CN111833252A - Image super-resolution method based on SAE dictionary learning and neighborhood regression - Google Patents

Abstract

The invention relates to an image super-resolution method based on SAE dictionary learning and neighborhood regression, which comprises the steps of firstly preparing input data aiming at a dictionary learning model SAE, and constructing and training a dictionary; then solving a projection matrix by combining a neighborhood regression theory and a dictionary; and finally, reconstructing the image based on the projection matrix to obtain a high-resolution image. On one hand, the method improves the feature expression capability of the dictionary and reduces the dependency of the reconstruction result on the dictionary; on the other hand, a neighborhood regression theory is integrated, and the reconstruction speed is improved.

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

In reality, due to the limitations of image acquisition equipment, scene changes, light sources and other factors, high-quality images cannot be obtained, and the requirements of practical application cannot be met when the resolution of the images is low. The Super-Resolution (SR) method utilizes an image signal processing technique to reconstruct a single or multiple low-Resolution (LR) images into High-Resolution (HR) images, and is characterized in that certain additional information is added during the reconstruction process to compensate for the detail information lost during the image degradation process. The SR reconstruction can break through the limitation of the intrinsic resolution of the imaging device to realize the improvement of the image resolution, so that the SR reconstruction has important application value in the fields of remote sensing, medical treatment, video monitoring and the like.

Currently, SR methods are mainly divided into 3 types: interpolation-based, reconstruction-based, and learning-based SR methods. Among them, the SR method based on learning is a hot spot direction in recent years, and the SR method based on dictionary learning is the most popular one among the SR methods based on learning, and was proposed by Yang and the like for the earliest time. The method is provided based on a compressed sensing theory, a dictionary joint learning method is adopted to learn HR and LR dictionary pairs, LR sparse coefficients are obtained by utilizing LR image blocks and an LR dictionary, and then the LR sparse coefficients and the HR dictionary are used for reconstructing HR image blocks on the basis of the assumption that the HR and LR image blocks have the same sparse representation coefficients. The algorithm can acquire sufficient priori knowledge, has a good subjective visual effect, but has a remarkable blocking effect, and the reconstructed effect has great dependence on a learned dictionary and the reconstruction consumes a long time.

Disclosure of Invention

In view of the above, the invention aims to provide an image super-resolution method based on SAE dictionary learning and neighborhood regression, which improves the feature expression capability of a dictionary and reduces the dependency of a reconstruction result on the dictionary; on the other hand, a neighborhood regression theory is integrated, and the reconstruction speed is improved.

The invention is realized by adopting the following scheme: an image super-resolution method based on SAE dictionary learning and neighborhood regression specifically comprises 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.

Further, the preparing input data for the dictionary learning model SAE specifically includes:

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]。

Further, when LR input data is prepared, the Principal Component Analysis (PCA) is adopted to reduce the dimension of the filtering image block.

Further, the constructing and training of the dictionary specifically includes:

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}。

Further, in combination with the requirement of dictionary learning, in the cost function of SAE, the mean absolute value error is used instead of 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 the number of samples of HR and LR input data, respectively; 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):

further, the 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.

Further, the solving of the projection matrix by combining the neighborhood regression theory and the dictionary specifically includes: 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.

Further, 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_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),

the qth atom representing the LR dictionary;

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, corresponding K HR adjacent image blocks N can be obtained from the HR training samples_h,qWhen traversing the entire LR dictionary D_lAll atoms of (2) can obtain a mapping relation N formed by combining 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}。

Further, the mapping relation is based on { 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

Reconstructed HR image X-passOver-mapping relation N_hSum coefficient

The method comprises the steps of (1) obtaining,

in the formula (6)

Is a projection matrix P.

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

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.

Compared with the prior art, the invention has the following beneficial effects: firstly, an improved sparse automatic encoder is adopted for dictionary learning, the outstanding feature learning capability of the improved sparse automatic encoder is fully utilized, the feature expression capability of the dictionary is enhanced, and the reconstruction quality of an image is improved; then, the invention integrates the neighborhood regression theory into the super-resolution frame based on dictionary learning, avoids the sparse coding process in the original frame, reduces the calculated amount and improves the reconstruction speed.

Drawings

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

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

Detailed Description

The invention is further explained below with reference to the drawings and the embodiments.

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, 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 is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

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

step S1: preparing input data aiming at a dictionary learning model SAE, and constructing and training a dictionary;

step S2: solving a projection matrix by combining a neighborhood regression theory and a dictionary;

step S3: and reconstructing the image based on the projection matrix to obtain a high-resolution image.

