CN103366347B - Image super-resolution rebuilding method based on rarefaction representation - Google Patents

Abstract

The invention discloses a kind of image super-resolution rebuilding method based on rarefaction representation, including sample training step and image super-resolution rebuilding step；Described sample training step includes: the gradient information of calculating low-resolution image and high-definition picture and the residual information of low-resolution image；Low resolution characteristic set and high-resolution features set is obtained by sparse expression method；Described image super-resolution rebuilding step includes: calculate the gradient information of pending low-resolution image；Its rarefaction representation coefficient vector is found in low resolution characteristic set；In high-resolution features set, find the residual information of correspondence, this residual information is fused on low-resolution image, it is thus achieved that high-definition picture.The high-definition picture details that the present invention obtains is more rich, edge is apparent, has more preferable visual effect.The present invention can become in HD video to apply in SD video conversion.

Description

Image super-resolution rebuilding method based on rarefaction representation

Technical field

The present invention relates to technical field of image processing, particularly relate to a kind of Image Super-resolution based on rarefaction representation Rate method for reconstructing.

Background technology

SD video (Standard Definition, SD), refer to resolution VCD about 400 lines, The video such as DVD, TV programme.High definition (High Definition, HD), refer at least to possess 720 lines by Row scanning or 1080 line interlaces and screen width high ratio are the video of 16:9.Relatively SD video and height The specification of clear video it will be seen that both difference are mainly in resolution and the ratio of width to height, that wherein change it is crucial that The raising of video resolution.

Image super-resolution rebuilding technology is a kind of resolution technique solution promoting image, the most conventional Image super-resolution method has three major types: based on interpolation, based on rebuilding and method based on study.Based on interpolation Method estimate the information of interpolation point mainly by the strong correlation of neighbor, such method speed fast and Simply, but the best for region, image border and texture region treatment effect, and reconstructed results details is the abundantest. It is to use a priori assumption generating model from high-definition picture to low-resolution image based on the method rebuild Solving super-resolution problem, the shortcoming of such method is due to the life of high-definition picture to low-resolution image Become model a priori assumption inaccurate, based on rebuild method can along with the raising of amplification serious degradation, Two kinds of methods all can cause image detail and marginal portion poor effect.

Summary of the invention

Goal of the invention: based on the problems referred to above, the present invention proposes a kind of image super-resolution based on rarefaction representation Method for reconstructing.

Technical scheme: image super-resolution rebuilding method based on rarefaction representation, including sample training step and figure As super-resolution rebuilding step；Described sample training step includes: calculate low-resolution image gradient information and High-definition picture and the residual information of low-resolution image；Low resolution feature is obtained by sparse expression method Set and high-resolution features set；Described image super-resolution rebuilding step includes: calculate pending low resolution The gradient information of rate image；Its rarefaction representation coefficient vector is found in low resolution characteristic set；At high-resolution Rate characteristic set finds the residual information of correspondence, this residual information is fused on low-resolution image, it is thus achieved that High-definition picture.

Preferably, in described image super-resolution rebuilding step, fast orthogonal based on classificating thought is utilized to mate Tracing algorithm finds its rarefaction representation coefficient vector in low resolution characteristic set.

The present invention uses technique scheme, has the advantages that technical solution of the present invention has added up a large amount of Image, and the extraction of feature is all relevant with gradient and high-frequency information, therefore, the high-resolution finally obtained Image detail is more rich, edge is apparent, has more preferable visual effect.

Accompanying drawing explanation

Fig. 1 is sample training flow chart of steps of the present invention；

Fig. 2 is image super-resolution rebuilding flow chart of steps of the present invention；

Fig. 3 is the inventive method with bicubic interpolation algorithm at the comparison diagram of Y-PSNR (PSNR).

Detailed description of the invention

Below in conjunction with specific embodiment, it is further elucidated with the present invention, it should be understood that these embodiments are merely to illustrate this Invention rather than restriction the scope of the present invention, after having read the present invention, those skilled in the art are to this The amendment of the bright various equivalent form of values all falls within the application claims limited range.

