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

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 method for reconstructing based on doubledictionary study

Technical field

The invention belongs to technical field of image processing, specifically a kind of method that low resolution image is carried out the super-resolution reconstruction, this method can be used for the super-resolution of various natural images and rebuild.

Background technology

The super-resolution reconstruction of image is meant and utilizes the one or more low-resolution image; Reconstruct width of cloth high-definition picture clearly according to corresponding algorithm; It is an important and challenging research contents in the Flame Image Process, is widely used at aspects such as video monitoring, HDTV imagings.Rebuild to the super-resolution of image both at home and abroad at present and done number of research projects, propose the algorithm of many classics.

Relatively traditional image super-resolution method for reconstructing comprises bilinear interpolation, two cubes of interpolation, iteration back projection, convex set sciagraphy etc.These method calculated amount are little; Principle is simple; Be widely applied in the reconstruction of image super-resolution, but these classic methods can produce artificial traces such as ring, blocking effect in the super-resolution process of reconstruction, and the image quality decrease of under high amplification factor condition, rebuilding is more serious.

Relatively poor to above-mentioned traditional image super-resolution method for reconstructing effect, the problem that in practical application, can not realize has well at present proposed some in the world and has improved the super-resolution reconstruction algorithm of above-mentioned shortcoming.As, people such as Hong Chang propose a kind of image super-resolution reconstruction algorithm that embeds based on neighborhood, specifically referring to document " Super-resolution through neighbor embedding " .CVPR, and 2004.In this algorithm, suppose that the high-resolution and low-resolution image has similar structure, the low weights of differentiating the space are applied to the high-resolution space, reconstruct full resolution pricture.But the full resolution pricture that this algorithm obtains lacks detailed information, and the image border is fuzzyyer; After this, people such as Yang have proposed a kind of algorithm based on the study of rarefaction representation dictionary, specifically referring to document " Super-Resolution Via Sparse Representation " IEEE Trans.Image Process; 2010; Vol.19, pp:2861-2872, this algorithm at first obtain low dictionary and the high-resolution dictionary differentiated through the method for dictionary study; Then pending low resolution image is carried out projection low the resolution under the dictionary; Obtain the rarefaction representation coefficient of low resolution image, the rarefaction representation coefficient and the high-resolution dictionary that obtain according to projection at last just can obtain the full resolution pricture of reconstruct.But this method needs a large amount of low-resolution images and high-definition picture piece to guarantee the adequacy of priori profile detailed information, and calculated amount is huge, and the image reconstruction time is long, causes efficient on the low side.

Summary of the invention

The objective of the invention is to deficiency to above-mentioned prior art; Propose a kind of image super-resolution method for reconstructing,, can remove these artificial traces of ring and blocking effect with when the image super-resolution is rebuild based on doubledictionary study; Recover the more images detailed information, improve quality of reconstructed images.

For realizing above-mentioned purpose, technical scheme of the present invention comprises the steps:

(1) pending low resolution image X of input _L, the image size is m * n, the enlargement factor of setting image is 2;

(2) to pending low resolution image X _LCarry out size and be 3 * 3 piecemeal, overlapping 2 pixels between the adjacent block obtain G pending low resolution image piece P _l(i), i=1 ..., G;

(3) input 5 panel heights are differentiated training image and the low training image of differentiating of corresponding 5 width of cloth, utilize 5 high-resolution dictionary D of training image structure _H1, D _H2..., D _H5With corresponding 5 low dictionary D that differentiate _L1, D _L2..., D _L5

(4) at the 1st pair of high-resolution and the low dictionary (D that differentiates _H1, D _L1) under, the reconstruct size is the high-resolution estimated image X of 2m * 2n _H1:

4a) extract pending low resolution image piece P _l(i), initialization P _l(i) be labeled as i=1;

4b) utilize following formula to calculate pending low resolution image piece P _l(i) with the low dictionary D that differentiates _L1In the distance B IST1 (t) of each element:

DIST1(t)＝|P _l(i)-D _l1(t)| ²，

D wherein _L1(t), t=1,2 ..., T, t represent the low dictionary element of differentiating of t, T representes the low total quantity of differentiating the dictionary element, i.e. and T=20000, || ²The squared absolute value operation of () is got in expression;

