CN103325091A - Low-frequency frequency spectrum data zero-padding method image obtaining method and system - Google Patents

Abstract

The invention provides a low-frequency frequency spectrum data zero-padding method image obtaining method and system. The method comprises the steps of obtaining the number of transverse or longitudinal pixel points of a high-resolution image to be restored and a low-resolution image, and obtaining low-frequency frequency spectrum data of the high-resolution image according to the number of the pixel points and the low-resolution image; obtaining zero-padding method frequency spectrum data of the high-resolution image according to the low-frequency frequency spectrum data of the high-resolution image; conducting Fourier transformation on the zero-padding method frequency spectrum data so as to obtain a low-frequency frequency spectrum data zero-padding method image of the high-resolution image, and being capable of rapidly and efficiently obtaining the low-frequency frequency spectrum data zero-padding method image so as to be supplied to restoration of the high-resolution image under the condition that high-frequency frequency spectrum data are lost.

Description

Low-frequency spectra data padding method image acquiring method and system

Technical field

The present invention relates to a kind of low-frequency spectra data padding method image acquiring method and system.

Background technology

Satellite remote sensing have wide coverage, longer duration, real-time, be not subjected to the unique advantages such as national boundaries, regional limits, be widely used in the fields such as development of resources, environmental monitoring, Disaster Study, whole world change analysis, deeply be subjected to the great attention of various countries.The spatial resolution of satellite image is to weigh a leading indicator of satellite remote sensing ability, also is the important symbol of weighing a national spacer remote sensing level.Improve the moonscope spatial resolution and become satellite engineering technical research focus.Satellite obtains image and crosses in the kind, there is several factors can cause image quality decrease, atmospheric disturbance, move, defocus, transmission and noise all can directly have influence on image resolution ratio and descend, particularly satellite cuts lotus and limits and make the optical system cutoff frequency that limit for height be arranged, and CCD chip pixel dimension is limited little, placed restrictions on satellite image spatial high-frequency component, so that image resolution ratio is not high enough.

Theoretical according to the optics Fourier spectrum, there is cutoff frequency c in optical system _f=(D-l)/(2f λ), wherein D is the equivalent lens diameter, and l is the CCD chip size, and f is that the focal length of lens and λ are optical wavelength.If the pixel dimension of CCD chip is w, then by sampling thheorem, it is u that cutoff frequency is also arranged _w=1/ (2w).In the object, only have simultaneously less than u _wAnd c _fSpatial frequency component just can obtain and imaging, if c _f≠ u _w, resource or the optical imagery wasting of resources then cause sampling.If the distance of satellite and subject is R, then satellite image is distinguishable apart from △ x=wR/f=λ R/ (D-l).Improve u if reduce the pixel dimension of CCD chip _w, and optical cut-off also improves c thereupon _f=u _w, (at present minimum value is 50 μ m then can to improve the spatial resolution of image ²), but CCD chip pixel dimension w is too little, and signal to noise ratio (S/N ratio) is too low, so that can't normally use.Therefore, the high fdrequency component of satellite image disappearance is the science difficult problem that can't steer clear of.Traditional high resolving power (list of references 1:J.L.Harris, Diffraction and resolving power, J.Opt.Soc.Amer., 54 (7): 931-133,1964 and document 2:W.Lukosz, Optical systems with resolving power exceeding the classical limit.J.Opt.Soc.Amer., 56 (11): 1463-1471,1966) refer to exceeding optical system cutoff frequency c _fAnd the image high-frequency information that is lost recovers, and this method is called the high resolution restoration technology.Majority think that the spectrum information that will accurately recover outside the cutoff frequency is impossible, and claim that this is that high resolving power is mythical.

