A face recognition method based on low-rank residual representation of deep dictionary

Abstract

The present invention discloses a face recognition method based on a deep dictionary low-rank residual representation, obtains an original face image, constructs and trains a deep network model suitable for a deep dictionary low-rank residual representation, inputs the preprocessed face image into the deep network model for training, and a feature extraction module in the deep network model extracts the face image to obtain a feature vector; the dictionary training module uses the feature vector to train the dictionary; the sparse representation module finds a set of bases in the dictionary so that the face data is represented as a linear combination of these bases, and then outputs sparse features; the sparse feature vectors corresponding to the real face image are compared and retrieved in a database to determine whether they can be recognized. The present invention innovatively combines low-rank residual representation and deep dictionary learning, which has significant advantages in processing high-dimensional data and feature extraction, and provides higher accuracy and robustness for face recognition.

Description

Technical Field

[0001] The present invention relates to the fields of machine learning and image processing, and in particular to a deep dictionary low-rank residual representation method for face recognition Background Art

[0002] Existing face recognition technologies mainly rely on feature extraction and classifier design during data dimensionality reduction. However, many methods have limited performance when processing images with complex backgrounds and variable lighting conditions. Traditional feature extraction methods are difficult to adapt to the needs of large-scale data, and the generalization ability of the model is poor. Low-rank representation effectively captures the edge information of the image by extracting the low-rank structural information of the data during the dimensionality reduction process. Deep dictionary learning improves the representation ability of the model by constructing a multi-layer network structure and extracting the features of the image layer by layer. However, existing low-rank representation and deep dictionary learning methods have problems such as high computational complexity and difficulty in processing high-dimensional data. Therefore, there is an urgent need for a deep dictionary learning method with low-rank residual representation that does not lose edge structure information during data dimensionality reduction to improve the accuracy and robustness of face recognition.

[0003] In recent years, the field of deep dictionary learning (DDL) has developed rapidly, and dictionary learning based on auto-encoders is one of the representative works in this field. Since then, many follow-up works have been carried out, including joint deep dictionary learning (JDDL), hierarchical location-aware deep dictionary learning for classification (HILADLE), dimension reduction and dictionary learning framework for high-dimensional data classification (NDRDL), and deep dictionary learning and coding network for limited data image recognition (DDLCN).

[0004] Despite rapid progress, processing high-dimensional data still requires a lot of time and computing resources. Some methods propose low-rank dictionary learning. Data dimensionality reduction can reduce the dimension of the data set, speed up the calculation, eliminate redundant features in the data set, and retain the most important features, thereby improving the performance and generalization ability of the model and enhancing the robustness and accuracy of the model. However, although data dimensionality reduction can remove noise in the data, it may also ignore discriminative detail features. The deep dictionary learning method based on low-rank residual representation uses deep learning to adaptively learn dictionaries from data, improving the robustness and adaptability of feature extraction. This integrated method not only enhances the discriminative ability of dictionary atoms, but also maintains the integrity of the original data structure through strategic constraints on the metric matrix and dictionary, while retaining the edge feature structure of image information and improving the classification ability of images. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to solve the deficiencies in the prior art. In order to overcome the deficiencies in the prior art, a face recognition method based on low-rank residual representation of a deep dictionary is provided. Dictionary learning based on low-rank residual representation makes the dictionary representation of discriminative edge features richer and enhances the expressive power of dictionary atoms. At the same time, sparse representation allows the original information to be represented by a linear combination of dictionary atoms through sparse vectors, which can not only improve the recognition accuracy of face images, but also speed up the recognition speed of faces.

[0006] Technical solution: A face recognition method based on deep dictionary low-rank residual representation of the present invention comprises the following steps:

[0007] Step 1: Obtain the original face image and preprocess it. The preprocessing here includes grayscale correction, noise filtering and other links;

[0008] Step 2: Build and train a deep network model suitable for deep dictionary low-rank residual representation, input the preprocessed face image into the deep network model for training to obtain the corresponding feature vector; the deep network model includes a feature extraction module, a dictionary training module and a sparse representation module:

[0009] The feature extraction module extracts the preprocessed face image to obtain a feature vector X; the dictionary training module uses the feature vector X to train the dictionary D; the sparse representation module finds a set of bases in the dictionary so that the face data is represented as a linear combination of these bases, and then outputs sparse features;

[0010] Step 3, collect the real face image from the camera, input the real face image into the deep network model represented by the low-rank residual of the deep dictionary trained in step 2 to obtain the corresponding face sparse vector, and compare and search the face sparse vector in the database: the feature vector with the smallest difference between the face sparse vector in the database, if it meets the expected error, is considered to be a face image that the system can recognize.

