CN102231204A - Sequence image self-adaptive regular super resolution reconstruction method - Google Patents

Abstract

The invention discloses a sequence image self-adaptive regular super resolution reconstruction method and is directed to the field of image enhancement technology. According to the invention, based on the present regularization reconstruction method, improvements are carried out to an image reconstruction regularization object equation, an edge maintenance operator based on morphology is introduced to have an effect on a regular item, different regular constraints are adopted towards different geometrical structures, the constraint reconstruction of the image is enhanced at the edge of the image, that is, a small regularization parameter is employed and a large regularization parameter is adopted in the smooth area of the image to enhance the regularization. Besides, each time the acquirement of the edge maintenance operator is self-adaptive based on a latest iteration result with the ongoing of the iteration. Compared to the prior art, according to the invention, a smoothing effect in the reconstruction process can be effectively inhibited and the quality of the reconstructed high resolution image is improved.

Description

A kind of sequence image self-adapting regular super resolution rate method for reconstructing

Technical field

The present invention relates to a kind of image rebuilding method, relate in particular to a kind of sequence image self-adapting regular super resolution rate method for reconstructing, belong to digital picture enhancement techniques field.

Background technology

Along with the fast development of Digital image technology, people have more and more higher requirement to high-resolution digital picture.The resolution of image is high more, and image detail is just clear more, can provide abundant information more.In recent years, the super-resolution rebuilding technology has become a research focus of image processing field, this technology is utilized the relative motion information between several low-resolution images, useful information in every width of cloth low-resolution image is extracted, be fused to the high-resolution image of one or more, remove the blurring effect that noise and optical element produced in the image simultaneously.Because the super-resolution rebuilding technology is to utilize several low-resolution images to handle, extract the additional spatial domain of different images, time-domain information makes the visual effect of rebuilding the high-definition picture that obtains be better than any width of cloth low-resolution image.Super-resolution technique is widely used in medical image, video monitoring, and remote sensing image, military information such as obtains at the field, has broad application prospects.For example in CT and nuclear magnetic resonance medical images such as (MRI), can obtain imaging more clearly, thereby help the doctor to make diagnosis more accurately; In daily safety monitoring, high-definition picture can more effectively be made detection to abnormal behaviour; Aspect Aero-Space remote sensing images information obtained, the super-resolution rebuilding technology was more great for the application value in fields such as national security.

The super-resolution rebuilding technology was proposed with the notion that single image restores by Harris and Goodman first the sixties in 20th century.Early 1980s proposes by Tsai and Huang first based on the super-resolution rebuilding of sequence image, and provided in the frequency domain solution based on discrete cosine transform.Present super-resolution rebuilding algorithm mainly is divided into two classes: frequency domain method and spatial domain method.The essence of frequency domain algorithm is to find the solution the problem of image interpolation in frequency field.Algorithm based on frequency domain mainly is based on following principle: the translation character of (1) Fourier transform; (2) spectral aliasing between the discrete Fourier transformation of the continuous fourier transform of high-definition picture and low-resolution image; (3) several low-resolution images are the results that carry out the conversion of pixel class under the Same Scene.It is theoretical simple that frequency domain algorithm has, and calculated amount is little, has the good characteristics such as deformation mechanism of going.Its shortcoming be embodied in based on theoretical premise too idealized, degradation model can only be applicable to global translation motion, and is limited in one's ability to comprising of spatial domain priori.Owing to have such shortcoming, in research afterwards, the spatial domain algorithm becomes the main flow of research gradually.

