CN101540039B - Method for super resolution of single-frame images - Google Patents

Abstract

The invention relates to a method for super resolution of single-frame images. In the imaging process, an imaging system fuzzes up and deforms the original object images; and at the same time, an analog-digital (A/D) conversion process CCD therein is lack of sampling, frequency aliasing is caused, high-frequency information is lost, and frequency spectrum aberrations appear at a frequency aliasing section, so not only the frequency spectrum of a real image scenery becomes narrow, but also the structure of a high frequency section is changed due to resolution losses caused by design limitations of an image device. The method for the super resolution of the single-frame images comprises the following steps of: firstly, analyzing images, and determining whether a single-frame frequency domain de-aliasing super resolution method is to be adopted to perform processing through frequency aliasing parameters; and secondly, enriching the texture and the detail of the images through a Fourier transform, a frequency domain de-aliasing algorithm and an inverse Fourier transform so as to improve the definition, the contrast and the resolution of the images and inhibit ringing pseudo images. The method is applied to the fields of satellite remote sensing image processing, medical image and earthquake image analysis and the like.

Description

Method for super resolution of single-frame images

Technical field:

The present invention relates to a kind of image is analyzed and handled, thereby significantly improve the method for resolution, sharpness and the contrast of image, belong to the category of image processing.

Background technology:

Imaging system is in imaging procedures, because atmospheric disturbance and interference, visibility influence, optical effect and the influences such as integrating effect in the photosignal transfer process make original thing image blurring and distortion; Simultaneously, the sampling of owing owing to modulus (A/D) conversion process, can cause frequency alias, lose high-frequency information, and make the frequency alias section frequency spectrum distortion occur, therefore, not only the frequency spectrum with real visual scenery has narrowed down, and having changed the structure of high band, this is because the resolution loss that the design limit of imaging device causes also is the subject matter that super-resolution will solve.In addition, in signal transmission and image formation process, also can be subjected to the pollution of multiple noises such as sky noise, grain noise, thermonoise, swept noise, also can reduce the resolution of actual image.

In three more than ten years in the past, about the degenerate recovery problem of image of single frames, people set up and have developed a series of classical theory.Closely during the last ten years, continual development along with computer science and engineering, allow more complicated more time-consuming algorithm, on the basis that solves the image restoration problem, people concentrate on main energy on non-traditional disposal route that super-resolution handles and the new second generation problem.In the world, can although there is the arguement realize visual super-resolution for a long time, the development of multiframe image ultra-resolution method be very fast, on process field, can be divided into frequency domain with the spatial domain.Recently, because the urgency of application demand, more and more higher about in this respect research enthusiasm both at home and abroad, new method also emerges in an endless stream, and has all obtained very big progress in the application facet in all fields such as satellite remote sensing image processing, medical images and earthquake vision analysis.

At present, various ultra-resolution methods are all very sensitive in they hypothesized models to data and noise usually, thereby limited application.Minimize regularization with robust by the L1 norm, not only calculation consumption is few, and the error in motion and the blur estimation is had robustness, causes image to have sharp-pointed edge.In order to overcome of the influence of coarse inferior pixel registration to high-resolution picture reconstruct, adopt the method for estimating regularization parameter automatically, can realize robustness to the registration error noise.

Summary of the invention:

The purpose of this invention is to provide a kind of method of handling single frame image, particularly, improve resolution, contrast and the sharpness of image by handling.The present invention has not only given certainly visual super-resolution, and has creatively realized the super-resolution of single frame image.

Above-mentioned purpose realizes by following technical scheme:

The present invention relates to the content of following four aspects: the proposition of super resolution of single-frame images, the frequency alias degree of depth (FAD) parameter, to the inhibition and the image restoration of illusion (ring).

1. whether method for super resolution of single-frame images is at first analyzed image, adopt the single frames frequency domain to separate the aliasing ultra-resolution method by the frequency alias parameter decision and handle; Separate aliasing algorithm and inverse fourier transform by Fourier transform, frequency domain then, the texture and the details of abundant image improve visual sharpness, contrast and resolution, and the suppressed ringing illusion.

Described method for super resolution of single-frame images, promptly described super-resolution are separated the aliasing processing and are comprised:

(1) to the single frame image f of low resolution (k l) carries out Fourier transform, with its transform to frequency spectrum F (m, n);

(2) to the frequency spectrum F that obtained (m n) carries out frequency domain transform filtering or compensation filter and handles, with the high-resolution picture frequency spectrum G that is expanded and strengthens (m, n);

(3) by inverse Fourier transform, will through the super-resolution image spectrum G of frequency domain expansion and enhancing (m, n) be transformed into high-resolution picture g (k, l).