In the time can obtaining the image sequence of several Same Scene, can set up mathematical model: g _i=Hs _i+ n _i, i=1,2 ..., k, wherein g _i, s _i, n _iRespectively table the i frame low-resolution image, high-definition picture and noise image, H represents the various various factorss that cause the image low resolution.By the multiframe interpolation method (referring to document 3:L.Zhang, X.Wu, An Edge-Guided Image Interpolation Algorithm via Directional Filtering and Data Fusion, IEEE Transaction on image processing, 15 (8): 2226-2238,2006, document 4:D.Rajan D, S.Chaudhuri, Generalized interpolation and its application in super-resolution imaging, Image and Vision Computing, 19 (13): 957-969,2001, document 5:A.S á nchez-Beato and G.Pajares, Non-iterative interpolation-based super-resolution minimizing aliasing in the reconstructed image, IEEE Trans.Image Process., 17 (10), pp.1817 – 1826,2008, document 6:S.Lertrattanapanich, N.K.BOSE, High resolution image formation from low resolution frames using Delaunay triangulation, IEEE Transaction on Image Processing, 11 (12): 1427-1441,2002 and document 7F.Zhou, W.Yang, and Q.Liao, Interpolation-Based Image Super-Resolution Using Multisurface Fitting, IEEE Transaction on Image Processing, 21 (7): 3312-28,2012), utilize priori to be optimized and find the solution (referring to document 8:X.Gao, K.Zhang, D.Tao and X.Li, Image Super-Resolution With Sparse Neighbor Embedding, I IEEETrans.on Image Processing, Vol.21, No.7, pp.3194-3205,2012, document 9:Z.M.Wang and W.W.Wang, Fast and Adaptive Method for SAR Superresolution Imaging Based on Point Scattering Model and Optimal Basis Selection, IEEE Tran.on Image Processing, 18 (7): 1477-1486,2009, document 10:A.Marquina and S.J.Osher, Image super-resolution by TV regularization and Bregman iteration, Journal of Scientific Computing, vol.37, no.3, pp.367 – 382,2008 and document 11:J.Yang, J.Wright, T.S.Huang and Y.Ma, " Image super-resolution via sparse representation; " IEEE Trans.Image Process., vol.19, no.11, pp.2861 – 2873,2010), based on learning method (referring to document 11, document 12:T.Goto, Y.Kawamoto, Y.Sakuta, A.Tsutsui and M.Sakurai, Learning-based Super-resolution Image Reconstruction on Multi-core Processor, IEEE Transactions on Consumer Electronics, 58 (3): 941～946,2012, document 13:P.Purkait and B.Chanda, Super Resolution Image Reconstruction Through BregmanIteration Using Morphologic Regularization, IEEE Trans.on Image Processing, 21 (9): 4029～4040,2012, document 14:P.P.Gajjar and M.V.Joshi, New learning basedsuper-resolution:Use of DWT and IGMR-F prior, IEEE Trans.on Image Processing, Vol.19, No.5, pp.1201-1213,2010, document 15:M.S.Crouse, R.D.Nowak, R.GBaraniuk, Wavelet-based statistical signal processing using hidden Markov models, IEEE Transactions on Signal Processing, 46 (4): 886-902,1998 and document 16:M N Do, M.Vetterli, The contourlet transform:An efficient directional multi-resolution image representation, IEEE Transactions on Image Processing, 14 (12): 2091-2106,2005) etc. (referring to document 17:D.D.-Y Po and DO M.N.Do, Directional multi-scale modeling of images using the contourlet transform, IEEE Transactions on Image Processing, 15 (6): 1610-1620,2006 and document 18:W.Dong, L.Zhang, G.Shi and X.Wu, Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization, IEEE Trans.Image Process., vol.20, no.7, pp.533 – 549, Jul.2011) obtain high-definition picture, improve the deteriroation of image quality of owing to sample and causing.But in the moonscope shooting, the multiple image collection of same visual field is utmost point waste resource and difficult accomplishing, single-frame images superresolution restoration technology is only the gordian technique of remote sensing images superresolution restoration, but does not have so far substantive breakthroughs.Be the high resolution restoration of research single-frame images, we consider that following low-resolution image forms the mathematical model of mechanism.