Than frequency domain algorithm, the spatial domain reconstruction algorithm can be introduced multiple spatial domain prior imformation in reconstruction model, therefore has more dirigibility, and actual range of application is also broad more.The spatial domain method combines with other image processing methods and derives many new methods and type.Document (IEEE Signal Processing Magazine, 2003 (5): 21-36) the hypothesis image statistical model of obeying Poisson distribution proposes the maximum likelihood probability method of image reconstruction thus; Document (Pro cedings of the SPIE, Neural and stochastic methods in image and signal processing Il.1993:2-3) obeys the characteristics of Poisson distribution according to image, maximum a posteriori probability method (Maximum a poster iori probability has been proposed, MAP), and the reconstruction quality of pointing out image depends on the space constraint of scene, the character of sampling rate and noise and size; Document (IEEE Transactions on Image Processing, 1996,5 (6): 996-1011) by research to image spectrum, the basic reason of pointing out image super-resolution rebuilding is because include high-frequency information in the low frequency component of image, thereby has proposed the feasibility of super-resolution rebuilding technology theoretically; Document (IEEE Transa ctions on Image Processing, 1997,6 (8): 1064-1076). on the basis of summing up previous work, proposed based on convex set sciagraphy (projection onto convex sets, image super-resolution rebuilding method POCS).In addition, the researcher is also at image type, and observation model and image priori are studied, and corresponding algorithm has been done a large amount of improvements.

Present most of image super-resolution rebuilding algorithm all is based on the research of spatial domain method.But the above-mentioned spatial domain method of mentioning has a defective, and that must suppose that moving scene is static.At this problem, the researchist has taken all factors into consideration nonparametric motion model and area tracking in the sequence image super-resolution reconstruction process, and has considered multiple different image deterioration model.Document (Journal of Computer Vision, Graphics, and Image Processing, 1991,53 (3): the image deterioration model 231-239) has comprised space quantization sum of errors optical dimming; Document (Proceed ing of ECCV, Springer-Verlag, 1996,312-320) considered motion blur; Document (IEEE Transactions on Image Processing, 1997,6 (12): 1621-1633) propose to carry out estimation and image reconstruction simultaneously based on the registration Algorithm of MAP objective function; Document (IEEE Transactions on Image Processing, 1996,5 (6): 996-1011) improved the method for Bayesian, in the super-resolution rebuilding process, used MRF priori based on the Huber penalty; Document (IEEE Transactions on Image Processing, 2004,13 (10): 1327-1344) propose a kind of super-resolution image reconstruction algorithm of the full variation model based on bilateral filtering and the coupling of L1 norm, and adopt the piece estimation approach to carry out estimation, these algorithms all make quality of reconstructed images obviously improve.

Current most super-resolution rebuilding algorithm is the thought that adopts regularization for the solution of the such ill-posed problem of super-resolution rebuilding.The regularization method that document (Solution of Ill-Posed Problems.1977) has at first proposed to find the solution ill-posed problem is decided finding the solution of indirect problem for discomfort and has been established theoretical foundation; Document (IEEE Tr ans.on Image Processing, 2001,4 (8): 573～583) introduce the Tikhonov-Arsenin regularization in order to solve the pathosis that MAP rebuilds problem.The regularization method for reconstructing can guarantee the effective of image reconstruction and reduce interference of noise by image in the process of reconstruction is introduced certain constraint.Smoothness constraint is generally adopted in constraint to image, but there is tangible problem in this smoothness constraint, has promptly also blured edge of image in smoothed image in the noise.In order in smooth noise, to keep edge of image detailed information, researchist to propose many improved regularization algorithms, document (IEEE Trans on Image Processing, 1999,8 (3): 396-407) proposed anisotropic approaches; Document (Pr oceedings of International Conference on Pattern Recognition, 2000,1:600-605) propose based on continuously full variation model (Total Variation, TV) sequence image super-resolution reconstruction algorithm; Document (IEEE Tr ans on Image Processing, 1995,4 (5): 594-602) iteration self-adapting method of Ti Chuing and document (IEEE Inter national Conference on Pattern Recognition, Cambridge, United Kingdom, 2004,3:662-665) the spatially adaptive method of Ti Chuing. these improved algorithms all are to smooth noise in essence and keep the compromise of edge, because these methods require the image border is accurately located, and owing to the defective and the parameter of image super-resolution rebuilding itself are selected reasons such as improper, Gibbs effect in various degree inevitably can appear in reconstructed image, polytype pseudomorphisms such as grain noise and edge ring, and pseudomorphism often has the characteristic at similar edge.Therefore, the research of sequence image super-resolution reconstruction algorithm still needs to consider how problems such as staircase effect and ringing effect are located, eliminated to true edge.