2. in the described method for super resolution of single-frame images, the described frequency alias degree of depth:

Wherein, spectrum width is 2 π; C ₁₁Be the frequency alias degree of depth (FAD) parameter, the degree of the high-end aliasing of reaction frequency spectrum.C ₁₁Leaching process comprises: the low resolution image to owing to sample, carry out Fourier transform; Frequency spectrum to low resolution image carries out overall polynomial expression least square fitting; To low-frequency component in the later frequency spectrum of match and high frequency central energy, carry out secondary and block match; The frequency spectrum that secondary is blocked match carries out the frequency spectrum expansion, and then calculates the FAD parameters C ₁₁

If FAD parameters C ₁₁≤ 0.4, then adopt single frames super resolution technology of the present invention, if the FAD parameters C ₁₁＞0.4, then adopt the multiframe super resolution technology.

3. the method that described suppressed ringing illusion produces, the controlled variable C of described control frequency-domain correction ₁₂Reciprocal each other with normalization high frequency central energy parameter p, if C ₁₂Greater than setting, then in the processing of super-resolution, introduce the operation of suppressed ringing illusion, in order to avoid illusion occurs in the high-resolution picture after processing.C ₁₂Leaching process comprises: the spectral amplitude value root variance that obtains image from the frequency spectrum of low resolution image; Handle by spectral amplitude value root variance being carried out fitting of a polynomial, obtain high frequency normalized energy parameters C ₁₂

4. the method for described image restoration, at first the satellite imagery to input carries out fuzzy analysis, Analysis signal-to-noise ratio (SNR) and cloud and mist analysis respectively, then analysis result is compared with fuzzy standard, signal to noise ratio (S/N ratio) standard and cloud and mist standard respectively, judge whether to carry out the ambiguity solution operation, strengthen the signal to noise ratio (S/N ratio) operation and suppress thin cloud mist operation, judged result is separately used controlled variable C respectively ₂, C ₃And C ₄Expression, and they are passed to the combination of controller and image restoration handle accordingly.

Image restoration is the basis of super-resolution, and the new technology of this part is as follows:

(1) based on the blindness of the iteration on the limited support region of Fourier transform (FT) Deconvolution Algorithm Based on Frequency

Utilize FT can realize the repeatedly conversion of picture intelligence from the time domain to the frequency domain, in conversion repeatedly, add the restriction of expectation signal is revised in two territories repeatedly, make to produce the image of expectation at last.For blindness deconvolution problem, frequency domain is estimated to realize with improved Wiener filtering, make the FT iterative algorithm become more reasonable.Do not have stable convergence though experience shows the iterative algorithm that utilizes FT, more approaching separating usually can be provided.Because the iteration blindness Deconvolution Algorithm Based on Frequency based on FT has fast algorithm, handles so utilizing this algorithm to carry out ambiguity solution in true remote sensing image experiment.The present invention on the basis of theory analysis and a large amount of experimental demonstrations, the conclusion of algorithm effect the best when having drawn iteration twice.

(2) Anisotropic Nonlinear based on second-order partial differential coefficient spreads denoise algorithm

Under the situation that single source (frame) remote sensing image is only arranged, be one based on partial differential equation (PDE) denoising method and select preferably.The present invention is directed to more ubiquitous Gaussian noise and poisson noise in the image, with the Anisotropic Nonlinear diffusion process of second derivative factor introducing based on PDE, set up improved diffusion denoise algorithm, not only can suppress the noise of smooth region effectively, and can suppress the noise at texture place, edge effectively; Not only the strong edge of step evolution can be protected well, and more weak detail textures can be protected even strengthen well; The edge texture is subjected to displacement, does not have false texture to produce.Handle the image that Gaussian noise is polluted, can make PSNR improvement value＞3～4dB; Handle the image that poisson noise pollutes, can make PSNR improvement value＞2～3dB.

(3) cloud and mist composition and atural object composition are the relations of multiplying each other in the cloud and mist pollution image

Cloud and mist also is a key factor polluting image, at the image that contains thin cloud mist, also there is considerable ground object target information, the present invention is on the basis of analyzing cloud and mist image imaging model, provide based on homomorphic filter with based on two kinds of methods (non-invention) of wavelet multiresolution analysis, experiment shows, has all obtained effect preferably.The application scenario difference of two kinds of methods, the former is used for providing the situation of no cloud and mist reference picture, and the latter can be used for providing the situation of no cloud and mist reference picture.

Effect of the present invention:

The present invention can use the imaging system of low resolution by the processing of image, obtain high-resolution image by processing to image, can break through cost obstacle and technology barrier that remote sensing high-resolution imaging system causes its imaging apparatus, memory device, development and operation etc., obtain more economical cost, reach the top standard that international civilian and military purposes super-resolution is handled.