If do not consider disturbing factor, can be described as with following formula for its imaging process of imaging system:

g(x,y)=p(x,y)*s(x,y)

Here g (x, y), p (x, y), s (x, y) represents respectively remote sensing images, visual field and imaging system point spread function, * represents convolution algorithm.To the image spectrum function be: G (u, v)=P (u, v) S (u, v), the frequency spectrum function P (u, v) of point spread function=1, | u|＜c _f﹠amp; | v|＜c _fIt is band-limited rectangular window.As practical field of view cutoff frequency c _sGreater than optical imaging system cutoff frequency c _fThe time, the c of visual field _fHigh fdrequency component is in addition lost, and becomes low-resolution image.Traditional habit is thought c outside the optical imaging system cutoff frequency _fFrequency spectrum cannot restore.But according to the analytical continuation theorem: be known if resolve in a certain finite interval, just Zone Full is arrived in continuation uniquely.Also just say " if two analytical functions are in full accord on arbitrary given zone " then they are necessarily in full accord on the whole " is Same Function (referring to civilian 19:E.B.Saff and A.D.Snider; Fundamentals of Complex Analysis with Applications to Engineering and Science; 2003, Pearson Education).The visual field can be regarded as a function on the bounded field of definition, and its spectral function is an analytical function.Therefore, according to the analytical continuation theorem, can be by image spectrum data G (u, v)=P (u, v) S (u, v), | u|＜c _f﹠amp; | v|＜c _f, continuation is to whole spectrum space, cutoff frequency c _f=∞.It is that the frequency spectrum extrapolation is (referring to document 20:H.Greenspan that early stage research is carried out the high resolution restoration main method from single-frame images, C.H.Anderson, S.Akber, Image enhancement by nonlinear extrapolation in frequency space, IEEE Trans.Im age Processing, vol.9, no6, pp.1035-1048,2000), the prolate ellipsoid Wave function method is (referring to document 21:H.A.Brown, Effect of Truncation on Image Enhancement by Prolate Spheroidal Functions, Journal of the Optical Society of America, Vol.59, no2, pp.228-229,1969), the sinusoidal template of superposition is (referring to document 22:S.Wadaks, T.Sato, Superresolution in Incoherent Imaging System, Journal of the Optical Society of America, 65 (3): 354-355,1975), the superresolution restoration technology such as interpolation method (referring to document 3).But these methods take full advantage of and are implying image high-resolution information in the low-resolution image, do not understand and utilization analytical continuation theorem mathematical principle, thereby can't or seldom study from low resolution image and obtain the high-frequency information method, thereby effect is very limited (referring to document 23:S.C.Park, M.K.Park, M.G.Kang, Super-resolution image reconstruction:a technical overview, IEEE Signal Processing Magazine, Vol.20, no.3, pp.21-36, May2003).

Summary of the invention

The object of the present invention is to provide a kind of low-frequency spectra data padding method image acquiring method, can be in the situation that the high frequency spectrum shortage of data obtains low-frequency spectra data padding method image quickly and efficiently for the recovery of high-definition picture.

For addressing the above problem, the invention provides a kind of low-frequency spectra data padding method image acquiring method, comprising:

Obtain horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtain the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image;

Zero padding method frequency spectrum data according to the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture;

Described zero padding method frequency spectrum data is made Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture.