Because super-resolution rebuilding the complex nature of the problem of sequence image, the present achievement in research in this field is relatively limited, so the super-resolution rebuilding of sequence image is worth showing great attention to and furtheing investigate.

Summary of the invention

Technical matters to be solved by this invention is to overcome the existing existing smoothing effect problem of super-resolution regularization method for reconstructing, a kind of sequence image self-adapting regular super resolution rate method for reconstructing is provided, this method can be when finishing super-resolution image reconstruction, effectively suppress smoothing effect, thereby improve the effect of image reconstruction.

Thinking of the present invention is: on the basis of existing regularization method for reconstructing, image reconstruction regularization target equation is improved, introducing one keeps operator to act on regular terms based on morphologic edge, different geometries is adopted different canonical constraints, strengthen the constraint of image rebuilds in edge of image, promptly adopt less regularization parameter, and adopt bigger regularization parameter to strengthen regularization at the smooth region of image.And each time the edge keep obtaining of operator all be carrying out along with iteration according to the adaptive adjustment of up-to-date iteration result, can obtain littler iteration error like this, better rebuild effect.

Particularly, sequence image self-adapting regular super resolution rate method for reconstructing of the present invention may further comprise the steps:

Steps A, utilize following observation model, obtain several low resolution observed images a panel height image in different resolution (also can be described as and the degrade) processing of degenerating,

y _k＝H _kz+n _k，1≤k≤p，

In the formula, y _kRepresent k width of cloth low resolution observed image, z represents the high-definition picture that is used to degenerate, H _kBe singular matrix, n _kBe the noise vector that adds, p is the figure film size number that image sequence comprised;

Step B, utilize iterative algorithm to image reconstruction regularization target equation optimization find the solution, obtain final super-resolution reconstruction image;

It is characterized in that described image reconstruction regularization target equation is shown below:

$\hat{z}=\arg \underset{z}{\min }\{{\left|\right|y-\mathrm{Hz}\left|\right|}_2^2+\mathrm{\α}{\mathrm{AE}}_N*{\left|\right|\mathrm{Qz}\left|\right|}_2^2\},$

In the formula,

Be the super-resolution reconstruction image; Y is the sequence low-resolution image, and z is the simulation high-definition picture that is used to degenerate, and H is the degradation model matrix, and α is a regularization parameter, and Q is a regularizing operator, AE _NFor the edge keeps operator, and AE _NWith iterative process self-adaptation adjustment in accordance with the following methods:

S1, the simulation high-definition picture that previous iteration is obtained expands respectively and corrosion obtains corresponding gray matrix AE _dWith gray matrix AE _eIf iteration then adopts the method to the low-resolution image interpolation to obtain the simulation high-definition picture first;

S2, with the gray matrix AE after the expansive working _dDeduct the gray matrix AE after corrosion is operated _eAnd, obtain a gray matrix AE that can embody image different shape composition to its normalization;

S3, (x y), carries out following processing respectively according to a pre-set threshold, and the edge that obtains this iteration keeps operator AE for each the elements A E among the gray matrix AE _N:

If (x y) greater than described threshold value, then dwindles this element N doubly to AE;

If (x y) less than described threshold value, then amplifies N doubly with this element to AE.