A kind of image super-resolution rebuilding method based on rarefaction representation, is divided into two parts, is sample instruction respectively Practice step and image super-resolution rebuilding step.In sample training step, first calculate the ladder of low-resolution image The residual information of degree information and high-definition picture and low-resolution image, and then obtained by sparse expression method Low resolution characteristic set and high-resolution features set.In image super-resolution rebuilding step, first calculate and treat Process the gradient information of image, in low resolution characteristic set, then find its approximate representation, the most permissible In high-resolution features set, find the residual information of correspondence, this residual information is fused to low-resolution image On, it is possible to obtain high-definition picture.Concrete technical scheme is as follows:

Concrete:

Sample training step, as shown in Figure 1:

1, high-definition picture training sample database is builtImage in Sample Storehouse carries out bicubic fall adopt Sample processes, and obtains low-resolution imageThe most rightCarry out bicubic liter sampling and obtain super-resolution reconstruction Image { T_l ^j}。

2, high-definition picture and the residual image rebuild between image are calculatedTo residual Difference imageTravel through with the window of 6 × 6, extract 6 × 6 image block and be converted into a length of 36 to Amount, is designated asWherein K is the sequence number of block.

3, for each panel height resolution reconstruction image { T_l ^j, respectively both horizontally and vertically with 1 × 3 and 1 × 5 Gradient operator is filtered, and obtains four filtering images(r=1,2,3,4).Same with 6 × 6 Window is to imageTravel through, the image block of 46 × 6 in extraction same position, and change growth Degree is the vector of 144, is designated asWherein K is the sequence number of block.

4, rightCarry out dimension-reduction treatment to obtainWherein B isDimensionality reduction base vector matrix.

5, following formula is utilized to calculateRarefaction representation coefficient and characteristic set:

$\begin{array}{ccc}\{A_l,q^k\}=\underset{\{A_l,q^k\}}{\arg \min }\underset{k}{\mathrm{\Σ}}{\left|\right|p_l^k-A_l{q}^k\left|\right|}^2& s.t.{\left|\right|q^k\left|\right|}_0\≤L& \∀k.\end{array}$

Wherein A_lIt is low resolution characteristic set, q^kFor character pairRarefaction representation coefficient in Al characteristic set Vector.

6, following formula is utilized to calculate high-resolutionCharacteristic set A_h:

$A_h=\underset{A_h}{\arg \min }\underset{k}{\mathrm{\Σ}}{\left|\right|p_h^k-A_h{q}^k\left|\right|}_2^2.$

Image super-resolution rebuilding step, as shown in Figure 2:

1, to pending low-resolution image s_lCarry out the image y that bicubic interpolation is amplified_l。

2, to image y_lBoth horizontally and vertically it is being filtered by 1 × 3 and 1 × 5 gradient operator respectively, is obtaining Four filtering image { y_f}_r(r=1,2,3,4).Window with 6 × 6 is to image { y_f}_rCarry out traversing operation, The image block of 46 × 6 in extraction same position, and it is converted into the one-dimensional vector of a length of 144, it is designated as Wherein k is the sequence number of block.

3, the base vector matrix B of step 4 during utilization training, obtainsCharacteristic after dimensionality reduction ${\left\{m_l^k\right\}}_k=B^T*{\tilde{m}}_l^k.$

4, forUtilize fast orthogonal matching pursuit algorithm at low resolution characteristic set A_lIn find Its rarefaction representation coefficient vector { n^k}_k。

5, by coefficient vector { n^k}_kFeature corresponding with high-resolution features set is multiplied, and obtains high-resolution BlockThe high-resolution block that will obtainWith y_lImage carries out fusion treatment, it is thus achieved that Whole high-definition picture

The core of process of reconstruction is a kind of fast orthogonal matching algorithm based on classificating thought.Conventional orthogonal Joining algorithm algorithm essential idea is: with the row of the method choice sensing matrix Φ of greedy iteration so that the most repeatedly Row selected in Dai are relevant to current redundancy vector maximum degree ground, deduct relevant portion from measuring vector And iterate, until iterations reaches degree of rarefication K, force iteration stopping.Its step is as follows:

Input: sensing matrix Φ, vector of samples y, degree of rarefication K；

Output: sparse the approaching of K-of x

Initialize: residual error r_t-1=y, rebuilds atom set Λ_t-1=φ (t=1)；

Circulation performs step 1-4.