In this embodiment, as shown in fig. 1, the step S1 of preparing the input data for the dictionary learning model SAE specifically includes:

step S11: HR image sample I_hDownsampling to obtain LR image I_lAnd up-sampling the LR image to obtain an intermediate image I_m；

Step S12: HR input data preparation: HR image I_hAnd an intermediate image I_mSubtracting to obtain a difference image I_dFor difference image I_dBlocking and normalizing asHR input data, note

m is the number of samples of HR input data;

step S13: 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;

step S14: input data of the dictionary learning model SAE is represented as S ═ S_h,S_l]。

When LR input data is prepared, the Principal Component Analysis (PCA) is adopted to reduce the dimension of the filtering image block.

In this embodiment, the constructing and training of the dictionary in step S1 specifically includes:

step S15: 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;

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 as Mean Squared Error (MSE), where m and n represent the number of samples of HR and LR input data, respectively; 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_lNumber of nodes representing layer l， 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 hidden layer neurons, ρ is the set expected activation, with a value close to 0, γ is the regulatory parameter of the term, N₂Represents the number of nodes of layer 2; for the

The case of significant deviation ρ is generally penalized with relative entropy, as shown in equation (2):

step S16: 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}。

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; in dictionary learning, input data can be represented by a dictionary matrix and sparsely, whereas in SAE, input data can be represented by a hidden layer representation and learning weights, from the relationship between which it is known that dictionary D is equivalent to the link weights W of the input layer and 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.

In this embodiment, step S2 specifically includes:

step S21: HR and LR dictionary pair { D is calculated by adopting nearest neighbor method_h,D_lEach atom in the lattice space S ═ S_h,S_l]Nearest neighbor mapping of { N }_h,N_l}; that is to say that the first and second electrodes,

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),

the qth atom representing the LR dictionary;

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, corresponding K HR adjacent image blocks N can be obtained from the HR training samples_h,qWhen traversing the entire LR dictionary D_lAll atoms of (2) can obtain a mapping relation N formed by combining 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}。

Step S22: based on the mapping relation { N_h,N_lSolving a projection matrix P by a ridge regression method, namely,

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,

in the formula (6)

Is a projection matrix P.

In this embodiment, step S3 specifically includes:

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 use the tableExpression 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.

Next, the present embodiment will be further described using the following simulation experiment.

The simulation tool adopted in the embodiment is MATLAB, and the evaluation indexes are peak signal-to-noise ratio PSNR and structural similarity SSIM, wherein the larger the PSNR, the closer the SSIM is to 1, and the better the super-resolution effect is.

The simulation experiment is specifically set as follows:

preparing data: in order to ensure the objectivity of the experiment, 91 universal standard HR training samples are adopted in dictionary learning, and test images are derived from standard test libraries Set5 and Set 14. In order to quantitatively evaluate the quality of the reconstructed images, these test images are taken as HR reference images, and LR images to be processed are acquired by down-sampling.

And (3) comparison algorithm: 5 SR algorithms such as Bicubic, L1SR (Super Resolution with L1 Resolution), SISR (Single Image Super Resolution), ANR (ordered neighbor Resolution), SRCNN (Super Resolution using volumetric Neural network) and the like are compared.

Setting important parameters: the sampling factor is 3 and the number of nodes of the SAE hidden layer is 1024.

The simulation experiments were mainly divided into 2 groups, as follows.

Experiment set 1: compared to different SR methods.

Table 1 lists PSNR and SSIM corresponding to the reconstructed images obtained by different SR algorithms, where the values in the last column indicate that the performance of the corresponding algorithm of this embodiment is optimal under the corresponding evaluation indexes, and 10 images are from Set5 and Set14, respectively. As can be seen from table 1, the PSNR and SSIM values obtained by the method of the present embodiment are substantially optimal, which indicates that the reconstruction effect is better.

TABLE 1 comparison of PSNR (dB) and SSIM values for different SR methods

Experiment set 2: and (4) comparing reconstruction speeds.

In the experiment, different algorithms are operated in the same equipment and environment, and the method is used for verifying the effect of reconstruction speed improved by blending the neighborhood regression thought into the SR algorithm based on dictionary learning. The average reconstruction times for the Set5 and Set14 test sets under different SR algorithms are listed in table 2. It can be seen that the present invention is significantly faster than other SR algorithms.

TABLE 2 comparison of different SR calculated mean reconstruction times(s)

Test image library	L1SR	SISR	SRCNN	Method for producing a composite material
					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 one skilled in the art, embodiments of the present application may be provided as a method, system, or 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, and the like) 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 application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution 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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