[0011] Furthermore, the deep network model expression suitable for deep dictionary low-rank residual representation is as follows:

[0012]

[0013] The constraints in the above formula are as follows:

[0014] sP T P=I,E=X-DA

[0015] H(Ω) represents the encoder, which is used to extract high-level features of the data; G(Ω) represents the decoder, which is used to recover the input data; D = [d1, d2, …, d n ] represents a low-dimensional dictionary, the basis vector of all input data;

[0016] A=[a1,a2,…,a n ] represents a sparse vector, ‖A‖1 is a sparse constraint that makes the elements in the sparse vector A contain fewer non-zero elements, which is used for the linear combination of atoms in D;

[0017] The purpose is to preserve the edge structure information in the residual E as much as possible. Extract the low-rank structure in the residual E, P is the dimension reduction projection matrix of the low-dimensional dictionary D and the residual E, through

[0018] It means to make the structure of P's tensor space consistent with that in dictionary D.

[0019] Furthermore, the feature extraction model in the deep network model of step 2 uses the SIFT (Scale Invariant Feature Transform) algorithm to extract features (equivalent to the process of feature modeling of the face), and the obtained face feature vector X = [x1, x2, ..., x N ] indicates; x i Vectorization of two-dimensional data representing a sliding window;

[0020] The specific method is:

[0021] The input face image is divided into 8×8 small image blocks, and each image block is processed using the SIFT algorithm. The processed 8×8 block matrix is ​​vectorized to obtain a 64×1 feature vector. Finally, the obtained feature vectors are arranged together to obtain a 64*N matrix, where N is the number of feature vectors; X = [x1, x2, …, x N ].

[0022] Furthermore, the process of training the dictionary by the dictionary training module in the deep network model in step 2 is as follows:

[0023] The decoder recovers the reduced-dimensional data to obtain reconstructed data, and then calculates the difference between the reconstructed data and the original face image to obtain the residual structure, i.e., the residual E, which includes edge structure information.

[0024] The encoder performs PCA dimensionality reduction on the residual E to obtain a low-rank residual structure. When updating the dictionary D, the low-rank residual structure is used to enhance the representation of the dictionary D on the features, so that the atomic vectors in the trained dictionary matrix are more discriminative for the features (in the process of dimensionality reduction, there will be a certain loss of edge feature information between the reconstructed data and the original data. By extracting the edge information in the residual and performing a feature enhancement on the dictionary atoms, the trained dictionary can be more discriminative for the representation of the features).

[0025] Furthermore, the method for obtaining the sparse feature vector through the sparse representation module in the deep network model in step 2 is:

[0026] Combine the dictionary D obtained by the dictionary training module with the feature vector X obtained by the feature extraction module, and update the corresponding sparse vector A through solving the formula;

[0027] The goal of dictionary representation is to find a set of bases so that the information can be represented as a linear combination of these bases; the goal of sparse representation is to minimize the number of these bases to make the representation more concise and efficient.

[0028] Furthermore, the method for training a deep network model suitable for low-rank residual representation of a deep dictionary is:

[0029] Step I: Use the feature matrix obtained by the feature extraction module as the input of the autoencoder network, learn the more advanced feature representation in the encoding process, and perform residual calculation on the reconstructed data and the original data in the decoding stage to enter the next stage; learn the low-rank structural information in the residual, and update the dictionary and sparse representation coefficients in the dictionary learning stage;

[0030] Step II: Continuously train network parameters and calculate the loss values ​​of reconstructed data and original data. At the same time, use the back propagation of the deep network to update the network parameters to continuously reduce the loss value; modify the gradient descent weights after a certain number of iterations to better meet the target requirements;

[0031] Step III: Repeat steps I and II to optimize and adjust the parameters of the function and finally obtain a satisfactory loss value. When the loss value is less than the set threshold, it means that the training requirements are met.