The present invention has creatively realized the super-resolution of single frame image, frequency spectrum to the picture intelligence of low resolution is expanded and enhancement process, thereby compensation is because the high-frequency information of frequency alias loss, untie frequency alias, eliminate the frequency discontinuity that may cause ring illusion phenomenon simultaneously again, improved visual resolution, contrast and sharpness.The present invention handles image analysis, image restoration and visual super-resolution and combines, and forms a complete image processing solution efficiently, and its effect is remarkable and be easy to realization, has good application prospects and value.

It is pointed out that we progressively recognize in research process, the FAD parameter all is of great importance to visual super-resolution operation and treatment effect, and the important application of three aspects can be arranged, and is discussed below respectively:

(1), optimizes the super-resolution Processing Algorithm as prior imformation

Before a class satellite imagery being carried out the super-resolution processing, analyze the FAD parameters C of this class satellite imagery earlier ₁₁, C ₁₂, and at C ₁₁, C ₁₂Size and the concrete condition of frequency alias, optimize and separate aliasing operation, frequency compensation operation and the operation of suppressed ringing illusion etc. in the super-resolution algorithm, revise wherein controlled variable and the number of times of interative computation, form optimum super-resolution algorithm at this class satellite imagery.

(2) with electing the controlled variable of ultra-resolution method

According to the size of FAD parameter, can select suitable super-resolution algorithm.For example, the result of study in face of us shows, works as C ₁₁, can select easier single frames super-resolution algorithm for use at≤0.4 o'clock; Work as C ₁₁, should select multiframe (source) super-resolution algorithm for use at＞0.4 o'clock.

(3) as the objective evaluation of visual super-resolution treatment effect

Utilize visual particularly satellite imagery to carry out the ability of Target Recognition and the precision of location survey in order to improve, research by the image processing gordian technique, set up and recovery of optimization satellite imagery and super-resolution processing method, algorithm, improve the resolution of satellite imagery significantly, contrast and sharpness, wherein super-resolution is brought up to the resolution of image about original 1.6 times, ambiguity solution improves the Y-PSNR of image more than the 10dB, contrast improves more than the 8dB, denoising has then improved 2～4dB with the signal to noise ratio (S/N ratio) of image, greatly improve the ability that image comprises space image identification, finish the development of utility system software, for practical application lays the foundation.

Description of drawings

Fig. 1 is an overall technological scheme sketch of the present invention;

Fig. 2 is a theory diagram of the present invention;

Fig. 3 has shown the relation of frequency domain compensation filtering and p index variation:

Fig. 4 is the correction and the compensation synoptic diagram (A=2) of frequency alias;

Fig. 4 (a) one-dimensional signal normalization frequency spectrum F (k) (N=128);

The frequency transfer function H (k) of Fig. 4 (b) one dimension frequency domain compensation filtering (A=2);

Signal spectrum G (k) after Fig. 4 (c) one dimension frequency domain compensation Filtering Processing (2N=256);

Fig. 5 is the ambiguity solution embodiment;

Fig. 6 is the algorithm arrangement that suppresses thin cloud mist, wherein:

Fig. 6 (a) suppresses the algorithm arrangement of technology based on the thin cloud mist of homomorphic filtering;

Fig. 6 (b) suppresses the algorithm arrangement of technology based on the thin cloud mist of wavelet multiresolution analysis;

Fig. 7 is single frames super-resolution algorithm process result, wherein:

Fig. 7 (a) single frames super-resolution algorithm process " No. two, resource " (3 meters resolution) image result (2 width of cloth).

Fig. 7 (b) single frames super-resolution algorithm process Spot5 image result (2 width of cloth).

Fig. 7 (c) single frames super-resolution algorithm process Ikonos (1 meter resolution) image result (2 width of cloth).

Fig. 8 is ambiguity solution algorithm process result, wherein:

Fig. 8 (a) multiframe (source) ambiguity solution arithmetic result: PSNR increases 23dB;

A-1) a frame low resolution blurred image (17.40dB); A-2) ambiguity solution image (40.65dB);

Fig. 8 (b) based on FT blindly Deconvolution Algorithm Based on Frequency to " No. two, resource " visual ambiguity solution effect: contrast increases 10dB;

Fig. 9 is the denoise algorithm result, wherein:

Fig. 9 (a) multiframe (source) denoising algorithm effect: PSNR increases 4.5dB;

Wherein left side figure is low resolution noisy image (16.89dB), and right figure is an image (21.65dB) after the denoising;

The improved Anisotropic Nonlinear diffusion of Fig. 9 (b) denoise algorithm effect;

A left side 2 width of cloth figure: poisson noise image (27.54dB); Right 2 width of cloth figure: image (30.26dB) after the denoising;

Fig. 9 (c) trap rejection filter is eliminated the band noise effects:

C-1 is actual remote sensing image; C-2 is the trap rejection filter;

The band noise of c-3 for eliminating; C-4 is filtered output image;

Figure 10 suppresses thin cloud mist algorithm process result:

Figure 10 (a) suppresses cloud and mist effect image based on homomorphic filtering; Wherein left side figure is the cloud and mist image; Right figure is an image behind the inhibition cloud and mist;

Figure 10 (b) suppresses cloud and mist effect image based on wavelet multiresolution analysis, and wherein left figure is: no cloud and mist reference picture; Middle figure is: the cloud and mist image; Right figure is: image behind the inhibition cloud and mist;

Embodiment:

Embodiment 1:

Method for super resolution of single-frame images is at first analyzed image, and whether decision eliminates noise according to analysis result, image restoration fuzzy and cloud and mist is handled; Carry out super-resolution then and handle, whether adopt the single frames frequency domain to separate the aliasing ultra-resolution method by the frequency alias parameter decision and handle; Separate aliasing algorithm and inverse fourier transform by Fourier transform, frequency domain then, the texture and the details of abundant image improve visual sharpness, contrast and resolution, and the suppressed ringing illusion.

The described frequency alias degree of depth:

Wherein spectrum width is 2 π; C ₁₁Be the frequency alias degree of depth (FAD) parameter, the degree of the high-end aliasing of reaction frequency spectrum.C ₁₁Leaching process comprises: the low resolution image to owing to sample, carry out Fourier transform; Frequency spectrum to low resolution image carries out overall polynomial expression least square fitting; To low-frequency component in the later frequency spectrum of match and high frequency central energy, carry out secondary and block match; The frequency spectrum that secondary is blocked match carries out the frequency spectrum expansion, and then calculates the FAD parameters C ₁₁

If FAD parameters C ₁₁≤ 0.4, then adopt the single frames super resolution technology, if the FAD parameters C ₁₁＞0.4, then adopt the multiframe super resolution technology; And C ₁₂Be high frequency normalized energy parameter, if C ₁₂Then need in the processing of super-resolution, introduce the operation of suppressed ringing illusion greatly, can avoid illusion occurring in the high-resolution picture after processing.

Specify as follows:

(x y) obtains one group of sight images f by the visual g of the thing of an actual scene _i(k, l) i=1,2 ..., p, the quality degradation of every frame image, resolution and contrast have all reduced.So, f _i(k l) is the low resolution sight images, and g (x y) is high-resolution original thing image.f _i(k l) is the digital image that degrades, and g (x y) is distortionless sequential image.For convenience, suppose and satisfying under the condition of sampling theorem that (x y) does not convert digital image to with not losing any information, and promptly high-resolution original figure thing image is with g (k, l) expression g.

Described image analysis comprises at first carries out fuzzy analysis, Analysis signal-to-noise ratio (SNR) and cloud and mist analysis respectively to the image of importing, then analysis result is compared with fuzzy standard, signal to noise ratio (S/N ratio) standard and cloud and mist standard respectively, judge whether to carry out the ambiguity solution operation, strengthen the signal to noise ratio (S/N ratio) operation and suppress the cloud and mist operation, judged result is separately used controlled variable C respectively ₂, C ₃And C ₄Expression, and they are passed to the combination of controller and image restoration handle accordingly.

Image restoration is conciliate the aliasing process and is comprised: the repetition recursive iteration mathematical model of foundation and optimization solution aliasing, ambiguity solution and enhancing signal to noise ratio; By spectrum analysis, fuzzy analysis and the signal to noise ratio analysis of described image analysis, be based upon separating frequency alias algorithm, ambiguity solution algorithm and suppressing the criterion of noise algorithm of needing in the recursive operation to introduce; Finish the development that frequency domain repeats the recursive algorithm software module, and by experiment software module is optimized.

1. operate about image restoration

(1) Mo Hu inhibition technology

As a gordian technique, the embodiment of definite reconciliation Fuzzy Processing of ambiguity function is at first carried out fuzzy analysis to the real satellite image, the type of identification image blurring.If there is defocusing blurring, then further determine its ambiguity function, and the extraction fuzzy parameter is blur level C ₂If there is motion blur, then need to carry out kinematic parameter and estimate, identification is space-variant or empty constant, and different fuzzy regions is cut apart, wherein may comprise no fuzzy region, each different fuzzy region is further determined ambiguity function and blur level C ₂The ambiguity function of determining through above-mentioned analysis is respectively applied for corresponding ambiguity solution algorithm, obtains restoring image, and the blur level parameters C ₂Then be used as the controlled variable of algorithm.

We know that the ambiguity solution process nature is the deconvolution process.The present invention introduces based on the blindness of the iteration on the limited support region of Fourier transform (FT) Deconvolution Algorithm Based on Frequency.