5 4c) that preceding 5 results minimum among the distance B IST1 (t) are corresponding low dictionary elements of differentiating are designated as D _L1(k), k=1 ..., 5, through the low dictionary D that differentiates _L1With high-resolution dictionary D _H1Between corresponding relation, find high-resolution dictionary D _H1In corresponding 5 high-resolution dictionary element D _H1(k), k=1 ..., 5;

4d) utilize the partial weight formula to calculate 5 low dictionary element D that differentiate _L1(k) reconstructed image piece P _l(i) reconstruction coefficients w (k), k=1 ..., 5;

4e) with reconstruction coefficients w (k) and step 4c) in 5 high-resolution dictionary element D searching _H1(k) sue for peace, obtain full resolution pricture piece P _h(i), its computing formula is:

$P_h\left(i\right)=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}w\left(k\right)D_{h1}\left(k\right),$

4f) mark i=i+1 is set, judges whether the i＞G that satisfies condition,, then obtain the high-resolution estimated image X of reconstruct if satisfy _H1, execution in step (5), otherwise return step 4b);

(5) utilization obtains at dictionary (D respectively with step (4) same procedure _H2, D _L2), (D _H3, D _L3) ..., (D _H5, D _L5) under high-resolution estimated image X _H2, X _H3, X _H4, X _H5

(6) utilize pending low resolution image X _LConstruct a pair of low-and high-frequency dictionary D _f={ D _Hf, D _Lf;

(7) establish neighbour's parameter A=5, at low-and high-frequency dictionary D _f={ D _Hf, D _LfDown the reconstruct size be the high-resolution estimated image X of 2m * 2n _H6:

7a) utilize imresize function in the matlab software with pending low resolution image X _LAmplify in advance, enlargement factor 2 obtains preparatory enlarged image X _L ^*, the image size is 2m * 2n;

7b) to preparatory enlarged image X _L ^*Carry out size and be 3 * 3 piecemeal, overlapping 2 pixels of adjacent block obtain preparatory enlarged image piece P _l(j) ^*, j=1 ..., S;

7c) utilize following formula to calculate preparatory enlarged image piece P _l(j) ^*With low frequency dictionary D _LfIn the distance B IST2 (u) of each element:

DIST2(u)＝|P _l(j) ^*-D _lf(u)| ²，

D wherein _Lf(u), u=1,2 ..., U, u represent u low frequency dictionary element, U representes the total quantity of low frequency dictionary element, || ²The square operation of () absolute value is got in expression;

7d) A corresponding low frequency dictionary element of preceding A result minimum among the distance B IST2 (u) is designated as D _Lf(r), r=1,2 ... A, through low frequency dictionary D _LfWith high-resolution dictionary D _HfCorresponding relation, find high frequency dictionary D _HfCorresponding A high frequency dictionary element D _Hf(r), r=1 ..., A;

7e) utilize the partial weight formula to calculate A low frequency dictionary element D _Lf(r) the preparatory enlarged image piece of reconstruct P _l(j) ^*Reconstruction coefficients c (r), r=1 ..., A;

7f) with reconstruction coefficients c (r) and step 7d) in A high frequency dictionary element D searching _Hf(r) sue for peace, obtain the high frequency imaging piece P of reconstruct _h(j) ^*:

$P_h{\left(j\right)}^{*}=\underset{r=1}{\overset{A}{\mathrm{\Σ}}}c\left(r\right)D_{\mathrm{hf}}\left(r\right),$

7g) with the high frequency imaging piece P that obtains _h(j) ^*With preparatory enlarged image piece P _l(j) ^*Addition, the full resolution pricture piece X that obtains rebuilding _h(j) ^*

7h) mark j=j+1 is set, judges whether the j＞S that satisfies condition,, then obtain amplifying 2 times full resolution pricture X if satisfy _H6, execution in step (8), otherwise return step 7c);

Neighbour's parameter of (8) establishing respectively in the step (7) is established neighbour's parameter A=4 in the step (7) respectively, A=3, and A=2, A=1, repeating step (7) obtains high-resolution estimated image X _H7, X _H8, X _H9, X _H10

10 panel heights that (9) will obtain are differentiated estimated image X _H1, X _H2..., X _H10All pull into row, constitute high dimensional data X, utilize the low-rank decomposition algorithm that high dimensional data X is carried out low-rank and decompose, obtain low-rank matrix L and the sparse matrix S of X;

(10) through the reshape function in the matlab software, each row in the low-rank matrix L are reduced into image format, obtain 10 width of cloth low-rank image L (z), z=1 ..., 10;

(11) by following formula 10 width of cloth low-rank image L (z) are done average and handle, obtain final picture rich in detail X _H:

$X_H=\frac{{\mathrm{\Σ}}_{z=1}^{10}L\left(z\right)}{10}.$

The present invention has the following advantages compared with prior art:

The present invention utilizes 5 pairs of outside height to differentiate dictionary and 1 pair of inner low-and high-frequency dictionary carries out the super-resolution reconstruction to low resolution image; The own high-frequency information that has kept image when introducing external details information; Compare with traditional super-resolution reconstruction algorithm; The image outline of rebuilding is more clear, and detailed information is abundanter.Emulation experiment shows that the present invention can effectively carry out super-resolution to low resolution image and rebuild, and increases the detailed information of image, has improved the sharpness of reconstructed image.

Description of drawings

Fig. 1 is a process flow diagram of the present invention;

Fig. 2 is that 5 panel heights that the present invention uses when in emulation experiment, setting up the high-resolution dictionary are differentiated training image;

Fig. 3 is that the present invention sets up the low training image of differentiating of 5 width of cloth that use when hanging down the resolution dictionary in emulation experiment;

Fig. 4 is the low resolution chart picture of Lena that the present invention uses in emulation experiment;

Fig. 5 is the Lena high-resolution reconstructed image that the present invention obtains in emulation experiment;

Fig. 6 is the existing Lena high-resolution reconstructed image that in experiment, obtains based on the neighborhood embedding grammar;

Fig. 7 is the existing Lena high-resolution reconstructed image that in experiment, obtains based on the method for rarefaction representation dictionary study.

Embodiment

With reference to Fig. 1, concrete performing step of the present invention is following:

Step 1 is imported pending low resolution image X _L, as shown in Figure 4, the image size is m * n, and wherein m is a picturedeep, and n is a picturewide, and setting enlargement factor is 2, with pending low resolution image X _LCarry out size and be 3 * 3 piecemeal, overlapping 2 pixels between the adjacent block obtain G pending low resolution image piece P _l(i), i=1 ..., G.

Step 2 is imported the low training image of differentiating of the 5 panel heights resolution training image and corresponding 5 width of cloth, and it is as shown in Figure 2 that wherein 5 panel heights are differentiated training image, and the low resolution of 5 width of cloth training image is as shown in Figure 3, utilizes 5 high-resolution dictionary D of training image structure _H1, D _H2..., D _H5With corresponding 5 low dictionary D that differentiate _L1, D _L2..., D _L5

2a) 5 panel heights of input being differentiated training image, to carry out size be 6 * 6 piecemeal, and overlapping 4 pixels between the adjacent block obtain Y high-resolution training image blocks H _y, y=1,2 ..., Y, wherein 100000≤Y≤30000;

2b) differentiate training image to carry out size be 3 * 3 piecemeal 5 width of cloth of input are low, overlapping 2 pixels between the adjacent block obtain Y the low training image blocks L that differentiates _y, y=1,2 ..., Y, wherein 100000≤Y≤30000;

2c) from Y full resolution pricture piece H _y100,000 full resolution pricture piece H of middle extraction _q, q=1,2 ..., 100000, accordingly from Y the low training image blocks L that differentiates _y100,000 low resolution image piece L of middle extraction _q, q=1,2 ..., 100000;

100,000 full resolution pricture piece H that 2d) will extract respectively _qWith 100,000 low resolution image piece L _qBe divided into 5 groups at random, obtain 5 high-resolution dictionary D _H1, D _H2..., D _H5With corresponding 5 low dictionary D that differentiate _L1, D _L2..., D _L5

Step 3 is at the 1st pair of high-resolution and the low dictionary (D that differentiates _H1, D _L1) down the reconstruct size be the full resolution pricture X of 2m * 2n _H1

3a) extract pending low resolution image piece P _l(i), initialization P _l(i) be labeled as i=1;

3b) utilize following formula to calculate pending low resolution image piece P _l(i) with the low dictionary D that differentiates _L1In the distance B IST1 (t) of each element:

DIST1(t)＝|P _l(i)-D _l1(t)| ²，

D wherein _L1(t), t=1,2 ..., T, t represent the low dictionary element of differentiating of t, T representes the low total quantity of differentiating the dictionary element, i.e. and T=20000, || ²The squared absolute value operation of () is got in expression;

5 3c) that preceding 5 results minimum among the distance B IST1 (t) are corresponding low dictionary elements of differentiating are designated as D _L1(k), k=1 ..., 5, through the low dictionary D that differentiates _L1With high-resolution dictionary D _H1Between corresponding relation, find high-resolution dictionary D _H1In corresponding 5 high-resolution dictionary element D _H1(k), k=1 ..., 5;

3d) utilize the partial weight formula to calculate 5 low dictionary element D that differentiate _L1(k) reconstructed image piece P _l(i) reconstruction coefficients w (k), k=1 ..., 5, computing formula is following:

w(k)＝((P _l(i)-D _l1(k)) ^T×(P _l(i)-D _l1(k))/I _k)/c，

Wherein, normalized factor $c=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{(P_l\left(i\right)-D_{l1}\left(k\right))}^T\×(P_l\left(i\right)-D_{l1}\left(k\right))/I_k,$ I _kBe that size is complete 1 matrix of 5x1, () ^TOperation expression matrix transpose operation;

3e) with reconstruction coefficients w (k) and step 3c) in 5 high-resolution dictionary element D searching _H1(k) sue for peace, obtain full resolution pricture piece P _h(i):

$P_h\left(i\right)=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}w\left(k\right)D_{h1}\left(k\right),$

3f) mark i=i+1 is set, judges whether the i＞G that satisfies condition,, then obtain the high-resolution estimated image X of reconstruct if satisfy _H1, execution in step 4, otherwise return step 3b).

Step 4 utilizes the method identical with step 3 to obtain at dictionary (D respectively _H2, D _L2), (D _H3, D _L3) ..., (D _H5, D _L5) under high-resolution estimated image X _H2, X _H3, X _H4, X _H5

Step 5 is utilized pending low resolution image X _LConstruct a pair of low-and high-frequency dictionary D _f={ D _Hf, D _Lf.

5a) to pending low resolution image X _LCarry out Gauss's high-pass filtering and handle, obtain pending low resolution image X _LHigh fdrequency component X _H0With low frequency component X _L0

5b) respectively to high fdrequency component X _H0With low frequency component X _L0Carry out size and be 3 * 3 piecemeal, overlapping 2 pixels of adjacent block obtain 1 couple of low-and high-frequency dictionary D _f={ D _Hf, D _Lf.

Step 6 is established neighbour's parameter A=5, at low-and high-frequency dictionary D _f={ D _Hf, D _LfDown the reconstruct size be the high-resolution estimated image X of 2m * 2n _H6

6a) utilize imresize function in the matlab software with pending low resolution image X _LAmplify in advance, enlargement factor 2 obtains preparatory enlarged image X _L ^*, the image size is 2m * 2n;

6b) to preparatory enlarged image X _L ^*Carry out size and be 3 * 3 piecemeal, overlapping 2 pixels of adjacent block obtain preparatory enlarged image piece P _l(j) ^*, j=1 ..., S;

6c) utilize following formula to calculate preparatory enlarged image piece P _l(j) ^*With low frequency dictionary D _LfIn the distance B IST2 (u) of each element:

DIST2(u)＝|P _l(j) ^*-D _lf(u)| ²，

D wherein _Lf(u), u=1,2 ..., U, u represent u low frequency dictionary element, U representes the total quantity of low frequency dictionary element, || ²The square operation of () absolute value is got in expression;

6d) A corresponding low frequency dictionary element of preceding A result minimum among the distance B IST2 (u) is designated as D _Lf(r), r=1,2 ... A, through low frequency dictionary D _LfWith high-resolution dictionary D _HfCorresponding relation, find high frequency dictionary D _HfCorresponding A high frequency dictionary element D _Hf(r), r=1 ..., A;

6e) utilize the partial weight formula to calculate A low frequency dictionary element D _Lf(r) the preparatory enlarged image piece of reconstruct P _l(j) ^*Reconstruction coefficients c (r), r=1 ..., A, the partial weight computing formula is:

c(r)＝((P _l(j) ^*-D _lf(r)) ^T×(P _l(j) ^*-D _lf(r))/I _r)/h，

Wherein, normalized factor $h=\underset{r=1}{\overset{A}{\mathrm{\Σ}}}{(P_l{\left(j\right)}^{*}-D_{\mathrm{Lf}}\left(r\right))}^T\×(P_l{\left(j\right)}^{*}-D_{\mathrm{Lf}}\left(r\right))/I_r,$ I _rBe that size is complete 1 matrix of Ax1, () ^TOperation expression matrix transpose operation;

6f) with reconstruction coefficients c (r) and step 6d) in A high frequency dictionary element D searching _Hf(r) sue for peace, obtain the high frequency imaging piece P of reconstruct _h(j) ^*:

$P_h{\left(j\right)}^{*}=\underset{r=1}{\overset{A}{\mathrm{\Σ}}}c\left(r\right)D_{\mathrm{hf}}\left(r\right),$

6g) with the high frequency imaging piece P that obtains _h(j) ^*With preparatory enlarged image piece P _l(j) ^*Addition, the full resolution pricture piece X that obtains rebuilding _h(j) ^*

6h) mark j=j+1 is set, judges whether the j＞S that satisfies condition,, then obtain amplifying 2 times full resolution pricture X if satisfy _H6, execution in step 7, otherwise return step 6c).

Step 7 is established neighbour's parameter A=4 in the step 6 respectively, A=3, and A=2, A=1, repeating step 6 obtain high-resolution estimated image X _H7, X _H8, X _H9, X _H10

Step 8 is differentiated reconstructed image X with 10 panel heights that obtain _H1, X _H2..., X _H10All pull into row, constitute high dimensional data X, utilize the low-rank decomposition algorithm that high dimensional data X is carried out low-rank and decompose, obtain low-rank matrix L and the sparse matrix S of high dimensional data X.

Utilizing the low-rank decomposition algorithm that high dimensional data X is carried out low-rank in above-mentioned decomposes; Realize through existing low-rank decomposition method; This method is proposed in 2009 by people such as Emmanuel candes and Yi Ma, referring to document " Robust Principal Component Analysis " Computing Research Repository-CORR, and vol.abs/0912.3; 2009, concrete operations are following:

8a) initialization iterations t=0, iteration error ε are 0.0001;

8b) establish t=t+1, utilize the randn function in the matlab software to generate the random gaussian matrix M, obtain 3 intermediate variable matrixes according to following formula:

G ₁＝X×M，G ₂＝X ^T×G ₁，G ₃＝X×G ₂；

8c) calculate the low-rank matrix L in the iteration the t time _tWith sparse matrix S _t:

L _t＝G ₃×(G ₁ ^T×G ₃) ^-1G ₂ ^T，

S _t＝P _Ω|X-L _t|，

Wherein () ^TOperation expression matrix transpose operation, () ^-1The representing matrix operation of inverting, P _ΩPreceding Ω maximum in () numerical value is got in () expression, and Ω gets 30000 among the present invention;

8d) judge stopping criterion for iteration: if

Set up, then stop iteration, and with matrix L _tBe made as the low-rank matrix L of being asked, matrix S _tBe made as the sparse matrix S that is asked, otherwise return step 8b),

Wherein,

representing matrix 2 norms square.

Step 9 utilizes the low-rank matrix L to obtain 10 width of cloth low-rank image L (z), z=1, and 2 ..., 10, it is done average handle, obtain final high-resolution reconstructed image X _H

9a) the reshape function in the use matlab software with being reduced into image, obtains 10 width of cloth low-rank image L (z) with each row in the low-rank matrix L, z=1, and 2 ..., 10;

9b) press following formula to low-rank image L (z), z=1,2 ..., 10 do average handles, and obtains final high-resolution reconstructed image X _H:

$X_H=\frac{{\mathrm{\Σ}}_{z=1}^{10}L\left(z\right)}{10}.$

Effect of the present invention can specify through following experiment:

1. experiment condition: the CPU that tests used microcomputer is Intel Core2 Duo 2.33GHz, in save as 2GB, programming platform is Matlab R2009a.Test used image and derive from the standard picture storehouse, be respectively Lena, House, the Girl size is 256 * 256.

2. experiment content

This experiment specifically is divided into three experiments:

Experiment one: utilize the present invention that low resolution image is carried out super-resolution and rebuild, the result is as shown in Figure 5;

Experiment two: utilize the existing method that embeds based on neighborhood that low resolution image is carried out super-resolution and rebuild, the result is as shown in Figure 6;

Experiment three: utilize existing method based on the study of rarefaction representation dictionary that low resolution image is carried out super-resolution and rebuild, the result is as shown in Figure 7.

In the emulation experiment, use Y-PSNR PSNR evaluation index and estimate the quality of restoring the result, its PSNR is defined as:

$\mathrm{PSNR}=10{\log }_{10}\left(\frac{{255}^2\×M\×N}{\mathrm{\Σ}{\left|\right|x-f\left|\right|}^2}\right)$

Wherein, f is a picture rich in detail, and x is the image after rebuilding, and M and N are number of lines of pixels and the pixel columns of picture rich in detail f.

With the present invention and existing based on the field embedding grammar, based on rarefaction representation dictionary learning method, respectively to image Lena, House and Girl carry out super-resolution and rebuild emulation.Use Y-PSNR PSNR reconstructed results figure is estimated, evaluation result is as shown in table 1, and wherein, Alg1 is a method of the present invention, and Alg2 is based on the method that the field embeds, and Alg3 is based on the method for rarefaction representation dictionary study.

Table 1. the present invention and two kinds of PSNR values (unit is dB) that control methods obtains in emulation experiment

3. interpretation

As can beappreciated from fig. 5, the reconstructed results of the Lena that the present invention obtains has not only been replenished detail of the high frequency effectively, makes image edge clear, and visual effect is better simultaneously;

As can beappreciated from fig. 6, the reconstructed results that the existing method that embeds based on the field obtains is too level and smooth, and detailed information lacks, and image is fuzzyyer;

As can beappreciated from fig. 7, there is noise in the existing image border that obtains based on the method for rarefaction representation dictionary study, and visual effect is bad;

As can be seen from Table 1, the present invention has higher PSNR value, more effectively Reconstructing High than other two kinds of control methods.

Claims (6)

1. the image super-resolution method for reconstructing based on doubledictionary study comprises the steps:

(1) pending low resolution image X of input _L, the image size is m * n, the enlargement factor of setting image is 2;

(2) to pending low resolution image X _LCarry out size and be 3 * 3 piecemeal, overlapping 2 pixels between the adjacent block obtain G pending low resolution image piece P _l(i), i=1 ..., G;

(3) input 5 panel heights are differentiated training image and the low training image of differentiating of corresponding 5 width of cloth, utilize 5 high-resolution dictionary D of training image structure _H1, D _H2..., D _H5With corresponding 5 low dictionary D that differentiate _L1, D _L2..., D _L5

(4) at the 1st pair of high-resolution and the low dictionary (D that differentiates _H1, D _L1) under, the reconstruct size is the high-resolution estimated image X of 2m * 2n _H1:

4a) extract pending low resolution image piece P _l(i), initialization P _l(i) be labeled as i=1;

4b) utilize following formula to calculate pending low resolution image piece P _l(i) with the low dictionary D that differentiates _L1In the distance B IST1 (t) of each element:

DIST1(t)＝|P _l(i)-D _l1(t)| ²，

D wherein _L1(t), t=1,2 ..., T, t represent the low dictionary element of differentiating of t, T representes the low total quantity of differentiating the dictionary element, i.e. and T=20000, || ²The squared absolute value operation of () is got in expression;

5 4c) that preceding 5 results minimum among the distance B IST1 (t) are corresponding low dictionary elements of differentiating are designated as D _L1(k), k=1 ..., 5, through the low dictionary D that differentiates _L1With high-resolution dictionary D _H1Between corresponding relation, find high-resolution dictionary D _H1In corresponding 5 high-resolution dictionary element D _H1(k), k=1 ..., 5;

4d) utilize the partial weight formula to calculate 5 low dictionary element D that differentiate _L1(k) reconstructed image piece P _l(i) reconstruction coefficients w (k), k=1 ..., 5;

4e) with reconstruction coefficients w (k) and step 4c) in 5 high-resolution dictionary element D searching _H1(k) sue for peace, obtain full resolution pricture piece P _h(i), its computing formula is:

$P_h\left(i\right)=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}w\left(k\right)D_{h1}\left(k\right),$

4f) mark i=i+1 is set, judges whether the i＞G that satisfies condition,, then obtain the high-resolution estimated image X of reconstruct if satisfy _H1, execution in step (5), otherwise return step 4b);

(5) utilization obtains at dictionary (D respectively with step (4) same procedure _H2, D _L2), (D _H3, D _L3) ..., (D _H5, D _L5) under high-resolution estimated image X _H2, X _H3, X _H4, X _H5

(6) utilize pending low resolution image X _LConstruct a pair of low-and high-frequency dictionary D _f={ D _Hf, D _Lf;

(7) establish neighbour's parameter A=5, at low-and high-frequency dictionary D _f={ D _Hf, D _LfDown the reconstruct size be the high-resolution estimated image X of 2m * 2n _H6:

7a) utilize imresize function in the matlab software with pending low resolution image X _LAmplify in advance, enlargement factor 2 obtains preparatory enlarged image X _L ^*, the image size is 2m * 2n;

7b) to preparatory enlarged image X _L ^*Carry out size and be 3 * 3 piecemeal, overlapping 2 pixels of adjacent block obtain preparatory enlarged image piece P _l(j) ^*, j=1 ..., S;

7c) utilize following formula to calculate preparatory enlarged image piece P _l(j) ^*With low frequency dictionary D _LfIn the distance B IST2 (u) of each element:

DIST2(u)＝|P _l(j) ^*-D _lf(u)| ²，

D wherein _Lf(u), u=1,2 ..., U, u represent u low frequency dictionary element, U representes the total quantity of low frequency dictionary element, || ²The square operation of () absolute value is got in expression;

7d) A corresponding low frequency dictionary element of preceding A result minimum among the distance B IST2 (u) is designated as D _Lf(r), r=1,2 ... A, through low frequency dictionary D _LfWith high-resolution dictionary D _HfCorresponding relation, find high frequency dictionary D _HfCorresponding A high frequency dictionary element D _Hf(r), r=1 ..., A;

7e) utilize the partial weight formula to calculate A low frequency dictionary element D _Lf(r) the preparatory enlarged image piece of reconstruct P _l(j) ^*Reconstruction coefficients c (r), r=1 ..., A;

7f) with reconstruction coefficients c (r) and step 7d) in A high frequency dictionary element D searching _Hf(r) sue for peace, obtain the high frequency imaging piece P of reconstruct _h(j) ^*:

$P_h{\left(j\right)}^{*}=\underset{r=1}{\overset{A}{\mathrm{\Σ}}}c\left(r\right)D_{\mathrm{hf}}\left(r\right),$

7g) with the high frequency imaging piece P that obtains _h(j) ^*With preparatory enlarged image piece P _l(j) ^*Addition, the full resolution pricture piece X that obtains rebuilding _h(j) ^*

7h) mark j=j+1 is set, judges whether the j＞S that satisfies condition,, then obtain amplifying 2 times full resolution pricture X if satisfy _H6, execution in step (8), otherwise return step 7c);

Neighbour's parameter of (8) establishing respectively in the step (7) is established neighbour's parameter A=4 in the step (7) respectively, A=3, and A=2, A=1, repeating step (7) obtains high-resolution estimated image X _H7, X _H8, X _H9, X _H10

10 panel heights that (9) will obtain are differentiated estimated image X _H1, X _H2..., X _H10All pull into row, constitute high dimensional data X, utilize the low-rank decomposition algorithm that high dimensional data X is carried out low-rank and decompose, obtain low-rank matrix L and the sparse matrix S of X;

(10) through the reshape function in the matlab software, each row in the low-rank matrix L are reduced into image format, obtain 10 width of cloth low-rank image L (z), z=1 ..., 10;

(11) by following formula 10 width of cloth low-rank image L (z) are done average and handle, obtain final picture rich in detail X _H:

$X_H=\frac{{\mathrm{\Σ}}_{z=1}^{10}L\left(z\right)}{10}.$

2. the image super-resolution method for reconstructing based on doubledictionary study according to claim 1, wherein said 5 the high-resolution dictionary D of training image structure that utilize of step (3) _H1, D _H2..., D _H5With corresponding 5 low dictionary D that differentiate _L1, D _L2..., D _L5, performing step is following:

3a) 5 panel heights of input being differentiated training image, to carry out size be 6 * 6 piecemeal, and overlapping 4 pixels between the adjacent block obtain Y high-resolution training image blocks H _y, y=1,2 ..., Y, wherein 100000≤Y≤30000;

3b) differentiate training image to carry out size be 3 * 3 piecemeal 5 width of cloth of input are low, overlapping 2 pixels between the adjacent block obtain Y the low training image blocks L that differentiates _y, y=1,2 ..., Y, wherein 100000≤Y≤30000;

3c) from Y full resolution pricture piece H _y100,000 full resolution pricture piece H of middle extraction _q, q=1,2 ..., 100000, accordingly from Y the low training image blocks L that differentiates _y100,000 low resolution image piece L of middle extraction _q, q=1,2 ..., 100000;

100,000 full resolution pricture piece H that 3d) will extract respectively _qWith 100,000 low resolution image piece L _qBe divided into 5 groups at random, obtain 5 high-resolution dictionary D _H1, D _H2..., D _H5With corresponding 5 low dictionary D that differentiate _L1, D _L2..., D _L5

3. the image super-resolution method for reconstructing based on doubledictionary study according to claim 1, wherein step 4d) said 5 the low dictionary element D that differentiate of partial weight formula calculating that utilize _L1(k) reconstructed image piece P _l(i) reconstruction coefficients w (k), k=1 ..., 5, be to calculate through following formula:

w(k)＝((P _l(i)-D _l1(k)) ^T×(P _l(i)-D _l1(k))/I _k)/g，

Wherein, normalized factor $g=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{(P_l\left(i\right)-D_{l1}\left(k\right))}^T\×(P_l\left(i\right)-D_{l1}\left(k\right))/I_k,$ I _kBe that size is complete 1 matrix of 5x1, () ^TOperation expression matrix transpose operation.

4. the image super-resolution method for reconstructing based on doubledictionary study according to claim 1, wherein step (6) is said utilizes pending low resolution image X _LConstruct a pair of low-and high-frequency dictionary D _f={ D _Hf, D _Lf, performing step is following:

6a) to pending low resolution image X _LCarry out Gauss's high-pass filtering and handle, obtain pending low resolution image X _LHigh fdrequency component X _H0With low frequency component X _L0

6b) respectively to high fdrequency component X _H0With low frequency component X _L0Carry out size and be 3 * 3 piecemeal, overlapping 2 pixels of adjacent block obtain 1 couple of low-and high-frequency dictionary D _f={ D _Hf, D _Lf.

5. the image super-resolution method for reconstructing based on doubledictionary study according to claim 1, wherein step 7e) described A the low frequency dictionary element D of partial weight formula calculating that utilize _Lf(r) the preparatory enlarged image piece of reconstruct P _l(j) ^*Reconstruction coefficients c (r), r=1 ..., A is to calculate through following formula:

c(r)＝((P _l(j) ^*-D _lf(r)) ^T×(P _l(j) ^*-D _lf(r))/I _r)/h，

Wherein, normalized factor $h=\underset{r=1}{\overset{A}{\mathrm{\Σ}}}{(P_l{\left(j\right)}^{*}-D_{\mathrm{Lf}}\left(r\right))}^T\×(P_l{\left(j\right)}^{*}-D_{\mathrm{Lf}}\left(r\right))/I_r,$ I _rBe that size is complete 1 matrix of Ax1, () ^TOperation expression matrix transpose operation.

6. the image super-resolution method for reconstructing based on doubledictionary study according to claim 1, wherein the said low-rank decomposition algorithm that utilizes of step (9) carries out the low-rank decomposition to high dimensional data X, obtains low-rank matrix L and the sparse matrix S of X, and performing step is following:

9a) initialization iterations t=0, iteration error ε are 0.0001;

9b) establish t=t+1, utilize the randn function in the matlab software to generate the random gaussian matrix M, obtain 3 intermediate variable matrixes according to following formula:

G ₁＝X×M，G ₂＝X ^T×G ₁，G ₃＝X×G ₂；

9c) calculate the low-rank matrix L in the iteration the t time _tWith sparse matrix S _t:

L _t＝G ₃×(G ₁ ^T×G ₃) ^-1G ₂ ^T，

S _t＝P _Ω|X-L _t|，

Wherein () ^TOperation expression matrix transpose operation, () ^-1The representing matrix operation of inverting, P _ΩPreceding Ω maximum in () numerical value is got in () expression, and Ω gets 30000 among the present invention;

9d) judge stopping criterion for iteration: if

Set up, then stop iteration, and with matrix L _tBe made as the low-rank matrix L of being asked, matrix S _tBe made as the sparse matrix S that is asked, otherwise return step 9b),

Wherein, representing matrix 2 norms square.

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