Further, described multiple N determines according to following formula with iterative process:

$N_{k+1}=\log \left(\frac{1}{{\mathrm{\α}}_{k+1}\left({\mathrm{e\η}}_k\right)+r}\right)+\mathrm{\λ},$

In the formula, N _K+1It is the operator multiple of the k+1 time iteration; α _K+1It is the regularization parameter of the k+1 time iteration; η _kIt is the k time iteration result's error; E, r, λ are corrected parameter.

Further, utilize among the step B method of steepest descent to image reconstruction regularization target equation optimization find the solution.

The present invention improves by conventional images being rebuild regularization target equation, introducing one keeps operator to act on regular terms based on morphologic edge, different geometries is adopted different canonical constraints, strengthen the constraint of image rebuilds in edge of image, promptly adopt less regularization parameter, and adopt bigger regularization parameter to strengthen regularization at the smooth region of image.And to keep obtaining of operator all be that carrying out along with iteration is according to the adaptive adjustment of up-to-date iteration result at the edge each time.Smoothing effect in the time of can effectively suppressing super-resolution rebuilding, the effect of raising image reconstruction.

Description of drawings

Fig. 1 is a sequence image self-adapting regular super resolution rate method for reconstructing process flow diagram of the present invention;

Fig. 2 is the robustness comparing result of the inventive method and Tikhonov regularization method, and wherein (a) is the Y-PSNR contrast of two kinds of methods, (b) is the standard mean square deviation contrast situation of two kinds of methods;

Fig. 3 is the reconstruction effect comparison of the inventive method and Tikhonov regularization method, wherein the row's of going up 3 width of cloth images are respectively the lena that adopts after the Tikhonov regularization method is rebuild, boat and baboo, following row's 3 width of cloth images are respectively the lena that adopts after the inventive method is rebuild, boat and baboo;

Fig. 4 is the reconstruction effect comparison of the inventive method and adaptive regularization method, wherein the row's of going up 3 width of cloth images are respectively the lena that adopts after the adaptive regularization method is rebuild, boat and baboo, following row's 3 width of cloth images are respectively the lena that adopts after the inventive method is rebuild, boat and baboo;

Fig. 5 is the effect comparison that the inventive method and Tikhonov regularization method are rebuild real world images, wherein three width of cloth images of first row are the low-resolution image through degenerating after handling, second classifies the high-definition picture that adopts after the Tikhonov regularization method is rebuild as, and the 3rd classifies the high-definition picture that adopts after the inventive method is rebuild as.

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:

For ease of the understanding of the public to technical solution of the present invention, before the inventive method was described, the principle that existing regularization is rebuild briefly introduced earlier.

One panel height image in different resolution (HR) is obtained several low resolution (LR) image through degenerate handling, the process that degrades of Here it is image, image observation model commonly used when just carrying out super-resolution rebuilding by the sequence low-resolution image.The mathematical expression of image observation model is as follows,

y _k＝H _kz+n _k，1≤k≤p， (1)

In the formula, y _kRepresent k width of cloth low resolution observed image, z represents the high-definition picture that is used to degenerate, H _kBe singular matrix, n _kBe the noise vector that adds, p is the figure film size number that image sequence comprised;

The task of image super-resolution rebuilding is exactly to be rebuild by the low-resolution image that observation model obtained in the formula (1) to obtain the high resolving power original image, and is maximum even the posterior probability of high resolving power original image reaches:

$\hat{z}=\arg \underset{z}{\max }\mathrm{Pr}\left(z\right|y)---\left(2\right)$

Under the bayesian theory framework, distortion can get to (2) formula:

$\hat{z}=\arg \underset{z}{\max }\frac{\mathrm{Pr}\left(y\right|z)\mathrm{Pr}\left(z\right)}{\mathrm{Pr}\left(y\right)}---\left(3\right)$

By (3) formula right-hand member denominator independence, can get:

$\hat{z}=\arg \underset{z}{\max }\mathrm{Pr}\left(y\right|z)\mathrm{Pr}\left(z\right)---\left(4\right)$

The MAP estimation technique is final available as shown in the formula statement to finding the solution of this problem:

$\hat{z}=\arg \underset{z}{\min }\{-\log [\mathrm{Pr}\left(y\right|z)]-\log [\mathrm{Pr}\left(z\right)\left]\right\}---\left(5\right)$

Wherein, log[Pr (y|z)] be the logarithm of maximum likelihood function, suppose that noise is that average is 0, variance is Gaussian noise, and separate between each width of cloth low-resolution image, then the probability density function of whole sequence of low resolution pictures is:

$\mathrm{Pr}\left(y\right|z)=\underset{\∀k}{\mathrm{\Π}}\left[\underset{\∀z,y}{\mathrm{\Π}}\frac{1}{{\mathrm{\σ}}_k\sqrt{2\mathrm{\π}}}\exp (-\frac{{(\widehat{y_k}-y_k)}^2}{2{\mathrm{\σ}}_k^2})\right]---\left(6\right)$

In the formula (6),

Be the simulation low-resolution image; y _kBe the k frame in the sequence low-resolution image.Log[Pr (z)] be the logarithm of the prior probability of z, prior probability method of estimation commonly used is that image is carried out smoothness constraint, promptly the contiguous pixel that differs greatly on the image is punished that its probability density function can be assumed to following form:

$\mathrm{Pr}\left(z\right)=\exp [-\left(\frac{1}{\mathrm{\λ}}{\left|\right|\mathrm{Qz}\left|\right|}^2\right)]---\left(7\right)$

Wherein, Q represents linear high pass computing, is used for punishment to rough estimation.

Because super-resolution rebuilding is a typical ill-conditioning problem, promptly can not produce and satisfy separating of existence, uniqueness and stability simultaneously, Tikhonov has at first proposed to find the solution the regularization method of ill-conditioning problem, wushu (6), formula (7) substitution formula (5), and adopt the Tikhonov regularization method to obtain the target equation to be:

$\hat{z}=\arg \underset{z}{\min }\{{\left|\right|y-\mathrm{Hz}\left|\right|}_2^2+\mathrm{\α}{\left|\right|\mathrm{Qz}\left|\right|}_2^2\}---\left(8\right)$

In the formula: first description waits to ask the fitting degree between image and the observed image, is called data fidelity item; Second regularity such as slickness of describing image, sparse property, it comprises some prior imformation of understanding, is called regular terms; Q is a regularizing operator, is the block circulant matrix that has identical size with H that is generated by a high-pass filtering operator, and the high-pass filtering operator is selected the Laplacian operator of two dimension usually; α is a regularization parameter, is controlling data fidelity item and the regularization term proportion in solution procedure, is controlling the level and smooth performance of rebuilding the result.On the one hand, α crosses conference makes regular terms occupy bigger contribution amount, makes reconstructed results produce excessive smoothing effect, loses detailed information; On the other hand, the too small then noise problem of α is serious, makes that the reconstructed results distortion is bigger.As seen in the regularization super-resolution rebuilding, choosing of regularization parameter produces considerable influence to reconstructed results.

Thinking of the present invention is to introduce one to keep operator to act on regular terms based on morphologic edge in the super-resolution rebuilding process, different geometries is adopted different canonical constraints, strengthen the constraint of image rebuilds in edge of image, promptly adopt less regularization parameter, and adopt bigger regularization parameter to strengthen regularization at the smooth region of image.Particularly, the inventive method, as shown in Figure 1, carry out image reconstruction according to following process:

At first reconstruction algorithm is carried out initialization, the initialization among the present invention comprises: the initial value of simulation high-definition picture when adopting cubic spline interpolation to obtain iteration first; Adopt the Gaussian Blur kernel function as the optical dimming function; Adopt Laplace operator to obtain regularizing operator.

According to following steps the sequence low-resolution image of input is rebuild then:

Steps A, utilize following observation model, obtain several low resolution observed images the panel height image in different resolution processing of degenerating,

y _k＝H _kz+n _k，1≤k≤p，

In the formula, y _kRepresent k width of cloth low resolution observed image, z represents the high-definition picture that is used to degenerate, H _kBe singular matrix, n _kBe the noise vector that adds; For degenerative process and imaging actual conditions are coincide, degeneration of the present invention is handled and is also comprised shift transformation, optical dimming and down-sampled down, and described singular matrix obtains according to following formula,

H _k＝D _kB _kM _k，

In the formula, D _KBe down-sampling matrix, B _kBe optical dimming matrix, M _kBe transposed matrix.

Step B, utilize iterative algorithm to image reconstruction regularization target equation optimization find the solution, obtain final super-resolution reconstruction image;

The present invention introduces one and keeps operator to act on regular terms based on morphologic edge, and then the target equation of (8) formula correspondingly becomes (' * ' operation definition is the matrix dot product) herein:

$\hat{z}=\arg \underset{z}{\min }\{{\left|\right|y-\mathrm{Hz}\left|\right|}_2^2+\mathrm{\α}{\mathrm{AE}}_N*{\left|\right|\mathrm{Qz}\left|\right|}_2^2\}---\left(9\right)$

In the formula,

Be the super-resolution reconstruction image; Y is the sequence low-resolution image, and z is the simulation high-definition picture that is used to degenerate, and H is the degradation model matrix, and α is a regularization parameter, and Q is a regularizing operator, AE _NFor the edge keeps operator, and AE _NWith iterative process self-adaptation adjustment in accordance with the following methods:

S1, the simulation high-definition picture that previous iteration is obtained expands respectively and corrosion obtains corresponding gray matrix AE _dWith gray matrix AE _eIf iteration then adopts the method to the low-resolution image interpolation to obtain the simulation high-definition picture first;

S2, with the gray matrix AE after the expansive working _dDeduct the gray matrix AE after corrosion is operated _eAnd, obtain a gray matrix AE that can embody image different shape composition to its normalization;

S3, (x y), carries out following processing respectively according to a pre-set threshold thresh, and the edge that obtains this iteration keeps operator AE for each the elements A E among the gray matrix AE _N:

If (x y) greater than described threshold value, then dwindles this element N doubly to AE;

If (x y) less than described threshold value, then amplifies N doubly with this element to AE.

Above-mentioned threshold value thresh can choose according to actual conditions, the intermediate value of preferred described gray matrix AE greatest member of the present invention and least member, i.e. thresh=0.5* (AE _{Maximal value}-AE _{Minimum value}).

The present invention has introduced adaptive thought in the process of super-resolution rebuilding, effectively promoted the effect of reconstruction algorithm, keeps operator AE for the edge _NThe selection of multiple N is very crucial, though use a fixed numbers simpler, but consider that the edge that adopts different multiple N can obtain in various degree keeps operator, directly influence the quality of reconstructed image, the present invention further provides the method for a kind of definite N for this reason, its main thought is the carrying out along with iteration, constantly revise the value of N according to the variation of regularization parameter and iteration error, the reconstructed image that newly obtains is used for determining of next iteration again, loop iteration like this, the optimum solution that obtains rebuilding.In order to set up the solution formula of multiple N, N should satisfy following pacing items

(1) N should be greater than 1;

(2) N and the regularization parameter relation of being inversely proportional to;

(3) N and the iteration error relation of being inversely proportional to;

According to above condition, the solution formula of N is proposed:

$N_{k+1}=\log \left(\frac{1}{{\mathrm{\α}}_{k+1}\left({\mathrm{e\η}}_k\right)+r}\right)+\mathrm{\λ}---\left(10\right)$

In the formula, N _K+1It is the operator multiple of the k+1 time iteration; α _K+1It is the regularization parameter of the k+1 time iteration; η _kIt is the k time iteration result's error; E, r, λ are corrected parameter, and e is used for revising iteration error η _k, get η usually _kThe identical order of magnitude is as 1e+007; R is a very little number, is used to guarantee that denominator is non-vanishing; λ is used for revising the last value of operator multiple N, and the value that makes N is as far as possible between 1～4.

Formula (9) is carried out iterative, obtain iteratively be:

${\hat{z}}_{n+1}={\hat{z}}_n-\mathrm{\β}\{H^T(H{\hat{z}}_n-y)+\mathrm{\α}{\mathrm{AE}}_N*Q^{T}Q{\hat{z}}_n\}---\left(11\right)$

Wherein,

It is the super-resolution reconstruction image that the n time iteration obtains;

Be the n+1 time iteration obtain the super-resolution reconstruction image; Y is the sequence low-resolution image; H is the degradation model matrix; α is a regularization parameter; Q is a regularizing operator; AE _NFor the edge keeps operator; β is an iteration step length 9.

When sequence image is carried out super-resolution rebuilding, adopt certain optimization method significantly to reduce computing time.The present invention adopts method of steepest descent that (11) formula is optimized and finds the solution.

Judge whether stopping criterion for iteration reaches, as reach that then the simulation high-definition picture that this iteration is obtained is as final reconstructed image output; As not, then proceed next step iteration.

In order to verify beneficial effect of the present invention, carried out following contrast experiment.The lena of experimental selection 256 * 256 sizes, boat and baboo figure carry out translation successively, fuzzy, down-sampled generation 9 width of cloth low-resolution images are got and are of a size of 3 * 3, variance is 1 Gaussian Blur, and the down-sampled factor is 2, and method for registering adopts the LK optical flow approach based on gaussian pyramid.For weighing the effect of the inventive method, carried out improving the contrast of front and back in the test respectively with the kang regularization algorithm of conventional Tikhonov regularization algorithm and adaptive regularization parameter, and the image in the last employing reality of experiment has carried out algorithm relatively.Pass judgment on having adopted Y-PSNR (PSNR) and standard mean square deviation (NMSE) commonly used aspect the objective judgment criteria.Be the comparison that decision criteria has carried out arithmetic speed with iterations iter simultaneously.

At first turn to the regularization parameter robustness that framework is investigated the inventive method with Tikhonov canonical, get iteration step length β=0.001 and iterations iter=40, regularization parameter=0.05～1.5 o'clock, investigate the situation that algorithm improvement front and back Y-PSNR (PSNR) and standard mean square deviation (NMSE) change with regularization parameter, AE1 wherein, AE2, AE3, the operator multiple N=1 of the corresponding the inventive method of difference, N=2, the situation of N=3, experimental result as shown in Figure 2, for the bigger regularization parameter of variation range, the inventive method is more stable as can be seen, and choosing of regularization parameter had better robustness.

Secondly turn to framework with Tikhonov canonical, investigate the contrast of the inventive method and Tikhonov regularization method, get regularization parameter=0.25, iteration step length β=0.001, iteration stopping condition d=10 ^-7, respectively three width of cloth test patterns are handled the effect before and after comparison algorithm improves.Test findings such as table 1 and shown in Figure 3, among Fig. 3, above three width of cloth are original Tikhonov regularization methods, be the inventive method below.According to test findings as can be seen, though the PSNR of the inventive method descends slightly, actual observation effect details is more clear, and iterations obviously reduces, and arithmetic speed is obviously accelerated.

Table 1

Next the adaptive regularization method that proposes with kang is a framework, investigates the contrast of the inventive method and adaptive regularization method.Adopt iteration step length β=0.001, iteration stopping condition d=10 in the experiment ^-7Experimental result such as table 2 and shown in Figure 4, among Fig. 4, above three width of cloth are original adaptive regularization methods, be the inventive method below.As can be seen, though the PSNR of the inventive method descends slightly, the actual observation effect does not change, and importantly iterations obviously reduces, and arithmetic speed is obviously accelerated.

Table 2

Adopt real-life image (dog, dragon, building) to verify the effect of the inventive method at last, we have adopted the Tikhononv regularization method to carry out the comparison of visual effect and iteration speed aspect, experimental result such as table 3 and shown in Figure 5, as can be seen, utilization the inventive method is rebuild the HR image of gained, no matter be on iteration speed, still on the resolution detail of image, all good than primal algorithm.

Table 3

Claims (5)

1. sequence image self-adapting regular super resolution rate method for reconstructing may further comprise the steps:

Steps A, utilize following observation model, obtain several low resolution observed images the panel height image in different resolution processing of degenerating,

y _k＝H _kz+n _k，1≤k≤p，

In the formula, y _kRepresent k width of cloth low resolution observed image, z represents the high-definition picture that is used to degenerate, H _kBe singular matrix, n _kBe the noise vector that adds, p is the figure film size number that image sequence comprised;

Step B, utilize iterative algorithm to image reconstruction regularization target equation optimization find the solution, obtain final super-resolution reconstruction image;

It is characterized in that described image reconstruction regularization target equation is shown below:

$\hat{z}=\arg \underset{z}{\min }\{{\left|\right|y-\mathrm{Hz}\left|\right|}_2^2+\mathrm{\α}{\mathrm{AE}}_N*{\left|\right|\mathrm{Qz}\left|\right|}_2^2\},$

In the formula,

Be the super-resolution reconstruction image; Y is the sequence low-resolution image, and z is the simulation high-definition picture that is used to degenerate, and H is the model matrix that degrades, and α is a regularization parameter, and Q is a regularizing operator, AE _NFor the edge keeps operator, and AE _NWith iterative process self-adaptation adjustment in accordance with the following methods:

S1, the simulation high-definition picture that previous iteration is obtained expands respectively and corrosion obtains corresponding gray matrix AE _dWith gray matrix AE _eIf iteration then adopts the method to the low-resolution image interpolation to obtain the simulation high-definition picture first;

S2, with the gray matrix AE after the expansive working _dDeduct the gray matrix AE after corrosion is operated _eAnd, obtain a gray matrix AE that can embody image different shape composition to its normalization;

S3, (x y), carries out following processing respectively according to a pre-set threshold, and the edge that obtains this iteration keeps operator AE for each the elements A E among the gray matrix AE _N:

If (x y) greater than described threshold value, then dwindles this element N doubly to AE;

If (x y) less than described threshold value, then amplifies N doubly with this element to AE.

2. sequence image self-adapting regular super resolution rate method for reconstructing according to claim 1 is characterized in that, described multiple N determines according to following formula with iterative process:

$N_{k+1}=\log \left(\frac{1}{{\mathrm{\α}}_{k+1}\left({\mathrm{e\η}}_k\right)+r}\right)+\mathrm{\λ},$

In the formula, N _K+1It is the operator multiple of the k+1 time iteration; α _K+1It is the regularization parameter of the k+1 time iteration; η _kIt is the k time iteration result's error; E, r, λ are corrected parameter.

3. sequence image self-adapting regular super resolution rate method for reconstructing as claimed in claim 1 or 2 is characterized in that the value of described threshold value thresh is the intermediate value of described gray matrix AE greatest member and least member.

4. sequence image self-adapting regular super resolution rate method for reconstructing as claimed in claim 1 or 2 is characterized in that, utilize among the described step B method of steepest descent to image reconstruction regularization target equation optimization find the solution.

5. sequence image self-adapting regular super resolution rate method for reconstructing as claimed in claim 1 or 2 is characterized in that, described degeneration is handled and also comprised shift transformation, optical dimming and down-sampled down, and described singular matrix obtains according to following formula,

H _k＝D _kB _kM _k，

In the formula, D _KBe down-sampling matrix, B _kBe optical dimming matrix, M _kBe transposed matrix.

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