Further, in said method, obtain horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtain according to described pixel number and low-resolution image in the step of low-frequency spectra data of described high-definition picture

One width of cloth low-resolution image g _l(i, j), i, j=0,1 ..., l will reset into high-definition picture g (i, j), i, and j=0,1 ..., N, N＞＞l, the frequency spectrum data of g (i, j) image is expressed as G (k _x, k _y), k _x, k _y∈ Ω, Ω are the spectrum space of described high-definition picture, and l represents horizontal or vertical pixel number of low-resolution image, and N represents horizontal or vertical pixel number of the high-definition picture of parked, and the frequency spectrum data of low-resolution image is expressed as G _l(k _x, k _y), Then the low-frequency spectra data of g (i, j) image are expressed as

G(k _x,k _y)=(N/l) ²G _l(k _x,k _y)，-l/2≤k _x,k _y<l/2。

Further, in said method, in the step according to the zero padding method frequency spectrum data of the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture,

The zero padding method frequency spectrum data of described high-definition picture is expressed as G (k _x, k _y) P (k _x, k _y), wherein,

Further, in said method, described zero padding method frequency spectrum data is done in the step of Fourier transform with the low-frequency spectra data padding method image that obtains high-definition picture,

The low-frequency spectra data padding method image representation of described high-definition picture is

According to another side of the present invention, a kind of low-frequency spectra data padding method image-taking system is provided, comprising:

The low-frequency spectra data module is used for obtaining horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtains the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image;

Zero padding method frequency spectrum data module is used for the zero padding method frequency spectrum data according to the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture;

Zero padding method image module is used for described zero padding method frequency spectrum data is made Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture.

Further, in said system, described low-frequency spectra data module is used for a width of cloth low-resolution image is expressed as g _l(i, j), i, j=0,1 ..., l will reset into high-definition picture and be expressed as g (i, j), i, and j=0,1 ..., N, N＞＞l, the frequency spectrum data of g (i, j) image is expressed as G (k _x, k _y), k _x, k _y∈ Ω, Ω are the spectrum space of described high-definition picture, l ²Horizontal or vertical pixel number of expression low-resolution image, N ²Horizontal or vertical pixel number of the high-definition picture of expression parked, the frequency spectrum data of low-resolution image is expressed as G _l(k _x, k _y),

Then the low-frequency spectra data of g (i, j) image are expressed as

G(k _x,k _y)=(N/l) ²G _l(k _x,k _y)，-l/2≤k _x,k _y<l/2。

Further, in said system, described zero padding method frequency spectrum data module is expressed as G (k with the zero padding method frequency spectrum data of described high-definition picture _x, k _y) P (k _x, k _y), wherein,

Further, in said system, described zero padding method image module with the low-frequency spectra data padding method image representation of described high-definition picture is

Compared with prior art, horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of the present invention by obtaining parked obtain the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image; Zero padding method frequency spectrum data according to the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture; Described zero padding method frequency spectrum data is made Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture, can be in the situation that the high frequency spectrum shortage of data obtains low-frequency spectra data padding method image quickly and efficiently for the recovery of high-definition picture.

Description of drawings

Fig. 1 a is the process flow diagram that the high-definition picture of one embodiment of the invention restores;

Fig. 1 b is the detail flowchart of step S4 among Fig. 1 a;

Fig. 1 c is the detail flowchart of step S5 among Fig. 1 a;

Fig. 2 is the schematic diagram that the low-resolution image of a width of cloth 256X256 of one embodiment of the invention resets into the high-definition picture of 512X512;

Fig. 3 a be one embodiment of the invention be used for emulation with reference to image;

Fig. 3 b is that the cutoff frequency of one embodiment of the invention is 32～96 low resolution image, through the error peak signal to noise ratio (S/N ratio) of Sinc interpolation, TV regularization and SSIT method restored image;

Fig. 4 is that the cutoff frequency of one embodiment of the invention is 64 high-definition picture recovery experimental principle figure;

Fig. 5 a is as with reference to the variation with the noise size of the reset error Y-PSNR of image take Fig. 3 a

Fig. 5 b is that to add image behind the noise be with reference to the variation with the noise size of the reset error Y-PSNR of image;

Fig. 6 a is that the adding noise of one embodiment of the invention is with reference to the spectrogram of image;