1, residual error r is calculated_t-1Each column vector with in sensing matrixSimilarity, and it is maximum to extract similarity Column vector is designated asThis vector is added and rebuilds atom set, the reconstruction atom set after being updated

2, obtained by least square ${\hat{x}}_t=\arg \min {\left|\right|y-{\mathrm{\Λ}}_t\hat{x}\left|\right|}_2;$

3, residual error is updatedT=t+1；

4, judging whether to meet t ＞ K, if meeting, then stopping iteration；If being unsatisfactory for, then perform step 1.

Above-mentioned orthogonal matching pursuit algorithm carries out traversal search to each column vector in sensing matrix owing to needing, Time-consuming very serious, the searching that the present invention is directed to the maximum column vector of step 1 similarity for this improves, profit By the thought of classification, will sensing matrix arrangeIt is divided into K class, and continues to divide by each subclass Go down, until the atom number that subclass comprises is less than the number of initial setting up, and finding the atom of coupling recently Time, it is only necessary to compare with all kinds of center of each layer, the class center that chosen distance is nearest, press in this type of subclass According to same search mechanisms, until lowermost layer.The method can be greatly reduced the row of residual error r and sensing matrix VectorThe number of times of Similarity Measure, specifically comprises the following steps that

1, sensing matrix Φ is divided into K class, is designated as Φ respectively₁,Φ₂,...,Φ_k；

2, calculating Mei Lei center is to the ultimate range at other kinds center, is designated as D respectively₁,D₂,...,D_k；

3, the distance at sensing matrix Zhong Daomeilei center is combined into new sensing square less than the atom of ultimate range Battle array, is designated as

4, choose respectivelyAs new sensing matrix, if former in certain new sensing matrix Sub-number is less than the number of initial setting up, then this sensing matrix stops classification, otherwise performs step 1.

Seeing Fig. 3, this method uses Y-PSNR (PSNR) to weigh super-resolution image reconstruction result, Wherein, representing standard picture with B, standard picture is original the treating of the inventive method input after down-sampled Processing image, image X is the reconstructed results of the present invention.

Mean square error reflects the diversity between image to be evaluated, original image, shown in its computing formula following formula.

$\mathrm{MSE}=\frac{1}{M\×N}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{(B_{i,j}-X_{i,.j})}^2$

Wherein, M, N are the ranks number of view data, B_i,jFor the pixel point value of original image the i-th row jth row, X_i,j Pixel point value for image to be evaluated i-th row jth row.

Y-PSNR reflects the fidelity of image to be evaluated, and its computing formula is shown below.

$\mathrm{PSNR}=10{\log }_{10}\frac{L^2}{\mathrm{MSE}}$

Wherein, L is the dynamic range of pixel point value, for the image of common 8bit, takes L=255, PSNR It is worth the biggest, illustrates that image fidelity is the highest, i.e. the most close between reconstructed results and original image.

Claims (1)

1. image super-resolution rebuilding method based on rarefaction representation, it is characterised in that include that sample training walks Rapid and image super-resolution rebuilding step；

Described sample training step includes: the gradient information of calculating low-resolution image and high-definition picture are with low The residual information of image in different resolution；Obtain low resolution characteristic set by sparse expression method and high-resolution is special Collection is closed；

Described image super-resolution rebuilding step includes: calculate the gradient information of pending low-resolution image；? Low resolution characteristic set finds its rarefaction representation coefficient vector；Correspondence is found in high-resolution features set Residual information, this residual information is fused on low-resolution image, it is thus achieved that high-definition picture；

In described image super-resolution rebuilding step, utilize fast orthogonal matching pursuit algorithm based on classificating thought Its rarefaction representation coefficient vector is found in low resolution characteristic set；Specifically comprise the following steps that

One, sensing matrix Φ is divided into K class, is designated as Φ respectively₁, Φ₂..., Φ_k；

Two, calculating Mei Lei center is to the ultimate range at other kinds center, is designated as D respectively₁,D₂,...,D_k；

Three, the distance at sensing matrix Zhong Daomeilei center is combined into new sensing square less than the atom of ultimate range Battle array, is designated as

Four, choose respectivelyAs new sensing matrix, if certain new sensing square Atom number in Zhen is less than the number of initial setting up, then this sensing matrix stops classification, otherwise performs step one.