The mathematical model that image degrades on the limited support region generally can be expressed as a convolution integral

$f(x,y)=\underset{D}{\∫}\∫h(x-s,y-t)g(s,t)\mathrm{dsdt}+\mathrm{\ξ}(x,y)---\left(1\right)$

In the formula, D is a limited support region on the two dimensional surface.Here, sight images f (x y) is a complete convolution, thus realistic images g (x, y) and point spread function h (x y) is limited support.

Two dimension blindly deconvolution has a fuzzy problem of separating, what pay close attention to is that displacement is fuzzy herein, because as if do not influence the fuzzy of the profile of separating on this surface, cause very big difficulty in fact but for the convergence of iteration Deconvolution Algorithm Based on Frequency, overcoming this difficult method is the support region that restriction is separated.Two dimension on the limited support region blindly deconvolution problem is overdetermination in general, thereby has solvability.But this problem also is non-linear simultaneously, and promptly separating may be not unique.

Utilize Fourier transform (FT) can realize the repeatedly conversion of picture intelligence from the time domain to the frequency domain, in conversion repeatedly, add the restriction of expectation signal is revised in two territories repeatedly, make to produce the image of expectation at last.The further evolution of this idea becomes one of basic skills of image restoration and reconstruction, and many successful application have been arranged.Because the restriction to signal often can be interpreted as the convex set projection, so this class alternative manner can range the algorithm based on the convex set projection.

For blindness deconvolution problem, frequency domain is estimated to realize with Wiener filtering, make the Fourier transform iterative algorithm become more reasonable.The computing formula that frequency domain is estimated is

$\hat{G}(m,n)=\frac{{\hat{H}}^{*}(m,n)F(m,n)}{{\left|\hat{H}(m,n)\right|}^2+\frac{S_{\mathrm{nn}}(m,n)}{S_{\mathrm{gg}}(m,n)}}---\left(2\right)$

$\hat{H}(m,n)=\frac{{\hat{G}}^{*}(m,n)F(m,n)}{{\left|\hat{G}(m,n)\right|}^2+\frac{S_{\mathrm{nn}}(m,n)}{S_{\mathrm{hh}}(m,n)}}---\left(3\right)$

Wherein, S _Gg(m, n), S _Hh(m, n) and S _Nn(m n) is the power spectrum of input signal, convolution kernel and noise respectively.

Wiener filtering is replaced to increment Wiener filtering, and its frequency domain estimation formulas is

${\hat{G}}_{\mathrm{new}}(m,n)={\hat{G}}_{\mathrm{old}}(m,n)+\frac{{\hat{H}}^{*}(m,n)S(m,n)}{{\left|\hat{H}(m,n)\right|}^2+{\mathrm{\γ}}_g}---\left(4\right)$

${\hat{H}}_{\mathrm{new}}(m,n)={\hat{H}}_{\mathrm{old}}(m,n)+\frac{{\hat{G}}^{*}(m,n)S(m,n)}{{\left|\hat{G}(m,n)\right|}^2+{\mathrm{\γ}}_h}---\left(5\right)$

Wherein, $S(m,n)=F(m,n)-\hat{G}(m,n)\hat{H}(m,n),$ γ _gAnd γ _hBe two little constants.In general, if signal to noise ratio (S/N ratio) is lower, with bigger γ _gAnd γ _hCan guarantee the flatness of separating, but improvement speed is slower.Otherwise, too little γ _gAnd γ _hThe result is separated near a rough liftering quickly.Do not have stable convergence though experience shows the iterative algorithm that utilizes Fourier transform, more approaching separating usually can be provided.Because the iteration blindness Deconvolution Algorithm Based on Frequency based on Fourier transform has fast algorithm,, we handle so utilizing this algorithm to carry out ambiguity solution in the realistic images experiment.

(2) Noise Suppression

The invention provides the Anisotropic Nonlinear diffusion denoise algorithm that suppresses pattern noise, but also propose and set up the median filter of the trap rejection filter that can reject the band noise and the introducing gradient restriction that can eliminate grain noise based on second-order partial differential coefficient.

(i) Anisotropic Nonlinear based on second-order partial differential coefficient spreads denoise algorithm

Under the situation that single source (frame) image is only arranged, be one based on partial differential equation (PDE) denoising method and select preferably.The present invention is directed to more ubiquitous Gaussian noise and poisson noise in the image, with the Anisotropic Nonlinear diffusion process of second derivative factor introducing based on PDE, set up improved diffusion denoise algorithm, not only can suppress the noise of smooth region effectively, and can suppress the noise at texture place, edge effectively; Not only the strong edge of step evolution can be protected well, and more weak detail textures can be protected even strengthen well; The edge texture is subjected to displacement, does not have false texture to produce.Handle the image that Gaussian noise is polluted, can make PSNR improvement value＞3～4dB; Handle the image that poisson noise pollutes, can make PSNR improvement value＞2～3dB.