Fig. 6 b is the spectrogram of the Sinc method restored image of one embodiment of the invention;

Fig. 6 c is the spectrogram of the TV method restored image of one embodiment of the invention;

Fig. 6 d is the spectrogram of the SSIT method restored image of one embodiment of the invention;

Fig. 7 a be one embodiment of the invention be used for test first with reference to image;

Fig. 7 b be one embodiment of the invention be used for test second with reference to image;

Fig. 7 c be one embodiment of the invention be used for test the 3rd with reference to image;

Fig. 7 d be one embodiment of the invention be used for test the 4th with reference to image;

Fig. 7 e be one embodiment of the invention be used for test the 5th with reference to image;

Fig. 7 f be one embodiment of the invention be used for test the 6th with reference to image;

Fig. 8 a is the low-resolution image of the 128X128 of one embodiment of the invention;

Fig. 8 b is the 256X256 image behind the Sinc method high resolution restoration of one embodiment of the invention;

Fig. 8 c is the 256X256 image behind the TV method high resolution restoration of one embodiment of the invention;

Fig. 8 d is the 256X256 image behind the SSIT method high resolution restoration of one embodiment of the invention;

Fig. 8 e is the spectrogram of Fig. 8 b;

Fig. 8 f is the spectrogram of Fig. 8 c;

Fig. 8 g is the spectrogram of 8d;

Fig. 9 be one embodiment of the invention with the low-resolution image of the width of cloth 128X128 in the lower left corner 512X512 image with SSTI method high resolution restoration;

Figure 10 is the module diagram of the low-frequency spectra data padding method image-taking system of one embodiment of the invention.

Embodiment

For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, the present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.

Embodiment one

As shown in Figure 1a, the invention provides a kind of low-frequency spectra data padding method image acquiring method comprises:

Step S1 obtains horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtains the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image.

Preferably, among the described step S1, a width of cloth low-resolution image g _l(i, j), i, j=0,1 ..., l will reset into high-definition picture g (i, j), i, and j=0,1 ..., N, N＞＞l, the frequency spectrum data of g (i, j) image is expressed as G (k _x, k _y), concrete G (k _x, k _y) can comprise low-frequency spectra data and high frequency spectrum data, k _x, k _y∈ Ω, Ω are the spectrum space of described high-definition picture, and l represents horizontal or vertical pixel number of low-resolution image, and N represents horizontal or vertical pixel number of the high-definition picture of parked, and the frequency spectrum data of low-resolution image is expressed as G _l(k _x, k _y),

Then the low-frequency spectra data of g (i, j) image are expressed as

G (k _x, k _y)=(N/l) ²G _l(k _x, k _y) ,-l/2≤k _x, k _y＜l/2, concrete, horizontal or vertical pixel number of every width of cloth image is equal, and the pixel number of every width of cloth image is the vertical pixel number of pixels across point number X, such as 256X256,512X512, i.e. l ²Or N ²

Step S2 is according to the zero padding method frequency spectrum data of the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture.

Preferably, among the step S2, the zero padding method frequency spectrum data of described high-definition picture is expressed as G (k _x, k _y) P (k _x, k _y), wherein,

Concrete, as shown in Figure 2, low-frequency spectra data in the zero padding method frequency spectrum data of the high-definition picture of the parked of the 512X512 (b) come from the frequency spectrum data of the low-resolution image of the 256X256 of (a) among Fig. 2, the zero zero padding frequency spectrum data of filling up of the high frequency spectrum data division in the zero padding method frequency spectrum data of high-definition picture.

Step S3 makes Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture to described zero padding method frequency spectrum data.

