CN102800076A

CN102800076A - Image super-resolution reconstruction method based on double-dictionary learning

Info

Publication number: CN102800076A
Application number: CN2012102455303A
Authority: CN
Inventors: 王爽; 焦李成; 季佩媛; 马晶晶; 王蕾; 郑喆坤; 李婷婷; 李源
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2012-07-16
Filing date: 2012-07-16
Publication date: 2012-11-28
Anticipated expiration: 2032-07-16
Also published as: CN102800076B

Abstract

The invention discloses an image super-resolution reconstruction method based on double-dictionary learning, which mainly solves the problem that detailed information cannot be effectively supplemented in the prior art when super-resolution reconstruction is performed on a low-resolution image. A realization process comprises the following steps of: firstly, inputting a low-resolution image XL to be processed, constructing five pairs of high-resolution dictionaries and low-resolution dictionaries (Dh1, Dl1), (Dh2, Dl2),..., (Dh5, Dl5), and reconstructing five high-resolution estimation images under the five pairs of dictionaries; constructing one pair of high-frequency dictionary and low-resolution dictionary Df={Dhf, Dlf} by virtue of the high-frequency information and low-frequency information of the input low-resolution image, and reconstructing five pairs of high-resolution estimation images with different neighbor parameters; and finally, performing low-rank decomposition on the ten pairs of reconstructed high-resolution estimation images, and solving a mean value of a low-rank matrix obtained from the decomposition to obtain a final reconstructed high-resolution image XH. The method provided by the invention can be used for obtaining the high-resolution image with clear edges and rich details when being used for performing the super-resolution reconstruction on the low-resolution image and is suitable for super-resolution reconstruction on various natural images.

Description

Image super-resolution reconstruction method based on double-dictionary learning

Technical Field

The invention belongs to the technical field of image processing, in particular to a super-resolution reconstruction method for a low-resolution image.

Background

The super-resolution reconstruction of the image refers to reconstructing a clear high-resolution image according to a corresponding algorithm by using one or more low-resolution images, is an important and challenging research content in image processing, and is widely applied to the aspects of video monitoring, high-definition television imaging and the like. At present, a great deal of research work is carried out at home and abroad aiming at the super-resolution reconstruction of images, and a plurality of classical algorithms are provided.

The traditional image super-resolution reconstruction method comprises bilinear interpolation, bicubic interpolation, iterative back projection, convex set projection method and the like. The methods have small calculated amount and simple principle, and are widely applied to image super-resolution reconstruction, but the traditional methods can generate artificial traces such as ringing, blocking effect and the like in the super-resolution reconstruction process, and the quality of the reconstructed image is seriously reduced under the condition of high magnification factor.

Aiming at the problems that the traditional image super-resolution reconstruction method has poor effect and cannot be well realized in practical application, some super-resolution reconstruction algorithms for improving the defects are proposed internationally at present. For example, Hong Chang et al propose a neighborhood embedding based Super-resolution reconstruction algorithm, see document "Super-resolution through neighbor image embedding". CVPR, 2004. In the algorithm, the high-resolution image and the low-resolution image are assumed to have similar structures, and the weight of the low-resolution space is applied to the high-resolution space to reconstruct the high-resolution image. However, the high-resolution image obtained by the algorithm lacks detail information, and the edge of the image is fuzzy; later, Yang et al propose a sparse representation dictionary learning-based algorithm, see more specifically document "Super-Resolution Via sparse representation" IEEE trans. image processing, 2010, vol.19, pp: 2861-2872. the algorithm first obtains a low Resolution dictionary and a high Resolution dictionary through a dictionary learning method, then projects a low Resolution image to be processed under the low Resolution dictionary to obtain a sparse representation coefficient of the low Resolution image, and finally obtains a reconstructed high Resolution image according to the sparse representation coefficient and the high Resolution dictionary obtained by projection. However, the method needs a large number of low-resolution images and high-resolution image blocks to ensure the sufficiency of the detailed information of the prior contour, and has huge calculation amount and long image reconstruction time, which results in low efficiency.