$\left\{\begin{array}{c}{\∂}_{t}u=\mathrm{div}(\tilde{c}\left(({|\▿(G_{\mathrm{\σ}}\×u)|}^2+{(G_{\mathrm{\σ}}\×u_{\mathrm{xx}})}^2+{(G_{\mathrm{\σ}}\×u_{\mathrm{yy}})}^2){|\▿u|}^2\right)\▿u)\\ u(x,0)=u_0\left(x\right)\end{array}\right.---\left(6\right)$

(ii) trap rejection filter

In order to eliminate the band noise,, designed the trap rejection filter at frequency domain according to the characteristics of its frequency spectrum.The form of desirable rejection filter is

$H(u,v)=\left\{\begin{array}{cc}1& D(u,v)<D_0-W/2\\ 0& D_0-W/2\&le;D(u,v)\&le;{\mathrm{<figure-callout\; id="0"\; label="D"\; filenames="S2008100960547E00013.png,S2008100960547E00021.png"\; state="\{\{state\}\}">D</figure-callout>}}_0+W/2\\ 1& D(u,v)>{\mathrm{<figure-callout\; id="0"\; label="D"\; filenames="S2008100960547E00013.png,S2008100960547E00021.png"\; state="\{\{state\}\}">D</figure-callout>}}_0+W/2\end{array}\right.---\left(7\right)$

In the formula, and D (u, v)=[(u-M/2) ²+ (v-N/2) ²] ^1/2, M, N are the two-dimentional width of image spectrum, the center of two-dimensional circle function overlaps with the center of two-dimensional image frequency spectrum; (u has v) defined the trap rejection filter of an annular to H, and W is the width of stopband, D ₀It is the radius of circular stopband center.

(iii) introduce the median filter of gradient restriction

Carry out conditional medium filtering in having the image of serious grain noise, promptly introduce the restrictive condition based on gradient in the medium filtering of routine: the gradient of processed point is worth outside predetermined codomain less than predetermined thresholding and its ash.Like this, the relation of the gradient of image and its grain noise as prior imformation, has been set up conditional median filtering algorithm, not only can eliminate grain noise serious in the image, and can protect grain details effectively.

(3) thin cloud mist suppresses technology

Under the situation of thin cloud mist, image is mainly by two factors decisions: one is the influence of cloud and mist etc., be designated as i (x, y), another is the influence of ground return characteristic, be designated as r (x, y), both are the relations that multiply each other, (x y) is total influence factor f

f(x，y)＝i(x，y)r(x，y) (8)

According to the characteristics of cloud and mist and scenery distribution, comparatively speaking, cloud and mist mainly is distributed in low frequency, and scenery relatively mainly occupies high frequency.If remove the influence of cloud and mist, promptly remove i (x, y), ask r (x, y).Because f (x, y) be by i (x, y) and r (x y) multiplies each other and obtains, and (x y) removes i so can't use general wave filter.The invention provides solution to this problem.

(i) the thin cloud mist based on homomorphic filtering suppresses technology

Based on the thin cloud mist inhibition technology of homomorphic filtering is a kind of disposal route frequency is filtered and greyscale transformation combines, it is the basis that the visual reflection model of atural object and cloud and mist is handled as frequency domain, utilizes compression brightness range and enhancing contrast ratio to improve a kind of treatment technology of image quality.Utilize homomorphic filter to carry out the embodiment of cloud and mist inhibition shown in accompanying drawing 6 (a).

The cloud and mist component normally changes slowly, reflecting component then changes comparatively violent, this feature makes the low frequency component and the cloud and mist component of the Fourier transform after might taking the logarithm an images connect, and reflecting component and ground scenery component are connected so approximate essence that has reflected actual scenery basically.

(ii) carrying out cloud and mist based on wavelet multiresolution analysis suppresses:

With respect to traditional analytical approach, a major advantage of wavelet analysis has provided the ability of partial analysis and refinement, it can be better to the time spacing wave variation carry out modeling, more convenient aspect the details of describing signal.One images can be carried out multilayer by wavelet multiresolution analysis and decompose, form a plurality of low resolution compositions, each part has different frequencies and space attribute, and can utilize high-resolution picture of every part reconstruct by wavelet inverse transformation.Utilize wavelet multiresolution analysis to carry out the embodiment of cloud and mist inhibition shown in accompanying drawing 6 (b).