[0032] Furthermore, the detailed method of step 3 is:

[0033] The face sparse vector of the real face image is searched and compared with the face feature vector in the database, and the identity information of the face is identified and judged according to the similarity between the two. A threshold is set. When the error is not greater than the threshold, the matching result is output and the recognition is considered successful.

[0034] The calculation formula of the threshold is as follows:

[0035] threshold≤‖a1-a2‖ 2 ;

[0036] a1 represents the tested feature vector, and a2 represents the most similar feature vector in the database obtained according to the dictionary. By calculating the error between them, it is shown that they have a high similarity.

[0037] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0038] (1) The present invention better fully represents the edge features: The low-rank residual representation helps to better extract the important features in the data, thereby improving the data representation effect and classification performance. Compared with the general deep dictionary learning method, this new representation method may be more suitable for processing complex data sets and classification tasks.

[0039] (2) Reduce computational complexity: The sparse low-rank residual representation of the dictionary may reduce computational complexity and improve the efficiency of the algorithm. This is particularly important in the case of large-scale datasets and complex models, which helps to speed up the processing of recognition tasks.

[0040] (3) During the training process of the deep network model, the present invention learns high-level feature representation through the autoencoder network, uses low-rank residual information to enhance the dictionary's ability to discriminate features, continuously adjusts network parameters to optimize the model, and ultimately achieves efficient and accurate face recognition. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the overall model architecture diagram of the present invention;

[0042] Figure 2 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0043] Figure 3 2 is an example diagram of a facial image residual in an embodiment. DETAILED DESCRIPTION

[0044] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0045] like Figure 1 As shown, the present invention provides a face recognition method based on deep dictionary low-rank residual representation, comprising the following steps:

[0046] Step 1: Obtain the original face image and preprocess it;

[0047] Step 2: Build and train a deep network model suitable for deep dictionary low-rank residual representation, input the preprocessed face image into the deep network model for training to obtain the corresponding feature vector; the deep network model includes a feature extraction module, a dictionary training module and a sparse representation module:

[0048] The feature extraction module extracts the preprocessed face image to obtain a feature vector X; the dictionary training module uses the feature vector X to train the dictionary; the sparse representation module finds a set of bases in the dictionary so that the face data is represented as a linear combination of these bases, and then outputs sparse features;

[0049] Step 3, collect the real face image from the camera, input the real face image into the deep network model represented by the low-rank residual of the deep dictionary trained in step 2 to obtain the corresponding face sparse vector, and compare and search the face sparse vector in the database: the feature vector with the smallest difference between the face sparse vector in the database, if it meets the expected error, is considered to be a face image that the system can recognize.

[0050] In this embodiment, the deep network model expression suitable for the deep dictionary low-rank residual representation is as follows:

[0051]

[0052] The constraints in the above formula are as follows:

[0053] sP T P=I,E=X-DA

[0054] H(Ω) represents the encoder, which is used to extract high-level features of the data; G(Ω) represents the decoder, which is used to recover the input data; D = [d1, d2, …, d n ] represents a low-dimensional dictionary, the basis vector of all input data;

[0055] A=[a1,a2,…,a n ] represents a sparse vector, ‖A‖1 is a sparse constraint that makes the elements in the sparse vector A contain fewer non-zero elements, which is used for the linear combination of atoms in D; Extract the low-rank structure of the edge structure in the residual E; P is the dimensionality reduction projection matrix of the low-dimensional dictionary D and the residual E, through Make the tensor subspace of P consistent with the structure in dictionary D.

[0056] The feature extraction module uses the SIFT algorithm to extract features, and the resulting face feature vector X = [x1, x2, ..., x N ] indicates; x i Represents the vectorization of two-dimensional data of a sliding window. The specific method is:

[0057] The input face image is divided into 8×8 small image blocks, and each image block is processed using the SIFT algorithm. The processed 8×8 block matrix is ​​vectorized to obtain a 64×1 feature vector. Finally, the obtained feature vectors are arranged together to obtain a 64*N matrix, where N is the number of feature vectors; X = [x1, x2, …, x N ].

[0058] The process of training a dictionary in the dictionary training module is as follows:

[0059] The decoder recovers the reduced-dimensional data to obtain reconstructed data, and then calculates the difference between the reconstructed data and the original face image to obtain the residual structure, i.e., residual E, which includes edge structure information.

[0060] The encoder performs PCA dimensionality reduction on the residual E to obtain a low-rank residual structure. When updating the dictionary D, the low-rank residual structure is used to enhance the representation of the dictionary D on the features, so that the atomic vectors in the trained dictionary matrix are more discriminative in representing the features.

[0061] The method for the sparse representation module to obtain sparse feature vectors is:

[0062] Combine the dictionary D obtained by the dictionary training module with the feature vector X obtained by the feature extraction module, and update the corresponding sparse vector A through solving the formula;

[0063] The goal of dictionary representation is to find a set of bases so that the information can be represented as a linear combination of these bases; the goal of sparse representation is to minimize the number of these bases to make the representation more concise and efficient.

[0064] The above method for training a deep network model suitable for deep dictionary low-rank residual representation is:

[0065] Step I: Use the feature matrix obtained by the feature extraction module as the input of the autoencoder network, learn the more advanced feature representation in the encoding process, and perform residual calculation on the reconstructed data and the original data in the decoding stage to enter the next stage; learn the low-rank structural information in the residual, and update the dictionary and sparse representation coefficients in the dictionary learning stage;

[0066] Step II: Continuously train network parameters and calculate the loss values ​​of reconstructed data and original data. At the same time, use the back propagation of the deep network to update the network parameters to continuously reduce the loss value; modify the gradient descent weights after a certain number of iterations to better meet the target requirements;

[0067] Step III: Repeat steps I and II to optimize and adjust the parameters of the function and finally get a satisfactory loss value. When the loss value is less than the set threshold, it means that the training requirements are met. Figure 2 shown.

[0068] The detailed method of step 3 of this embodiment is:

[0069] The face sparse vector of the real face image is searched and compared with the face feature vector in the database, and the identity information of the face is identified and judged according to the similarity between the two. A threshold is set. When the error is not greater than the threshold, the matching result is output and the recognition is considered successful.

[0070] The calculation formula of the threshold is as follows:

[0071] threshold≤‖a1-a2‖ 2 ;

[0072] a1 represents the tested feature vector, and a2 represents the most similar feature vector in the database obtained according to the dictionary. By calculating the error between them, it is shown that they have a high similarity.

[0073] In order to verify the feasibility of the technical solution of the present invention, the following description is given.

[0074] The present invention creatively proposes a deep network model suitable for low-rank residual representation of deep dictionaries, which solves the drawbacks of the existing joint dimensionality reduction and dictionary learning (JDRDL) framework. The existing JDRDL structure only uses linear transformation and linear combination of dictionary atoms to model data, which cannot capture the nonlinear structure in high-dimensional data, thereby limiting its classification performance.

[0075] The deep network model suitable for the low-rank residual representation of the deep dictionary of the present invention is combined with an autoencoder to nonlinearly map high-dimensional data to a low-dimensional space. Since there will be a certain loss of edge feature information between the reconstructed data and the original data during the dimensionality reduction process, the present invention further extracts the edge information in the residual to perform a feature enhancement on the dictionary atoms, thereby making the trained dictionary more discriminative for the representation of features. The formula is as follows:

[0076]

[0077] sP T P=I,E=X-DA

[0078] Among them, H(Ω)=W1x+b1 represents the feature encoding matrix of the i-th layer, G(Ω)=W2x+b2 represents the feature decoding matrix of the j-th layer, and Ω=(W,b) is the network parameter.

[0079] Constraints It ensures that the structure of D in the tensor space of the projection matrix P of the residual E is consistent. Regularization term It aims to extract the low-rank structure in the residual E while reducing the impact of noise.

[0080] When training the deep network model suitable for the deep dictionary low-rank residual representation in the present invention, back propagation is used to update the network parameters, and H(Ω) and G(Ω) are simplified to H and G respectively. The key to this step is to calculate the partial derivatives and In order to enhance the generalization ability, a weight decay penalty is applied to limit the size of weights W1 and W2, and their solution formula is:

[0081]

[0082] Where ⊙ represents the element-wise product operator Δ1, which is calculated to obtain Δ2, as follows:

[0083]

[0084] Δ2=(GX)⊙G⊙(1-G).

[0085] The dictionary training module for deep network models suitable for deep dictionary low-rank residual representation is described in detail:

[0086] To enhance feature extraction and improve classification accuracy, during dictionary learning, residual constraints measure the similarity distance between input data and each layer of dictionary atoms to ensure more accurate representation. This residual constraint enhances image recognition and optimizes dictionary and feature representation to make it more discriminative. The dictionary training module includes the following five contents:

[0087] (1) Solving P

[0088] First, the solution formula for P is given:

[0089]

[0090] sP T P=I.

[0091] Among them, P must satisfy the orthogonal constraint and be able to maintain the geometric structure of the original data during the data dimensionality reduction process, so that the reduced data still retains the important characteristics of the original data.

[0092] Use SVD decomposition to solve the simplified P:

[0093]

[0094] The last item It has no effect on the solution of P, which can obviously be solved by applying SVD (singular value decomposition) to That is, P is determined by It consists of the eigenvectors associated with the first l smallest eigenvalues ​​of .

[0095] (2) Solving the sparse matrix A

[0096] Usually, an effective algorithm for solving sparse variables is the iterative soft threshold algorithm (ISTA), which guarantees convergence to the global optimal solution and simplifies the total formula to obtain the formula for A:

[0097]

[0098] where c is the squared spectral norm of D, S λ / c is a component soft threshold operator, and:

[0099]

[0100] (3) Solving D

[0101] Removing the terms that are not related to D yields:

[0102]

[0103]

[0104] By taking partial derivatives of the dictionary variable D and shifting the terms, we get the solution formula for D:

[0105] D=(AA T +μ(PP T -I)+βY1A) -1 (HA T +βY1(XE)).

[0106] (4) Solving the residual E

[0107] The optimization of variable E can be obtained by fixing other variables:

[0108]

[0109] The final solution of E can be obtained by simplifying the equation, taking partial derivatives, and moving terms:

[0110]

[0111] (5) Auxiliary variables for residuals Solution

[0112] By eliminating other irrelevant terms, we can obtain the following The formula is:

[0113]

[0114] By taking partial derivatives and shifting the terms, we get:

[0115]

[0116] Example 1

[0117] Will Figure 3 The original face image on the left (from the public database YaleB dataset) is input into the deep network model suitable for deep dictionary low-rank residual representation in the present invention. The low-rank image after dimensionality reduction is as follows: Figure 3 As shown in the middle image in , the residual between the original face image and the low-rank image is Figure 3 As shown in the right figure.

[0118] Example 2 In order to further understand the technical effect of the present invention, this example tests the technical solution of the present invention on different data sets and more advanced methods in current dictionary learning. The experimental environment is: GPU RTX 3090, memory 32G, SSD1TB, operating system Ubuntu 20.04LTS, deep learning framework pytorch, language version python3.8.

[0119] Table 1 Data comparison between the present invention and the existing method

[0120]

[0121]

[0122] It can be seen from Table 1 that the present invention has good results in classification accuracy.