Disclosure of Invention

The invention aims to provide an image super-resolution reconstruction method based on double-dictionary learning, aiming at overcoming the defects of the prior art, so that artificial traces such as ringing and blocking effects can be removed during image super-resolution reconstruction, more image detail information can be recovered, and the quality of a reconstructed image can be improved.

In order to achieve the purpose, the technical scheme of the invention comprises the following steps:

(1) inputting a low-resolution image X to be processed_LThe image size is mxn, and the magnification of the image is set to be 2;

(2) low resolution image X to be processed_L3 × 3 blocks are divided, 2 pixels are overlapped between adjacent blocks to obtain G low resolution image blocks P to be processed_l(i)，i＝1,...,G；

(3) 5 high-resolution training images and corresponding 5 low-resolution training images are input, and 5 high-resolution dictionaries D are constructed by using the training images_h1,D_h2,...,D_h5And corresponding 5 low resolution dictionaries D_l1,D_l2,...,D_l5；

(4) In the 1 st pair of high-resolution and low-resolution dictionaries (D)_h1,D_l1) Next, a high-resolution estimated image X of 2m × 2n in size is reconstructed_H1：

4a) Extracting a low resolution image block P to be processed_l(i) Initializing P_l(i) The label of (a) is 1;

4b) calculating the low resolution image block P to be processed by using the following formula_l(i) And low resolution dictionary D_l1DIST1(t) of elements:

DIST1(t)＝|P_l(i)-D_l1(t)|²，

wherein D_l1(T), T1, 2., T denotes the tth low-resolution dictionary element, T denotes the total number of low-resolution dictionary elements, i.e., T20000 | · linear²Represents an absolute value squaring operation of (-);

4c) recording 5 low-resolution dictionary elements corresponding to the first 5 smallest results in the distance DIST1(t) as D_l1(k) K 1.., 5, by low resolution dictionary D_l1And high resolution dictionary D_h1Corresponding relation between them, finding out high-resolution dictionary D_h1Corresponding 5 high resolution dictionary elements D_h1(k),k＝1,...,5；

4d) Calculating 5 low resolution dictionary elements D by using local weight formula_l1(k) Reconstructing an image block P_l(i) K ═ 1,.., 5;

4e) the reconstruction coefficient w (k) is compared with the 5 high-resolution dictionary elements D searched in the step 4c)_h1(k) Summing to obtain high-resolution image block P_h(i) The calculation formula is as follows:

4f) setting a mark i to i +1, judging whether a condition i > G is met, and if so, obtaining a reconstructed high-resolution estimated image X_H1Executing the step (5), otherwise, returning to the stepStep 4 b);

(5) respectively obtaining dictionary pairs (D) by the same method as the step (4)_h2,D_l2)，(D_h3,D_l3)，…，(D_h5,D_l5) High resolution estimate image X of_H2，X_H3，X_H4，X_H5；

(6) Using low-resolution images X to be processed_LConstruct a pair of high and low frequency dictionaries D_f＝{D_hf,D_lf}；

(7) Let neighbor parameter A equal to 5, in high and low frequency dictionary D_f＝{D_hf,D_lfLower reconstruction size of 2m 2n high resolution estimated image X_H6：

7a) Low resolution image X to be processed by utilizing imresize function in matlab software_LPre-amplifying by a magnification factor of 2 to obtain a pre-amplified image X_L ^*The image size is 2m × 2 n;

7b) for pre-amplified image X_L ^*Performing 3 × 3 block division, and overlapping adjacent blocks by 2 pixels to obtain a pre-magnified image block P_l(j)^*，j＝1,...,S；

7c) Calculating a pre-enlarged image block P using the following formula_l(j)^*And a low frequency dictionary D_lfDIST2(u) of elements:

DIST2(u)＝|P_l(j)^*-D_lf(u)|²，

wherein D_lf(U), U1, 2., U denotes the U-th low-frequency dictionary element, U denotes the total number of low-frequency dictionary elements, | U · luminance²Represents a squaring operation taking the absolute value of (-) and;