2. operate about the single frames super-resolution

Suppose the influence of having eliminated fuzzy, noise and cloud and mist, further analyze the real satellite image from frequency spectrum, the base attribute, the particularly situation of high-band frequency aliasing of research spectrum structure are so that be visual super-resolution exploration prior imformation.

As previously mentioned, in order to describe the frequency alias degree that image causes because of owing to sample, propose and set up the frequency alias degree of depth (FAD) parameters C ₁₁, the present invention studies C ₁₁Span, computing method and C ₁₁Relation with ultra-resolution method is selected provides C at last ₁₁Application.

The FAD parameters C ₁₁Be defined as

Following formula intermediate frequency spectrum width is 2 π.

The spectrum structure form and the low frequency part of sampling image remain unchanged, and only high frequency has loss, and may be because the high frequency aliasing changes spectrum structure.Therefore, only be concerned about HFS here.According to each group results of spectral, tabulation provides minimum, frequency alias width and the frequency alias parameters C of high-frequency energy respectively ₁₁Estimation.

The detailed process that described super-resolution is separated in the aliasing processing comprises:

(1) to the single frame image f of low resolution (k l) carries out Fourier transform, with its transform to frequency spectrum F (m, n);

(2) to the frequency spectrum F that obtained (m n) carries out frequency domain transform filtering or compensation filter and handles, with the high-resolution picture frequency spectrum G that is expanded and strengthens (m, n);

(3) by inverse Fourier transform, will through the super-resolution image spectrum G of frequency domain expansion and enhancing (m, n) be transformed into high-resolution picture g (k, l).

Wherein, described frequency domain compensation Filtering Processing comprises:

(1) (m n) carries out spectrum analysis, obtains normalization high frequency central energy parameter p to described frequency spectrum F;

(2) with resulting normalization high frequency central energy parameter p and thresholding p given in advance _ThCompare;

(3) be less than or equal to described thresholding p when described parameter p _ThThe time, (m n) carries out frequency domain compensation and handles to described frequency spectrum F to utilize the frequency domain compensation wave filter;

(4) when described parameter p greater than described thresholding p _ThThe time, (m n) carries out the conversion Filtering Processing to described frequency spectrum F.

Wherein, the One dimensional Mathematical Model of described frequency domain transform wave filter is:

$H\left(n\right)=\left\{\begin{array}{cc}\mathrm{Aexp}(-\frac{n^p}{\mathrm{\&omega;}})& 0\&le;n\&le;N/2\\ \mathrm{Aexp}(-\frac{{(N-n)}^p}{\mathrm{\&omega;}})& N/2<n\&le;N-1\end{array}\right.---\left(9\right)$

Wherein, n is the frequency spectrum point, and N is the number of pixels of former image row/row, and A is the super-resolution factor, and ω is a frequency domain high frequency aliasing central energy normalized parameter, and p is a normalization high frequency central energy parameter, p and C ₁₂Reciprocal each other;

Embodiment 2:

Actual image mostly contains noise more or less, at first utilize for this reason above-mentioned iteration based on FT blindly Deconvolution Algorithm Based on Frequency many groups of noisy blurred images have been carried out the emulation experiment of ambiguity solution recovery operation, the relation of research ambiguity solution effect and iterations N.In experiment, at first using size is that 3 * 3 defocusing blurring matrix is made convolution to raw image, and adds the Gaussian noise of N (0,5), obtains noisy blurred image; Noisy blurred image is carried out ambiguity solution handle, iterations N changes to 6 from 1, obtains the ambiguity solution image.Then, image behind blurred image and the ambiguity solution is calculated Y-PSNR PSNR, and then can obtain the PSNR added value of three groups of experimental results of blindness Deconvolution Algorithm Based on Frequency and the relation curve of iterations N, and then the PSNR added value reaches peak value before and after obtaining when iterations N=2 ambiguity solution, be about 4～6dB, along with the further increase of iterations, the PSNR of the image after the processing reduces on the contrary.

Extract and compare the FAD parameter of image before and after super-resolution is handled respectively, can obtain the objective evaluation of many super-resolution treatment effect, be about to the objective evaluation parameter of FAD parameter as super-resolution.For example, to certain width of cloth satellite imagery, the FAD parameter before and after super-resolution is handled is C respectively ₁₁₁And C ₁₁₂, then order

ΔC＝C ₁₁₁-C ₁₁₂ (10)

Or

${\mathrm{\&delta;}}_C=\frac{C_{111}-C_{112}}{C_{111}}\&times;100\%---\left(11\right)$

Or

Be understood that Δ C is the reduction that super-resolution is handled the FAD parameter of back image, δ _CBe the relative value of FAD parameter reduction, Be the ratio of visual FAD parameter before and after super-resolution is handled.Δ C or δ _COr

Big more, then the super-resolution treatment effect is good more.For example, suppose C ₁₁₁=2.0, C ₁₁₂=0.5, Δ C=1.5 then, δ _c=75%,

Obviously,

Be the multiple that the picture frequency aliasing improves, can represent, be referred to as frequency alias degree of depth improvement factor, promptly with decibel

Suppose C ₁₁₁=2.0, C ₁₁₁=0.5, then

Promptly after super-resolution was handled, the frequency alias of image had improved 12dB.