Preferably, among the step S3, the low-frequency spectra data padding method image representation of described high-definition picture is

Follow-up high-definition picture restored method (unusual information theory frequency spectrum continuation method, can carry out step S4～step S7 according to the low-frequency spectra data padding method image that obtains described high-definition picture in SSIT):

Step S4 according to the best unusualization operator of described low-frequency spectra data padding method Image Acquisition, obtains singular function according to described unusualization of the best operator, obtains Singularity spectrum function according to described singular function.Concrete, every width of cloth image has its best unusualization operator, is low-resolution image even become, and best unusualization operator can not change.Unusualization operator determines Singularity spectrum function, and best unusualization operator can obtain the simplest unusual information mathematical model of image.

Preferably, shown in Fig. 1 b, among the step S4, comprise according to the step of the best unusualization operator of described low-frequency spectra data padding method Image Acquisition:

Step S41, initialization:

Wherein, " * " represents convolution, and δ (i, j) is two-dimentional Dirac function, and is concrete, as shown in Figure 2, (c) is the image of described low-frequency spectra data padding method image after by described unusualization of the best operator convolution

Step S42, remember four substantially unusualization operator be:

φ ₁(i,j)=φ _i,j-(i,j)=δ(i,j)-δ(i,j-1),φ ₂(i,j)=φ _i-,j-(i,j)=δ(i,j)-δ(i-1,j-1)，

φ ₃(i,j)=φ _i+,j-(i,j)=δ(i,j)-δ(i+1,j-1),φ ₄(i,j)=φ _i-,j(i,j)=δ(i,j)-δ(i-1,j)；

Step S43 carries out $I=\underset{i=\mathrm{1,2,3,4}}{\arg \max }\left\{{|{\mathrm{\&phi;}}_i(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)|}_1\right\},$ Judge whether ${|{\mathrm{\&phi;}}_I(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)|}_1<\mathrm{mx},$ If, then forward step S44 to, if not, namely

Then forward step S45 to.

Step S44 will ${\mathrm{\&phi;}}_I(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)$ Assignment is given

Namely ${\tilde{g}}_{\mathrm{\&phi;}}(i,j)\&DoubleLeftArrow;{\mathrm{\&phi;}}_I(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j),$ And with φ (i, j) * φ _I(i, j) assignment to φ (i, j) namely

After, forward step S43 to.

Step S45 exports best unusualization operator φ (i, j).

Preferably, among the step S4, the step of obtaining singular function according to described unusualization of the best operator comprises:

According to difference equation φ (i, j) * h (i, j)=δ (i, the solution of zero condition j) is obtained singular function h (i, j), concrete, " * " represents convolution, δ (i, j) be two-dimentional Dirac function, if best unusualization operator is regarded as system, singular function h (i then, j) be the unit impulse response of best unusualization operator φ (i, j).

Preferably, among the step S4, obtain according to described singular function in the step of Singularity spectrum function, Singularity spectrum function is Concrete, according to the Singularity spectrum function H (k of unusualization of the best operator φ (i, j) generation _x, k _y), so that unusual information mathematical model parameter is as far as possible few

$G(k_x,k_y)=\underset{c=1}{\overset{q}{\mathrm{\&Sigma;}}}{a}_c{e}^{-\frac{2\mathrm{\&pi;}}{N}(k_x{i}_c+k_y{j}_c)\sqrt{-1}}H(k_x,k_y),k_x,k_y\&Element;\mathrm{\&Omega;,}$

H (k wherein _x, k _y) be called Singularity spectrum function, (a _c, i _c, j _c), c=1,2 ..., q is for treating rational method, q＜＜N ²Be quantity of information, require as far as possible little; Ω is the high-definition picture spectrum space, and singular function h (i, j) is the original function of Singularity spectrum function,

Step S5 obtains the coordinate parameters that high-definition picture restores according to described unusualization of the best operator and operating point spread function chromatography.Concrete, point spread function is defined as Wherein,

Here k _x, k _yThe spectrum space point that expression can be estimated from described low-resolution image.

Preferably, shown in Fig. 1 c, step S5 comprises:

Step S51, initialization: c=1,

Step S52, calculate: $(i_c,j_c)=\arg \underset{i,j\&Element;\mathrm{1,2},...,N}{\max }\left\{\right|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)\left|\right\},$ $b={\tilde{g}}_{\mathrm{\&phi;}}(i_c,j_c)/p\left(\mathrm{0,0}\right),$ Will ${\tilde{g}}_{\mathrm{\&phi;}}(i,j)-\mathrm{bp}(i-i_c,j-j_c)$ Assignment is given Namely ${\tilde{g}}_{\mathrm{\&phi;}}(i,j)\&DoubleLeftArrow;{\tilde{g}}_{\mathrm{\&phi;}}(i,j)-\mathrm{bp}(i-i_c,j-j_c),c=c+1,$ Wherein, (i _c, j _c) represent described coordinate parameters, c=1,2 ..., q, described coordinate parameters are nonzero coordinates, the set of described coordinate parameters is χ={ (i ₁, j ₁), (i ₂, j ₂) ..., (i _q, j _q);

Step S53 judges whether ${\left|\right|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)\left|\right|}_2\&NotEqual;{\left|\right|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)-\mathrm{bp}(i-i_c,j-j_c)\left|\right|}_2,$ Wherein, || || ₂Expression secondary norm, if, then forward step S52 to, if not, namely

Then forward step S54 to;

Step S54, q=c, output coordinate parameter { (i _c, j _c), c=1,2 ..., q }.

Step S6 obtains the weighting parameters that high-definition picture restores according to described Singularity spectrum function and described coordinate parameters.

Preferably, among the step S6, construct unusual information mathematical model according to the analytical continuation theorem $G(k_x,k_y)=\underset{c=1}{\overset{q}{\mathrm{\&Sigma;}}}{a}_c{e}^{-\frac{2\mathrm{\&pi;}}{N}(k_x{i}_c+k_y{j}_c)\sqrt{-1}}H(k_x,k_y),P(k_x,k_y)=0,$ Wherein, e=2.718281828459;

Obtain the weighting parameters a that high-definition picture restores with the pseudo inverse matrix method _c, c=1,2 ..., q, concrete, weighting parameters a _c, c=1,2 ..., q is function

In nonzero value.

Step S7, obtain the high frequency spectrum data of described high-definition picture according to described weighting parameters and Singularity spectrum function, according to low-frequency spectra data and the high frequency spectrum data acquisition complete frequency spectrum data of described high-definition picture, and export described high-definition picture according to described complete frequency spectrum data.

Preferably, among the step S7, obtain the high frequency spectrum data of described high-definition picture according to described weighting parameters and Singularity spectrum function, comprise according to the low-frequency spectra data of described high-definition picture and the step of high frequency spectrum data acquisition complete frequency spectrum data:

According to unusual information mathematical model $G(k_x,k_y)=\underset{c=1}{\overset{q}{\mathrm{\&Sigma;}}}{a}_c{e}^{-\frac{2\mathrm{\&pi;}}{N}(k_x{i}_c+k_y{j}_c)\sqrt{-1}}H(k_x,k_y),P(k_x,k_y)=0$ The high frequency spectrum data of the described high-definition picture of continuation, concrete, (d) among Fig. 2 is for to get unusual information coordinate parameters (i with the point spread function chromatography _c, j _c), and separate the unusual hum pattern that unusual information mathematical model obtains;

Low-frequency spectra data and the described complete frequency spectrum data of high frequency spectrum data acquisition G (k according to described high-definition picture _x, k _y).Concrete, (e) among Fig. 2 is the image of complete frequency spectrum data.

Preferably, among the step S7, export in the step of described high-definition picture according to described complete frequency spectrum data, according to described complete frequency spectrum data G (k _x, k _y) output described high-definition picture g (i, j),

Concrete, (f) among Fig. 2 is the high-definition picture of the 512X512 after restoring.