7d) recording A low-frequency dictionary elements corresponding to the first A smallest results in the distance DIST2(u) as D_lf(r), r ═ 1, 2.. a, by low frequency dictionary D_lfAnd high resolution dictionary D_hfFinding a high-frequency dictionary D_hfCorresponding A high-frequency dictionary elements D_hf(r),r＝1,...,A；

7e) Calculating A low-frequency dictionary elements D by using local weight formula_lf(r) reconstructing a pre-amplified image block P_l(j)^*The reconstruction coefficient of (a), (c) (r), r 1., a;

7f) the reconstruction coefficient c (r) and the A high-frequency dictionary elements D searched in the step 7D) are compared_hf(r) summing to obtain reconstructed high frequency image block P_h(j)^*：

7g) The obtained high-frequency image block P_h(j)^*And pre-magnified image block P_l(j)^*Adding to obtain a reconstructed high-resolution image block X_h(j)^*；

7h) Setting a mark j as j +1, judging whether a condition j is more than S is met, and if so, obtaining a high-resolution image X amplified by 2 times_H6Executing the step (8), otherwise, returning to the step 7 c);

(8) respectively setting the neighbor parameters in the step (7) as neighbor parameters A-4, A-3, A-2 and A-1 in the step (7), and repeating the step (7) to obtain the high-resolution estimated image X_H7，X_H8，X_H9，X_H10；

(9) 10 high-resolution estimated images X to be acquired_H1,X_H2,...,X_H10All the high-dimensional data X are pulled into columns to form high-dimensional data X, and low-rank decomposition is carried out on the high-dimensional data X by using a low-rank decomposition algorithm to obtain a low-rank matrix L and a sparse matrix S of the X;

(10) restoring each column in the low-rank matrix L into an image form through a reshape function in matlab software to obtain 10 low-rank images L (z), wherein z is 1.

(11) Carrying out mean value processing on 10 low-rank images L (z) according to the following formula to obtain a final clear image X_H：

Compared with the prior art, the invention has the following advantages:

according to the invention, the external high-low resolution dictionary 5 and the internal high-low resolution dictionary 1 are utilized to carry out super-resolution reconstruction on the low-resolution image, external detail information is introduced, and the high-frequency information of the image is kept. Simulation experiments show that the method can effectively perform super-resolution reconstruction on the low-resolution image, increase the detail information of the image and improve the definition of the reconstructed image.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a diagram of 5 high resolution training images used in the present invention to build a high resolution dictionary in a simulation experiment;

FIG. 3 is a diagram of 5 low resolution training images used in the invention to build a low resolution dictionary in a simulation experiment;

FIG. 4 is a Lena low resolution test image used in a simulation experiment of the present invention;

FIG. 5 is a Lena high resolution reconstructed image obtained in a simulation experiment according to the present invention;

FIG. 6 is a Lena high-resolution reconstructed image obtained in an experiment based on a neighborhood embedding method in the prior art;

fig. 7 is a Lena high-resolution reconstructed image obtained in an experiment by a conventional sparse representation dictionary learning-based method.

Detailed Description

Referring to fig. 1, the specific implementation steps of the present invention are as follows:

step 1, inputting a low-resolution image X to be processed_LAs shown in fig. 4, the image size is m × n, where m is the number of image rows and n is the number of image columns, the magnification is set to 2, and the low resolution image X to be processed is processed_L3 × 3 blocks are divided, 2 pixels are overlapped between adjacent blocks to obtain G low resolution image blocks P to be processed_l(i)，i＝1，...,G。

Step 2, inputting 5 high-resolution training images and 5 corresponding low-resolution training images, wherein 5 high-resolution training images are shown in figure 2, 5 low-resolution training images are shown in figure 3, and constructing 5 high-resolution dictionaries D by using the training images_h1,D_h2,...,D_h5And corresponding 5 low resolution dictionaries D_l1,D_l2,...,D_l5。

2a) For inputDividing the 5 high-resolution training images into 6 × 6 blocks, overlapping 4 pixels between adjacent blocks to obtain Y high-resolution training image blocks H_yY is 1,2, 9, Y, wherein Y is 100000 ≦ 30000;

