein eta is greater than 0.06 black line change trend in the figure; for the ORL library and the PIE library, the system identification rate is improved by properly selecting eta. Comprehensively, the fixed correction constant η is 0.03 in the subsequent simulation, and a good recognition effect can be obtained for all the four face libraries.

B. Selecting an M value:

from the CS theoretical analysis, when the compressed projection value M is larger, the accuracy of the system to reconstruct the image is relatively higher, but the corresponding pressure of the channel transmission data and the background processing data is also larger at this time. Therefore, for different application scenarios, the advantages and disadvantages are balanced. The influence of the selection of the M value on the system recognition rate is mainly verified, for different M values, a projection matrix phi is designed through the optimization algorithm, and a curve of the system recognition rate changing along with M for different face libraries is depicted in figure 2. From the analysis of fig. 2, the system recognition rate does not vary monotonically with the compressed projection value M. Different M values, the Yale library recognition rate is basically unchanged; for the ORL library and the Yale-E library, when M is 80, the system identification rate is stabilized at a more ideal position; on the other hand, the PIE library tends to increase in recognition rate as a whole, rather than monotonically increasing with the M value. In consideration of the effectiveness, M is fixed to 80 in the subsequent simulation, that is, the compression ratio is 1024/80.

(2) CSC Performance testing

The test signals are subjected to projection compression according to the designed projection matrix, and then the projection values are identified and classified, the classification method respectively adopts KNN, SVM, NNSRC and CSC of the text, and the identification rate statistics of the four face libraries are as follows 1:

TABLE 1 comparison of recognition rates of different classifiers

As can be seen from Table 1, the CSC all obtained the maximum system recognition rate for the three face libraries ORL, Yale and Yale-E, but the effect is slightly worse than that of the NNSRC system when the CSC is applied to the PIE library.

(3) Projection matrix optimization algorithm performance test

The test signal is subjected to projection compression according to the designed projection matrix, and then the projection values are identified and classified, wherein the classification method respectively adopts different compression algorithms, and the identification rate statistics of four face libraries are as follows 2:

TABLE 2 comparison of recognition rates for different compression methods

The data in table 2 show that the projection matrix design method of the present invention achieves the maximum value in the system recognition rate compared with the random sampling and the PCA, especially the improvement of the Yale library and the PIE library; but the PIE library recognition rate remains low relative to the case without compression. The simulation of the selected part of the M value of section 4.1 indicates that the system recognition rate of the PIE library has a tendency to improve along with the increase of M, so that the system recognition rate of the PIE library is attempted to be increased continuously, and the change curve of the system recognition rate of the PIE library is shown in figure 3. As can be seen from fig. 3, for the PIE face library, when the value of M is 120, the system recognition rate already exceeds the uncompressed condition in table 2, and when M is 240, the system recognition rate reaches 98.24%, and the compression rate is 1024/240.

(4) Image reconstruction effect testing

The projection matrix optimization algorithm is applied to the CSC, and image reconstruction is carried out on the classification result in the background. Let the test signal beReconstructing the signal asThe Mean Square Error (MSE) of the two is defined as:

the Signal reconstruction performance is measured by Peak Signal to Noise Ratio (PSNR), and is defined as follows:

wherein r ═ 8 represents the number of coded bits per pixel. FIG. 4 depicts σ_psnrThe variation curve of the projection value M is compressed. Each face bin σ in fig. 4_psnrThe trend along with M is basically consistent with the trend of the system identification rate in FIG. 4, and is not monotonically increased along with the value of M, but the general trend is rising.

Compared with the defects and shortcomings of the prior art, the invention has the following beneficial effects: the invention is based on a compressed sensing classifier, performs projection compression on input signals, transmits projection values, and a background uses sparse representation errors of the projection values to recognize and classify the input signals; in addition, the invention carries out optimization design aiming at the projection matrix of the system, defines a new measure, enables the Gram matrix of the equivalent dictionary to approach a corrected dictionary Gram matrix by designing the projection matrix, and utilizes matrix decomposition to obtain an analytic solution corresponding to the optimal projection matrix. Simulation results prove that for a proper projection matrix, the identification method can reduce the pressure of the system for processing data on one hand and can effectively improve the identification rate of the system on the other hand.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims

1. A face recognition method based on compressed sensing is characterized by comprising the following steps:

To pairPerforming discrimination and outputting discrimination typeWherein, thereinReferred to as a projection matrix;is a sample set of the p-th person,is the sparse coefficient of dictionary sub-block p;

2. The method for recognizing human face based on compressed sensing according to claim 1, further comprising before step S1

3. The compressed sensing-based face recognition method according to claim 1, wherein in step S1, the dictionary library is constructed by the following steps:

for any sub-block of dictionary with P being more than or equal to 1 and less than or equal to PIs a sample set of p individuals, where L = PQ; for L which is more than or equal to 1 and less than or equal to 1,and | | | ψ_l||₂1 is a column vector of the dictionary.

4. The method for recognizing a human face based on compressed sensing as claimed in claim 2, wherein in step S2, the projection matrix Φ is functionally defined as: