CN111833252A - Image Super-Resolution Method Based on SAE Dictionary Learning and Neighborhood Regression - Google Patents

Abstract

The present invention relates to an image super-resolution method based on SAE dictionary learning and neighborhood regression. First, input data is prepared for the dictionary learning model SAE, and a dictionary is constructed and trained; then, the projection matrix is solved by combining the neighborhood regression theory and the dictionary; finally, the image is reconstructed based on the projection matrix to obtain a high-resolution image. On the one hand, the present invention improves the feature expression ability of the dictionary and reduces the dependence of the reconstruction result on the dictionary; on the other hand, the neighborhood regression theory is incorporated to improve the reconstruction speed.

Description

Image Super-Resolution Method Based on SAE Dictionary Learning and Neighborhood Regression

technical field

The invention relates to the field of image super-resolution method design, in particular to an image super-resolution method based on SAE dictionary learning and neighborhood regression.

Background technique

In reality, due to factors such as the limitation of image acquisition equipment, scene changes, and light sources, high-quality images are often not obtained. When the resolution of the image is low, it cannot meet the requirements of practical applications. Image Super-Resolution (SR) method uses image signal processing technology to reconstruct existing single or multiple low-resolution (LowResolution, LR) images into high-resolution (High Resolution, HR) images. The key It is to add some additional information in the reconstruction process to make up for the detailed information lost in the process of image degradation. Since SR reconstruction can break through the limitation of the inherent resolution of the imaging device and improve the image resolution, it has important application value in remote sensing, medical treatment, video surveillance and other fields.

Currently, SR methods are mainly divided into three types: interpolation-based, reconstruction-based, and learning-based SR methods. Among them, the learning-based SR method is a hot topic in recent years, and the dictionary learning-based SR method is the most popular one among the learning-based SR methods, which was first proposed by Yang et al. The algorithm is based on the compressed sensing theory. It adopts the dictionary joint learning method to learn the HR and LR dictionary pairs. First, the LR image block and the LR dictionary are used to obtain the LR sparse coefficient, and then based on the assumption that the HR and LR image blocks have the same sparse representation coefficient , using LR sparse coefficients and HR dictionary to reconstruct HR image patches. The algorithm can obtain sufficient prior knowledge and has good subjective visual effect, but the block effect is obvious, and the reconstruction effect has a great dependence on the learned dictionary, and the reconstruction takes a long time.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to propose an image super-resolution method based on SAE dictionary learning and neighborhood regression. Neighborhood regression theory to improve reconstruction speed.

The present invention adopts the following scheme to realize: an image super-resolution method based on SAE dictionary learning and neighborhood regression, which specifically includes the following steps:

Prepare input data for the dictionary learning model SAE, and construct and train the dictionary;

Combine neighborhood regression theory and dictionary to solve projection matrix;

Image reconstruction is performed based on the projection matrix to obtain high-resolution images.

Further, the described preparation input data for the dictionary learning model SAE is specifically:

_The HR image sample _Ih is down-sampled to obtain the LR image Il, and the LR image is upsampled to obtain the intermediate image _Im ;

m为 HR输入数据的样本数；HR input data preparation: subtract the HR image I _h from the intermediate image _Im to obtain the difference image I _d , and block and normalize the difference image I _d as HR input data, denoted as

m is the number of samples of HR input data;

n为LR 输入数据的样本数；LR input data preparation: filter the intermediate image _Im to obtain a filtered image, then normalize and block the filtered image, and reduce the dimension of the filtered image block, denoted as

n is the number of samples of LR input data;

Denote the input data of the dictionary learning model SAE as S=[ _Sh , S _l ].

Further, when the LR input data is prepared, the principal component analysis method PCA is used to reduce the dimension of the filtered image block.

Further, the construction and training of the dictionary are specifically:

Combined with the needs of dictionary learning, in the cost function of SAE, the mean absolute value error is used to replace the mean square error, and an improved SAE dictionary learning model is obtained;

Input S=[S _h , S _l ], use the improved SAE dictionary learning model for learning, obtain the weight W ₁ between the input layer and the hidden layer, and convert the weight into HR and LR dictionary pairs {D _h , D _l } .

Further, in combination with the needs of dictionary learning, in the cost function of SAE, the mean absolute value error is used to replace the mean square error, and the improved SAE dictionary learning model is specifically:

Let s _i ∈ S be the input data and o _i ∈ O be the output data. The improved SAE dictionary model is as follows:

表示第l-1层节点i与第l层节点j 的连接权重，l表示网络的层数，N_l表示第l层的节点数，N_l+1第l+1层的节点数；第三项J_sparse(θ)为隐含层稀疏正则项，

为隐含层神经元的平均激活量，ρ为设定好的预期激活量，γ为调节参数，N₂表示第2层的节点数；其中，

采用式(2)表示：Among them, the first term J _MAE (θ) is the reconstruction error term, which is represented by the mean absolute error here, m and n represent the number of samples of HR and LR input data respectively; the second term J _weight (θ) is the weight decay term , used to reduce the magnitude of the weights and prevent overfitting, λ is the adjustment parameter of this item,

Represents the connection weight between the l-1 layer node i and the l layer node j, l represents the number of layers of the network, N _l represents the number of nodes in the l layer, N _l+1 The number of nodes in the l+1 layer; the third The term J _sparse (θ) is the hidden layer sparse regular term,

is the average activation of neurons in the hidden layer, ρ is the set expected activation, γ is the adjustment parameter, and N ₂ represents the number of nodes in the second layer; among them,

It is expressed by formula (2):

Further, the input S=[S _h , S _l ], the improved SAE dictionary learning model is used for learning, the weight W ₁ between the input layer and the hidden layer is obtained, and the weight is converted into the HR and LR dictionary pair {D _h , D _l } are specifically:

In the training process of the SAE dictionary learning model, the parameters are updated with the gradient descent method, and finally the connection weight W ₁ from the input layer to the hidden layer is obtained, where W ₁ ={ _wi }, i=1,2,... ,m+n; according to the relationship between the network weight and the dictionary, the dictionary D is equivalent to the link weight W ₁ of the input layer and the hidden layer, specifically expressed as HR dictionary D _h ={w ₁ ,w ₂ ,...,w _m } , LR dictionary D _l ={w _m+1 ,w _m+2 ,...,w _m+n }, the dictionary pair is expressed as D=(D _h , D _l ), where w _i ∈ W ₁ , and w _i = {w _1,i ,w _2,i ,...,w _k,i }, k is the dimension of the dictionary, w _k,i is the weight of the i-th dictionary atom in the k-th dimension.

Further, the combination of the neighborhood regression theory and the dictionary to solve the projection matrix is specifically: first, adopt the nearest neighbor method to calculate the HR and LR dictionary pairs {D _h , D _l } in the sample space S=[S _h for each atom in the , S _l ] the nearest neighbor mapping relationship {N _h , N _l }; then, based on the mapping relationship {N _h , N _l }, the projection matrix P is solved by the ridge regression method.

Further, the nearest neighbor method is used to calculate the nearest neighbor mapping relationship {N _h ,N of each atom in the sample space S=[ _Sh ,S _l ] in the HR and LR dictionary pair {D _h , D _l } _l }Specifically:

在LR 字典D_l中的K个最近邻域块集合N_l,q：Let S=[S _h , S _l ] be the training sample, {D _h , D _l } be the dictionary pair, and use the Euclidean distance to calculate the atoms

The set of K nearest neighbor blocks N _l,q in the LR dictionary D _l :

表示LR训练样本S_l中第p个训练样本，

表示LR字典的第q个原子；In the formula,

represents the p-th training sample in the LR training sample S _l ,

Represents the qth atom of the LR dictionary;

From equation (3), the K LR neighbor image blocks N _l,q corresponding to each LR dictionary atom can be calculated. According to the positions of the K neighbor image blocks, the corresponding K HR neighbor image blocks can be obtained from the HR training samples. N _h,q , when traversing all atoms of the entire LR dictionary D _l , the mapping relationship N _l composed of the nearest neighbor LR image blocks of all atoms can be obtained, and the nearest neighbor composed of the corresponding nearest neighbor HR image blocks. The mapping relation N _h is finally obtained {N _h , N _l }.

Further, based on the mapping relationship {N _h , N _l }, using the ridge regression method to solve the projection matrix P is specifically:

Replacing the dictionary D _l with the LR nearest neighbor mapping relation N _l , the expression for reconstructing β is

In the formula, β represents the coefficient matrix, Y represents the low-resolution image to be reconstructed, and η is the weight coefficient, which is used to alleviate the singularity problem and ensure the stability of the coefficient decomposition;

表示为The ridge regression method is used to solve equation (4), and the coefficients

Expressed as

获得，The reconstructed HR image X is mapped by N _h and coefficients

get,

为投影矩阵P。In Equation (6)

is the projection matrix P.

Further, performing image reconstruction based on the projection matrix to obtain a high-resolution image is specifically:

接着通过原子d_k找到其对应的投影矩阵P_t，然后利用表达式x_i＝P_ty_i，获得对应y_i的HR图像块x_i，以此重建所有的LR测试特征图像块，并组成HR图像X。First, preprocess the image Y to be reconstructed to obtain the LR test feature image Y _t ={y ₁ ,y ₂ ,...,y _i ,...,y _n }; then, use Euclidean distance to find LR in the LR dictionary D _l The nearest neighbor dictionary atom d _k corresponding to the test feature image block y _i is expressed as

Then find its corresponding projection matrix P _t through atom d _k , and then use the expression _xi =P _t y _i to obtain the HR image block _{xi corresponding to yi ,} so as to reconstruct all LR test feature image blocks, and form HR image X.

Compared with the prior art, the present invention has the following beneficial effects: the present invention firstly adopts an improved sparse auto-encoder for the learning of the dictionary, makes full use of its outstanding feature learning ability, enhances the feature expression ability of the dictionary, and improves the reconstruction quality of the image; Then, the present invention integrates the neighborhood regression theory into the super-resolution framework based on dictionary learning, avoids the sparse coding process in the original framework, reduces the amount of computation, and improves the speed of reconstruction.

Description of drawings

FIG. 1 is an SAE input data preprocessing process according to an embodiment of the present invention.

FIG. 2 is a schematic flowchart of a method according to an embodiment of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and embodiments.

It should be noted that the following detailed description is exemplary and intended to provide further explanation of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.

As shown in Figure 2, this embodiment provides an image super-resolution method based on SAE dictionary learning and neighborhood regression, which specifically includes the following steps:

Step S1: prepare input data for the dictionary learning model SAE, and construct and train the dictionary;

Step S2: combine the neighborhood regression theory and the dictionary to solve the projection matrix;

Step S3: Perform image reconstruction based on the projection matrix to obtain a high-resolution image.

In this embodiment, as shown in FIG. 1 , the preparation of input data for the dictionary learning model SAE described in step S1 is specifically:

Step S11: down-sampling the HR image sample _Ih to obtain the LR image _Il , and up-sampling the LR image to obtain the intermediate image _Im ;

m为HR输入数据的样本数；Step S12: HR input data preparation: subtract the HR image I _h and the intermediate image I _m to obtain a difference image I _d , and block and normalize the difference image I _d as HR input data, denoted as

m is the number of samples of HR input data;

n为LR输入数据的样本数；Step S13: LR input data preparation: filter the intermediate image _Im to obtain a filtered image, then normalize and block the filtered image, and reduce the dimension of the filtered image block, denoted as

n is the number of samples of LR input data;

Step S14: Denote the input data of the dictionary learning model SAE as S=[S _h , S _l ].

Among them, when the LR input data is prepared, the principal component analysis method PCA is used to reduce the dimension of the filtered image block.

In this embodiment, the construction and training of the dictionary in step S1 is specifically:

Step S15: Combined with the needs of dictionary learning, in the cost function of SAE, the mean absolute value error is used instead of the mean square error to obtain an improved SAE dictionary learning model;

Let s _i ∈ S be the input data and o _i ∈ O be the output data. The improved SAE dictionary model is as follows:

表示第l-1 层节点i与第l层节点j的连接权重，l表示网络的层数，N_l表示第l层的节点数， N_l+1第l+1层的节点数；第三项J_sparse(θ)为隐含层稀疏正则项，

为隐含层神经元的平均激活量，ρ为设定好的预期激活量，其值接近于0，γ为该项的调节参数， N₂表示第2层的节点数；对于

显著偏离ρ的情况，一般采用相对熵来惩罚，如式(2)所示：Among them, the first item J _MAE (θ) is the reconstruction error term, which is represented by the mean absolute error (Mean SquaredError, MSE) here, m and n represent the number of samples of HR and LR input data respectively; the second item J _weight ( θ) is the weight decay term, which is used to reduce the magnitude of the weight value and prevent over-fitting, and λ is the adjustment parameter of this term,

Represents the connection weight between the l-1 layer node i and the l layer node j, l represents the number of layers of the network, N _l represents the number of nodes in the l layer, N _l+1 The number of nodes in the l+1 layer; the third The term J _sparse (θ) is the hidden layer sparse regular term,

is the average activation of neurons in the hidden layer, ρ is the set expected activation, its value is close to 0, γ is the adjustment parameter of this item, N ₂ represents the number of nodes in the second layer; for

In the case of significant deviation from ρ, relative entropy is generally used to punish, as shown in formula (2):

Step S16: Input S=[S _h , S _l ], use the improved SAE dictionary learning model for learning, obtain the weight W ₁ between the input layer and the hidden layer, and convert the weight into HR and LR dictionary pairs {D _h , D _l }.

In the training process of the SAE dictionary learning model, the parameters are updated with the gradient descent method, and finally the connection weight W ₁ from the input layer to the hidden layer is obtained, where W ₁ ={ _wi }, i=1,2,... ,m+n; in dictionary learning, the input data can be represented by dictionary matrix and sparse representation, while in SAE, the input data can be represented by the representation of the hidden layer and the learning weight, according to the relationship between the two, the dictionary D, etc. It is equivalent to the link weight W ₁ between the input layer and the hidden layer, specifically expressed as HR dictionary D _h ={w ₁ ,w ₂ ,...,w _m }, LR dictionary D _l ={w _m+1 ,w _{m+2 , . _ _ _ _ _ _ k,i} }, k is the dimension of the dictionary, w _k,i represents the weight of the i-th dictionary atom in the k-th dimension.

In this embodiment, step S2 is specifically:

Step S21: Use the nearest neighbor method to calculate the nearest neighbor mapping relationship {N _h ,N _l } of each atom in the HR and LR dictionary pair {D _h ,D _l } in the sample space S=[ _Sh ,S _l ] ;which is,

在LR 字典D_l中的K个最近邻域块集合N_l,q：Let S=[S _h , S _l ] be the training sample, {D _h , D _l } be the dictionary pair, and use the Euclidean distance to calculate the atoms

The set of K nearest neighbor blocks N _l,q in the LR dictionary D _l :

表示LR训练样本S_l中第p个训练样本，

表示LR字典的第q个原子；In the formula,

represents the p-th training sample in the LR training sample S _l ,

Represents the qth atom of the LR dictionary;

From equation (3), the K LR neighbor image blocks N _l,q corresponding to each LR dictionary atom can be calculated. According to the positions of the K neighbor image blocks, the corresponding K HR neighbor image blocks can be obtained from the HR training samples. N _h,q , when traversing all atoms of the entire LR dictionary D _l , the mapping relationship N _l composed of the nearest neighbor LR image blocks of all atoms can be obtained, and the nearest neighbor composed of the corresponding nearest neighbor HR image blocks. The mapping relation N _h is finally obtained {N _h , N _l }.

Step S22: Based on the mapping relationship {N _h , N _l }, use the ridge regression method to solve the projection matrix P, that is,

Replacing the dictionary D _l with the LR nearest neighbor mapping relation N _l , the expression for reconstructing β is

In the formula, β represents the coefficient matrix, Y represents the low-resolution image to be reconstructed, and η is the weight coefficient, which is used to alleviate the singularity problem and ensure the stability of the coefficient decomposition;

表示为The ridge regression method is used to solve equation (4), and the coefficients

Expressed as

获得，The reconstructed HR image X is mapped by N _h and coefficients

get,

为投影矩阵P。In Equation (6)

is the projection matrix P.

In this embodiment, step S3 is specifically:

接着通过原子d_k找到其对应的投影矩阵P_t，然后利用表达式x_i＝P_ty_i，获得对应y_i的HR图像块x_i，以此重建所有的LR测试特征图像块，并组成HR图像X。First, preprocess the image Y to be reconstructed to obtain the LR test feature image Y _t ={y ₁ ,y ₂ ,...,y _i ,...,y _n }; then, use Euclidean distance to find LR in the LR dictionary D _l The nearest neighbor dictionary atom d _k corresponding to the test feature image block y _i is expressed as

Then find its corresponding projection matrix P _t through atom d _k , and then use the expression _xi =P _t y _i to obtain the HR image block _{xi corresponding to yi ,} so as to reconstruct all LR test feature image blocks, and form HR image X.

Next, this embodiment uses the following simulation experiments for further description.

The simulation tool used in this embodiment is MATLAB, and the evaluation indicators are peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). The larger the PSNR, the closer the SSIM is to 1, the better the super-resolution effect.

The specific settings of the simulation experiment are as follows:

Data preparation: In order to ensure the objectivity of the experiment, dictionary learning adopts 91 general standard HR training samples, and the test images come from standard test libraries Set5 and Set14. In order to quantitatively evaluate the quality of the reconstructed images, these test images are used as HR reference images, and the LR images to be processed are obtained by downsampling.

Comparison algorithms: 5 SR algorithms, including Bicubic, L1SR (Super Resolution with L1 Regression), SISR (Single Image Super Resolution), ANR (Anchored Neighborhood Regression), and SRCNN (Super Resolution using Convolution Neural Network), are compared.

Important parameter settings: the sampling factor is 3, and the number of nodes in the SAE hidden layer is 1024.

The simulation experiments are mainly divided into two groups, as follows.

Group 1 experiments: Comparison with different SR methods.

Table 1 lists the PSNR and SSIM corresponding to the reconstructed images obtained by different SR algorithms. The values marked in the last column indicate that the performance of the corresponding algorithm in this embodiment is the best under the corresponding evaluation indicators. The 10 images are from Set5 and Set14. It can be seen from Table 1 that the PSNR and SSIM values obtained by the method in this embodiment are generally optimal, indicating that the reconstruction effect is better.

Table 1 Comparison of PSNR (dB) and SSIM values for different SR methods

Experiment 2: Comparison of reconstruction speed.

In this group of experiments, different algorithms were run in the same equipment and environment to verify the effect of improving the reconstruction speed by incorporating the idea of neighborhood regression into the dictionary learning-based SR algorithm. Table 2 lists the average reconstruction time of Set5 and Set14 test sets under different SR algorithms. It can be seen from this that the speed of the present invention is significantly higher than other SR algorithms.

Table 2 Comparison of the average reconstruction time (s) of different SR algorithms

test image library L1SR SISR SRCNN this method Set 5 14.28 0.96 2.98 0.33 Set 14 31.93 1.93 8.03 0.65

As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flows of the flowcharts and/or the block or blocks of the block diagrams.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention in other forms. Any person skilled in the art may use the technical content disclosed above to make changes or modifications to equivalent changes. Example. However, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solutions of the present invention still belong to the protection scope of the technical solutions of the present invention.

Claims (10)

1. An image super-resolution method based on SAE dictionary learning and neighborhood regression is characterized by comprising the following steps:

preparing input data aiming at a dictionary learning model SAE, and constructing and training a dictionary;

solving a projection matrix by combining a neighborhood regression theory and a dictionary;

and reconstructing the image based on the projection matrix to obtain a high-resolution image.

2. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 1, wherein the preparation of input data for the dictionary learning model SAE is specifically as follows:

HR image sample I_hDownsampling to obtain LR image I_lAnd up-sampling the LR image to obtain an intermediate image I_m；

HR input data preparation: HR image I_hAnd an intermediate image I_mSubtracting to obtain a difference image I_dFor difference image I_dPartitioning and normalizing to obtain HR input data

m is the number of samples of HR input data;

LR input data preparation: for intermediate image I_mFiltering to obtain a filtered image, normalizing and partitioning the filtered image, and reducing dimensions of the filtered image block, which is recorded as

n is the number of samples of LR input data;

input data of the dictionary learning model SAE is represented as S ═ S_h,S_l]。

3. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 2, wherein in LR input data preparation, a Principal Component Analysis (PCA) method is used to reduce the dimension of the filtering image block.

4. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 1, wherein said constructing and training of the dictionary specifically comprises:

combining with the requirement of dictionary learning, in the cost function of SAE, adopting average absolute value error to replace mean square error to obtain an improved SAE dictionary learning model;

input S ═ S_h,S_l]Learning by adopting an improved SAE dictionary learning model to obtain the weight W between the input layer and the hidden layer₁The weights are converted into HR and LR dictionary pairs { D_h,D_l}。

5. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 4, wherein said combination of the requirement of dictionary learning, in the cost function of SAE, the mean absolute value error is used to replace the mean square error, and the improved SAE dictionary learning model is specifically:

let s_iE.g. S as input data, o_iE O is taken as output data, and the improved SAE dictionary model is as follows:

wherein the first item J_MAE(θ) is a reconstruction error term, here expressed in mean absolute error, m and n represent HR and HR, respectivelyNumber of samples of LR input data; second item J_weight(theta) is a weight decay term used to reduce the magnitude of the weights, preventing overfitting, lambda is the tuning parameter of this term,

represents the connection weight of the l-1 layer node i and the l layer node j, wherein l represents the layer number of the network, and N_lIndicates the number of nodes of the l-th layer, N_l+1Number of nodes of layer l + 1; third item J_sparse(theta) is a hidden layer sparsity regularization term,

for the mean activation of the neurons in the hidden layer, ρ is the set expected activation, γ is the regulatory parameter, N₂Represents the number of nodes of layer 2; wherein,

expressed by formula (2):

6. the image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 4, wherein said input S ═ S_h,S_l]Learning by adopting an improved SAE dictionary learning model to obtain the weight W between the input layer and the hidden layer₁The weights are converted into HR and LR dictionary pairs { D_h,D_lThe concrete steps are as follows:

in the training process of the SAE dictionary learning model, updating parameters by combining a gradient descent method, and finally obtaining the connection weight W from the input layer to the hidden layer₁Wherein W is₁＝{w_i1,2, i, m + n; according to the relation between the network weight and the dictionary, the dictionary D is equivalent to the link weight W of the input layer and the hidden layer₁Denoted HR dictionary D_h＝{w₁,w₂,…,w_mR, LR dictionary D_l＝{w_m+1,w_m+2,…,w_m+nDenoted D ═ D for dictionary pair_h,D_l) Wherein w is_i∈W₁And w is_i＝{w_1,i,w_2,i,...,w_k,iK is the dimension of the dictionary, w_k,iRepresenting the weight of the ith dictionary atom in the kth dimension.

7. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 1, wherein said solving of projection matrix in combination with neighborhood regression theory and dictionary specifically comprises: first, the HR and LR dictionary pair { D is calculated by adopting a nearest neighbor method_h,D_lEach atom in the lattice space S ═ S_h,S_l]Nearest neighbor mapping of { N }_h,N_l}; then, based on the mapping { N_h,N_lAnd solving a projection matrix P by using a ridge regression method.

8. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 7, wherein said computing HR and LR dictionary pair { D ] by nearest neighbor method_h,D_lEach atom in the lattice space S ═ S_h,S_l]Nearest neighbor mapping of { N }_h,N_lThe concrete steps are as follows:

let S be ═ S_h,S_l]For training samples, { D_h,D_lThe atom is calculated by Euclidean distance

In LR dictionary D_lK nearest neighbor domain block sets N in (1)_l,q：

In the formula,

represents the LR training sample S_lThe p-th training sample of (1),

representation of LR dictionary D_lThe qth atom of (1);

from equation (3), K LR neighboring image blocks N corresponding to each LR dictionary atom can be calculated_l,qAccording to the positions of the K adjacent image blocks, obtaining corresponding K HR adjacent image blocks N from HR training samples_h,qWhen traversing the entire LR dictionary D_lObtaining the mapping relation N formed by combining the nearest neighbor LR image blocks of all atoms_lAnd a nearest neighbor mapping relation N formed by combining the nearest neighbor HR image blocks corresponding to the nearest neighbor HR image blocks_hFinally obtain { N_h,N_l}。

9. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 7, wherein said mapping relation { N }_h,N_lSolving the projection matrix P by using a ridge regression method specifically comprises the following steps:

using LR nearest neighbor mapping relation N_lReplacing dictionary D_lThen the expression for the reconstruction of beta is

In the formula, beta represents a coefficient matrix, Y represents a low-resolution image to be reconstructed, and eta is a weight coefficient and is used for relieving the singularity problem and ensuring the stability of coefficient decomposition;

solving the formula (4) by using a ridge regression method, and calculating the coefficient

Is shown as

The reconstructed HR image X passes through the mapping relation N_hSum coefficient

The method comprises the steps of (1) obtaining,

note N in the formula (6)_h(N_l ^TN_l+ηI)^-1N_l ^TIs a projection matrix P.

10. The image super-resolution method based on SAE dictionary learning and neighborhood regression as claimed in claim 7, wherein said image reconstruction based on projection matrix to obtain high resolution image specifically comprises:

firstly, preprocessing an image Y to be reconstructed to obtain an LR test characteristic image Y_t＝{y₁,y₂,…,y_i,…,y_n}; then, the Euclidean distance is adopted to be in LR dictionary D_lFinding LR test characteristic image block y in_iCorresponding nearest neighbor dictionary atom d_kThe expression is

Then through atom d_kFind its corresponding projection matrix P_tThen using the expression x_i＝P_ty_iObtain a correspondence y_iHR image block x_iAll LR test characteristic image blocks are reconstructed in this way, and an HR image X is formed.

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