2b) dividing the input 5 low-resolution training images into 3 x 3 blocks, overlapping 2 pixels between adjacent blocks to obtain Y low-resolution training image blocks L_yY is 1,2, 9, Y, wherein Y is 100000 ≦ 30000;

2c) from Y high resolution image blocks H_yExtract 10 ten thousand high resolution image blocks H_qQ 1, 2., 100000, corresponding from Y low resolution training image blocks L_yExtract 10 ten thousand low resolution image blocks L_q，q＝1,2,...,100000；

2d) 10 ten thousand high resolution image blocks H to be extracted respectively_qAnd 10 ten thousand low resolution image blocks L_qRandomly dividing into 5 groups to obtain 5 high-resolution dictionaries D_h1,D_h2,...,D_h5And corresponding 5 low resolution dictionaries D_l1,D_l2,...,D_l5。

Step 3, in the 1 st pair of high-resolution and low-resolution dictionaries (D)_h1,D_l1) High resolution image X with lower reconstruction size of 2m X2 n_H1。

3a) Extracting a low resolution image block P to be processed_l(i) Initializing P_l(i) The label of (a) is 1;

3b) calculating the low resolution image block P to be processed by using the following formula_l(i) And low resolution dictionary D_l1DIST1(t) of elements:

DIST1(t)＝|P_l(i)-D_l1(t)|²，

3c) will be at a distance DThe 5 low resolution dictionary elements corresponding to the smallest first 5 results in IST1(t) are denoted as D_l1(k) K 1.., 5, by low resolution dictionary D_l1And high resolution dictionary D_h1Corresponding relation between them, finding out high-resolution dictionary D_h1Corresponding 5 high resolution dictionary elements D_h1(k)，k＝1,...,5；

3d) Calculating 5 low resolution dictionary elements D by using local weight formula_l1(k) Reconstructing an image block P_l(i) The reconstruction coefficient w (k), k being 1,.., 5, the calculation formula is as follows:

w(k)＝((P_l(i)-D_l1(k))^T×(P_l(i)-D_l1(k))/I_k)/c，

wherein the normalization factor

I_kIs a full 1 matrix of size 5x1 (.)^TThe operation represents a matrix transpose operation;

3e) the reconstruction coefficient w (k) and the 5 high-resolution dictionary elements D searched in the step 3c) are compared_h1(k) Summing to obtain high-resolution image block P_h(i)：

3f) Setting a mark i to i +1, judging whether a condition i > G is met, and if so, obtaining a reconstructed high-resolution estimated image X_H1And executing the step 4, otherwise, returning to the step 3 b).

Step 4, respectively obtaining dictionary pairs (D) by the same method as the step 3_h2,D_l2)，(D_h3,D_l3)，…，(D_h5,D_l5) High resolution estimate image X of_H2，X_H3，X_H4，X_H5。

Step 5, utilizing the low resolution image X to be processed_LConstruct a pair of high and low frequency dictionaries D_f＝{D_hf,D_lf}。

5a) Low resolution image X to be processed_LCarrying out Gaussian high-pass filtering processing to obtain a to-be-processed low-resolution image X_LHigh frequency component X of_H0And a low frequency component X_L0；

5b) For high frequency component X respectively_H0And a low frequency component X_L0Partitioning with size of 3 × 3, overlapping adjacent blocks by 2 pixels to obtain 1 pair of high and low frequency dictionaries D_f＝{D_hf,D_lf}。

Step 6, setting the neighbor parameter A to 5, and setting the neighbor parameter A to be 5 in a high-low frequency dictionary D_f＝{D_hf,D_lfLower reconstruction size of 2m 2n high resolution estimated image X_H6。

6a) Low resolution image X to be processed by utilizing imresize function in matlab software_LPre-amplifying by a magnification factor of 2 to obtain a pre-amplified image X_L ^*The image size is 2m × 2 n;

6b) for pre-amplified image X_L ^*Performing 3 × 3 block division, and overlapping adjacent blocks by 2 pixels to obtain a pre-magnified image block P_l(j)^*，j＝1,...,S；

6c) Calculating the pre-amplified image block P using the following formula_l(j)^*And a low frequency dictionary D_lfDIST2(u) of elements:

DIST2(u)＝|P_l(j)^*-D_lf(u)|²，

6d) recording A low-frequency dictionary elements corresponding to the first A smallest results in the distance DIST2(u) as D_lf(r), r ═ 1, 2.. a, by low frequency dictionary D_lfAnd high resolution dictionary D_hfFinding a high-frequency dictionary D_hfCorresponding A high-frequency dictionary elements D_hf(r),r＝1,...,A；

6e) Calculating A low-frequency dictionary elements D by using local weight formula_lf(r) reconstructing a pre-amplified image block P_l(j)^*The local weight calculation formula of (a) is:

c(r)＝((P_l(j)^*-D_lf(r))^T×(P_l(j)^*-D_lf(r))/I_r)/h，

wherein the normalization factor

I_rIs a full 1 matrix of size Ax 1(·)^TThe operation represents a matrix transpose operation;

6f) the reconstruction coefficient c (r) and the A high-frequency dictionary elements D searched in the step 6D) are compared_hf(r) summing to obtain reconstructed high frequency image block P_h(j)^*：

6g) The obtained high-frequency image block P_h(j)^*And pre-magnified image block P_l(j)^*Adding to obtain a reconstructed high-resolution image block X_h(j)^*；

6h) Setting a mark j as j +1, judging whether a condition j is more than S is met, and if so, obtaining a high-resolution image X amplified by 2 times_H6Step 7 is executed, otherwise step 6c) is returned to.

And 7, respectively setting the neighbor parameters A and A in the step 6 to be 4, A to be 3, A to be 2 and A to be 1, and repeating the step 6 to obtain the high-resolution estimated image X_H7，X_H8，X_H9，X_H10。

Step 8, obtaining 10 high-resolution reconstruction images X_H1,X_H2，...,X_H10And all the high-dimensional data X are drawn into columns to form high-dimensional data X, and low-rank decomposition is carried out on the high-dimensional data X by using a low-rank decomposition algorithm to obtain a low-rank matrix L and a sparse matrix S of the high-dimensional data X.

The above-mentioned low-rank decomposition of the high-dimensional data X by using the low-rank decomposition algorithm is implemented by the existing low-rank decomposition method, which is proposed in 2009 by Emmanuel candes and Yi Ma et al, see document "Robust Principal Component Analysis" Computing Research reproduction-CORR, vol.

8a) Initializing the iteration time t =0, and the iteration error epsilon is 0.0001;

8b) setting t = t +1, generating a random gaussian matrix M by using a randn function in matlab software, and obtaining 3 intermediate variable matrices according to the following formula:

G₁＝X×M，G₂＝X^T×G₁，G₃＝X×G₂；

8c) computing a low rank matrix L in the t-th iteration_tAnd a sparse matrix S_t：

L_t＝G₃×(G₁ ^T×G₃)^-1G₂ ^T，

S_t＝P_Ω|X-L_t|，

Wherein (·)^TThe operation represents a matrix transpose operation, (-)^-1Representing a matrix inversion operation, P_Ω(. cndot.) represents taking the maximum first omega values in (. cndot.), wherein omega takes 30000 in the present invention;

8d) judging an iteration termination condition: if it is

If true, the iteration is stopped and the matrix L is applied_tSet as the low rank matrix L, matrix S sought_tSetting the sparse matrix S as the sparse matrix, otherwise returning to step 8b),

wherein,

representing the square of the norm of the matrix 2.

Step 9, obtaining 10 low-rank images L (z) by using the low-rank matrix L, wherein z is 1,2_H。

9a) Restoring each column in the low-rank matrix L into an image by using a reshape function in matlab software to obtain 10 low-rank images L (z), wherein z is 1, 2.

9b) Carrying out mean processing on a low-rank image L (z), wherein z is 1,2, 10 according to the following formula to obtain a final high-resolution reconstructed image X_H：

The effects of the present invention can be specifically illustrated by the following experiments:

1. the experimental conditions are as follows: the CPU of the microcomputer used for the experiment is Intel Core2 Duo 2.33GHz, the internal memory is 2GB, and the programming platform is Matlab R2009 a. The images used in the experiment are from a standard image library, and are Lena, House and Girl, which are 256 × 256 respectively.

2. Content of the experiment

The experiment is divided into three experiments:

experiment one: the super-resolution reconstruction is carried out on the low-resolution image by using the method, and the result is shown in figure 5;

experiment two: performing super-resolution reconstruction on the low-resolution image by using the existing neighborhood embedding-based method, wherein the result is shown in fig. 6;

experiment three: the existing sparse representation dictionary learning-based method is used for performing super-resolution reconstruction on the low-resolution image, and the result is shown in fig. 7.

In a simulation experiment, a peak signal-to-noise ratio (PSNR) evaluation index is applied to evaluate the quality of a restoration result, wherein the PSNR is defined as:

wherein f is a clear image, x is a reconstructed image, and M and N are the number of pixel rows and the number of pixel columns of the clear image f.

The invention and the prior field-based embedding method and sparse representation dictionary learning method are used for respectively carrying out super-resolution reconstruction simulation on the images Lena, House and Girl. The reconstructed result graph is evaluated by applying the peak signal-to-noise ratio (PSNR), and the evaluation result is shown in table 1, wherein Alg1 is the method, Alg2 is the method based on the field embedding, and Alg3 is the method based on the sparse representation dictionary learning.

TABLE 1 PSNR values (in dB) obtained in simulation experiments for the present invention and two comparative methods

3. Analysis of Experimental results

As can be seen from FIG. 5, the reconstruction result of Lena obtained by the invention not only effectively supplements high-frequency detail information, makes the image edge clear, but also has better visual effect;

as can be seen from fig. 6, the reconstruction result obtained by the existing domain-based embedding method is too smooth, the detail information is lacking, and the image is blurred;

as can be seen from fig. 7, the image edge obtained by the existing method based on sparse representation dictionary learning has noise and is poor in visual effect;

as can be seen from Table 1, the present invention has higher PSNR values than the other two comparative methods, and can reconstruct a high resolution image more effectively.

Claims

1. An image super-resolution reconstruction method based on double-dictionary learning comprises the following steps:

(3) Inputting 5 high-resolution training images and corresponding 5 low-resolution trainingImage, constructing 5 high-resolution dictionaries D by using training image_h1,D_h2,...,D_h5And corresponding 5 low resolution dictionaries D_l1,D_l2,...,D_l5；

DIST1(t)＝|P_l(i)-D_l1(t)|²，

4f) setting a mark i to i +1, judging whether a condition i > G is met, and if so, obtaining a reconstructed high-resolution estimated image X_H1Executing the step (5), otherwise, returning to the step 4 b);

DIST2(u)＝|P_l(j)^*-D_lf(u)|²，

wherein D_lf(U), U1, 2, said, U representing the U-th low frequency dictionary element,u represents the total number of low-frequency dictionary elements, | · non-woven²Represents a squaring operation taking the absolute value of (-) and;

(8) respectively setting the neighbor parameters in the step (7)And (4) repeating the step (7) to obtain the high-resolution estimation image X, wherein the neighbor parameters A in the step (7) are 4, A is 3, A is 2 and A is 1_H7，X_H8，X_H9，X_H10；

(9) 10 high-resolution estimated images X to be acquired_H1,X_H2，...,X_H10All the high-dimensional data X are pulled into columns to form high-dimensional data X, and low-rank decomposition is carried out on the high-dimensional data X by using a low-rank decomposition algorithm to obtain a low-rank matrix L and a sparse matrix S of the X;

2. The image super-resolution reconstruction method based on dual-dictionary learning as claimed in claim 1, wherein said step (3) of constructing 5 high-resolution dictionaries D by using training images_h1,D_h2,...,D_h5And corresponding 5 low resolution dictionaries D_l1,D_l2,...,D_l5The method comprises the following implementation steps:

3a) dividing the input 5 high-resolution training images into 6 x 6 blocks, overlapping 4 pixels between adjacent blocks to obtain Y high-resolution training image blocks H_yY is 1,2, 9, Y, wherein Y is 100000 ≦ 30000;

3b) for 5 input framesThe low resolution training image is divided into 3 multiplied by 3 blocks, and 2 pixels are overlapped between adjacent blocks to obtain Y low resolution training image blocks L_yY is 1,2, 9, Y, wherein Y is 100000 ≦ 30000;

3c) from Y high resolution image blocks H_yExtract 10 ten thousand high resolution image blocks H_qQ 1, 2., 100000, corresponding from Y low resolution training image blocks L_yExtract 10 ten thousand low resolution image blocks L_q，q＝1,2,...,100000；

3d) 10 ten thousand high resolution image blocks H to be extracted respectively_qAnd 10 ten thousand low resolution image blocks L_qRandomly dividing into 5 groups to obtain 5 high-resolution dictionaries D_h1,D_h2,...,D_h5And corresponding 5 low resolution dictionaries D_l1,D_l2,...,D_l5。

3. The image super-resolution reconstruction method based on dual dictionary learning of claim 1, wherein said step 4D) uses local weight formula to calculate 5 low-resolution dictionary elements D_l1(k) Reconstructing an image block P_l(i) The reconstruction coefficient w (k), k being 1,.., 5, is calculated by the following formula:

w(k)＝((P_l(i)-D_l1(k))^T×(P_l(i)-D_l1(k))/I_k)/g，

wherein the normalization factor

I_kIs a full 1 matrix of size 5x1 (.)^TThe operation represents a matrix transpose operation.

4. The image super-resolution reconstruction method based on dual dictionary learning of claim 1, wherein the step (6) of utilizing the low resolution image X to be processed_LConstruct a pair of high and low frequency dictionaries D_f＝{D_hf,D_lfThe implementation steps are as follows:

6a) low resolution image X to be processed_LCarrying out Gaussian high-pass filtering processing to obtain a to-be-processed low-resolution image X_LHigh frequency component X of_H0And a low frequency component X_L0；

6b) For high frequency component X respectively_H0And a low frequency component X_L0Partitioning with size of 3 × 3, overlapping adjacent blocks by 2 pixels to obtain 1 pair of high and low frequency dictionaries D_f＝{D_hf,D_lf}。

5. The image super-resolution reconstruction method based on dual dictionary learning of claim 1, wherein the step 7e) of calculating a low frequency dictionary elements D by using local weight formula_lf(r) reconstructing a pre-amplified image block P_l(j)^*The reconstruction coefficient c (r), r 1, a, is calculated by the following formula:

c(r)＝((P_l(j)^*-D_lf(r))^T×(P_l(j)^*-D_lf(r))/I_r)/h，

wherein the normalization factor

I_rIs a full 1 matrix of size Ax 1(·)^TThe operation represents a matrix transpose operation.

6. The image super-resolution reconstruction method based on dual-dictionary learning of claim 1, wherein in the step (9), the low-rank decomposition algorithm is used for performing low-rank decomposition on the high-dimensional data X to obtain a low-rank matrix L and a sparse matrix S of X, and the implementation steps are as follows:

9a) initializing the iteration time t =0, and the iteration error epsilon is 0.0001;

9b) setting t = t +1, generating a random gaussian matrix M by using a randn function in matlab software, and obtaining 3 intermediate variable matrices according to the following formula:

G₁＝X×M，G₂＝X^T×G₁，G₃＝X×G₂；

9c) computing a low rank matrix L in the t-th iteration_tAnd a sparse matrix S_t：

L_t＝G₃×(G₁ ^T×G₃)^-1G₂ ^T，

S_t＝P_Ω|X-L_t|，

9d) judging an iteration termination condition: if it is

If true, the iteration is stopped and the matrix L is applied_tSet as the low rank matrix L, matrix S sought_tSetting the sparse matrix S as the sparse matrix, otherwise returning to step 9b),

wherein,representing the square of the norm of the matrix 2.