Claims

1. A face recognition method based on deep dictionary low-rank residual representation, characterized in that: The steps include: Step 1: Obtain the original face image and preprocess it; Step 2: Build and train a deep network model suitable for deep dictionary low-rank residual representation, input the preprocessed face image into the deep network model for training to obtain the corresponding feature vector; the deep network model includes a feature extraction module, a dictionary training module and a sparse representation module: The feature extraction module extracts the preprocessed face image to obtain a feature vector X; the dictionary training module uses the feature vector X to train the dictionary D; the sparse representation module finds a set of bases in the dictionary so that the face data is represented as a linear combination of these bases, and then outputs sparse features; The deep network model expression suitable for deep dictionary low-rank residual representation is as follows: The constraints in the above formula are as follows: stP T P=I,E=X-DA H(Ω) represents the encoder, which is used to extract high-level features of the data; G(Ω) represents the decoder, which is used to recover the input data; D = [d1, d2, …, d n ] represents a low-dimensional dictionary, the basis vector of all input data; A = [a1, a2, ..., a n ] represents a sparse vector, ‖A‖1 is a sparse constraint that makes the elements in the sparse vector A contain fewer non-zero elements, which is used for the linear combination of atoms in D; Extract the low-rank structure of the edge structure in the residual E; P is the dimensionality reduction projection matrix of the low-dimensional dictionary D and the residual E, through Make the tensor subspace of P consistent with the structure in dictionary D; The method for training a deep network model suitable for low-rank residual representation of a deep dictionary is: Step I: Use the feature matrix obtained by the feature extraction module as the input of the autoencoder network, learn the more advanced feature representation in the encoding process, and perform residual calculation on the reconstructed data and the original data in the decoding stage to enter the next stage; learn the low-rank structural information in the residual, and update the dictionary and sparse representation coefficients in the dictionary learning stage; Step II: Continuously train network parameters and calculate the loss values ​​of reconstructed data and original data. At the same time, use the back propagation of the deep network to update the network parameters to continuously reduce the loss value; modify the gradient descent weights after a certain number of iterations to better meet the target requirements; Step III: Repeat steps I and II to optimize and adjust the parameters of the function and finally obtain a satisfactory loss value. When the loss value is less than the set threshold, it means that the training requirements are met. Step 3, collect the real face image from the camera, input the real face image into the deep network model represented by the low-rank residual of the deep dictionary trained in step 2 to obtain the corresponding face sparse vector, and compare and search the face sparse vector in the database: the feature vector with the smallest difference between the face sparse vector in the database, if it meets the expected error, is considered to be a face image that the system can recognize.

2. The face recognition method based on deep dictionary low-rank residual representation according to claim 1, characterized in that: In the step 2, the feature extraction module in the deep network model uses the SIFT algorithm to extract features, and the obtained face feature vector X=[x1, x2,…, x N ] indicates; x i Represents the vectorization of two-dimensional data of a sliding window. The specific method is: The input face image is divided into 8×8 small image blocks, and each image block is processed using the SIFT algorithm. The processed 8×8 block matrix is ​​vectorized to obtain a 64×1 feature vector. Finally, the obtained feature vectors are arranged together to obtain a 64*N matrix, where N is the number of feature vectors, X=[x1,x2,…,x N ].

3. The face recognition method based on deep dictionary low-rank residual representation according to claim 1, characterized in that: The process of training the dictionary by the dictionary training module in the deep network model in step 2 is as follows: The decoder recovers the reduced-dimensional data to obtain reconstructed data, and then calculates the difference between the reconstructed data and the original face image to obtain the residual structure, i.e., the residual E, which includes edge structure information. The encoder performs PCA dimensionality reduction on the residual E to obtain a low-rank residual structure. When updating the dictionary D, the low-rank residual structure is used to enhance the representation of the dictionary D on the features, so that the atomic vectors in the trained dictionary matrix are more discriminative in representing the features.

4. The face recognition method based on deep dictionary low-rank residual representation according to claim 1, characterized in that: The method of obtaining the sparse feature vector through the sparse representation module in the deep network model in step 2 is: The dictionary D obtained by the dictionary training module is combined with the feature vector X obtained by the feature extraction module, and the corresponding sparse vector A is solved and updated.

5. The face recognition method based on deep dictionary low-rank residual representation according to claim 1, characterized in that: The detailed method of step 3 is: The face sparse vector of the real face image is searched and compared with the face feature vector in the database, and the identity information of the face is identified and judged according to the similarity between the two. A threshold is set. When the error is not greater than the threshold, the matching result is output and the recognition is considered successful. The calculation formula of the threshold is as follows: <h2 style=";text-align:left;direction:ltr">threshold≤‖a1-a2‖<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ; a1 represents the tested feature vector, and a2 represents the most similar feature vector in the database obtained according to the dictionary. By calculating the error between them, it is shown that they have a high similarity.

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