The single frames super-resolution processing method

In order to suppress the noise in the image, there are a lot of conventional methods, wave filter and frame filter device in for example various frames, filtering noise to a certain extent, but there is the contradiction between the reservation of noise filtering and edge grain details, edge texture region with image when noise is carried out filtering has blured, thereby causes the reduction of resolution and contrast.Therefore, the new denoising method of essential research in filtering noise, can keep even strengthen edge grain details information again, so that improve the spatial resolution of image effectively.For this reason, primary study of the present invention four kinds of denoise algorithm, provide four kinds of denoise algorithm below, and provide result.

(1) based on the frequency domain denoise algorithm of multiframe (source) information fusion

Separate on the aliasing theoretical foundation at multiframe (source) frequency domain, utilize the irrelevance of noise, adopt the lowest mean square technology, derive a cover circulation recursive iteration algorithm:

$E^{(k+1)}=P(k+1)Y_{k+1}^{*}[Z_{k+1}-Y_{k+1}^T{\hat{F}}^{\left(k\right)}]\&LeftRightArrow;{\hat{F}}^{(k+1)}={\hat{F}}^{(k+1)}+E^{(k+1)}$

Can make PSNR improvement value＞4.5dB.

(2) the Anisotropic Nonlinear diffusion denoise algorithm of introducing second-order partial differential coefficient

Under the situation that single source (frame) satellite imagery is only arranged, be one based on partial differential equation (PDE) denoising method and select preferably.The second-order partial differential coefficient of image is introduced coefficient of diffusion, sets up new Anisotropic Nonlinear broadcast algorithm:

$\left\{\begin{array}{c}{\&PartialD;}_{t}u=\mathrm{div}(\tilde{c}\left(({|\&dtri;(G_{\mathrm{\&sigma;}}\&times;u)|}^2+{(G_{\mathrm{\&sigma;}}\&times;u_{\mathrm{xx}})}^2+{(G_{\mathrm{\&sigma;}}\&times;u_{\mathrm{yy}})}^2){|\&dtri;u|}^2\right)\&dtri;u)\\ u(x,0)=u_0\left(x\right)\end{array}\right.$

Compare with some classical denoising method in the past, this method not only can suppress noise preferably, and can keep even strengthen features such as edge and grain details, improves the effect that suppresses noise and image restoration.Handle the image that Gaussian noise is polluted, can make PSNR improvement value＞3～4dB; Handle the image that poisson noise pollutes, can make PSNR improvement value＞2～3dB.

Claims (2)

1. a method for super resolution of single-frame images is characterized in that: at first image is analyzed, judged that by the frequency alias degree of depth whether adopting the single frames frequency domain to separate the aliasing ultra-resolution method handles; Separate aliasing algorithm and inverse fourier transform by Fourier transform, frequency domain then, the texture and the details of abundant image improve visual sharpness, contrast and resolution, and the suppressed ringing illusion, the described frequency alias degree of depth:

C ₁₁ =aliasing width/spectrum width,

Wherein, spectrum width is 2 π; C _Ll Be frequency alias degree of depth FAD parameter, the degree of the high-end aliasing of reaction frequency spectrum;

C _Ll Leaching process comprises: the low resolution image to owing to sample, carry out Fourier transform; Frequency spectrum to low resolution image carries out overall polynomial expression least square fitting; To low-frequency component in the later frequency spectrum of match and high frequency central energy, carry out secondary and block match; The frequency spectrum that secondary is blocked match carries out the frequency spectrum expansion, and then estimates the FAD parameters C _Ll

If FAD parameters C _Ll ≤ 0. 4, then adopt the single frames super resolution technology, if the FAD parameters C _Ll 0.4, then adopt the multiframe super resolution technology

2. method for super resolution of single-frame images according to claim 1 is characterized in that: described single frames frequency domain is separated the aliasing ultra-resolution method and is handled and comprise:

(1) to the single frame image f of low resolution (k l) carries out Fourier transform, obtain its frequency spectrum F (m, n);

(2) to the frequency spectrum F that obtained (m n) carries out frequency domain transform filtering or compensation filter and handles, with the high-resolution picture frequency spectrum G that is expanded and strengthens (m, n);

(3) by inverse Fourier transform, will through the high-resolution picture frequency spectrum G of frequency domain expansion and enhancing (m, n) be transformed into high-resolution picture g (k, l)

Images