In more detail, be the validity of unusual information theory frequency spectrum continuation method (SSIT) for verifying high-definition picture restored method of the present invention, study with emulation experiment first, determine method validity.The emulation experiment scheme is: according to the mechanism of losing the high frequency spectrum component and cause low-resolution image, high frequency spectrum data beyond the cutoff frequency of high-definition picture are removed, obtain low-resolution image, then use sinc interpolation method, TV regularization method and the inventive method (SSIT) to carry out high-definition picture and restore.Emulation experiment is as follows:

Test one, investigate cutoff frequency to the impact of algorithm.

With the 256X256 size such as Fig. 3 a Chinese Shanghai Hongqiao Airport, the remote sensing images of tonal range (0～255) are with reference to image, get the cutoff frequency scope and be (32～96), generation is of a size of the low resolution image of 64x64～192x192, carries out high resolution restoration with sinc interpolation method, TV regularization method and SSIT method respectively.Each restored image with reference to the error peak signal to noise ratio (S/N ratio) of image shown in Fig. 3 b.On the whole, the error peak signal to noise ratio (S/N ratio) (PSNR) of the whole bag of tricks all improves and improves along with cutoff frequency (Cut Frequency), and the SSIT method is under various cutoff frequencys, and the superresolution restoration precision of images all is higher than sinc and TV method.The SSIT method is about 45 at cutoff frequency, and the PSNR value reaches more than the 30dB.

Fig. 4 is that the cutoff frequency of one embodiment of the invention is 64 high-definition picture recovery experimental principle figure, it is 64 o'clock at cutoff frequency, the 128X128 low-resolution image sees that (a) is the 128X128 low-resolution image among Fig. 4, the image that restores with Sinc, TV and SSIT method is image, (c) that the Sinc method restores such as (b) among Fig. 4 and is image that the TV method restores and (d) is shown in the image that the SSIT method restores, and their error peak signal to noise ratio (S/N ratio) is PSNR=32.2 decibel, 32.8 decibels and 33.6 decibels respectively.Although PSNR is more or less the same, image difference is comparatively obvious.The image ratio of Sinc method is fuzzyyer, can clearly find gibbs artifact on two airplanes side.The image of TV method has a small amount of pseudo-shadow.The image of SSIT method and the most approaching with reference to image does not almost have pseudo-shadow.The image of three kinds of methods can more easily be found out to each other difference with the error image of reference image respectively, be that Error Graph, (f) of (b) and Fig. 3 a among Fig. 4 is (c) among Fig. 4 with the Error Graph of Fig. 3 a and (g) be shown in the Error Graph of (d) and Fig. 3 a among Fig. 4 such as (e) among Fig. 4, the pseudo-shadow of Sinc method is remarkable, the TV method is taken second place, the pseudo-shadow of SSIT method is minimum, and the error range of demonstration is-31%～31%.

Experiment two, investigation noise affect restoration algorithm

In order to investigate noise to the impact of the high resolution restoration precision of the inventive method, the white Gaussian noise that reference image 3a is added zero-mean, mean square deviation is respectively 1～10, get cutoff frequency and be 64 low resolution 128X128 image, carry out high resolution restoration with Sinc interpolation, TV regularization and SSIT method respectively, and respectively behind Fig. 2 and the plus noise image the results are shown in Figure 5a and 5b as with reference to image calculation reset error peak noise ratio.Three kinds of methods are along with the increase of noise (Noise Level), with all downtrendings of PSNR value, (a) that compares in Fig. 2 is slower as the PSNR with reference to image descends, and that is to say the image before restored image is closer to plus noise, illustrates that three kinds of methods all have the denoising effect.PSNR increases along with noise and descends, and the details of image that meaned noise corrupted affects the recovery accuracy of three kinds of methods.Under noise situations at different levels, the PSNR of SSIT method always is higher than Sinc and TV method, and from quantitative target PSNR, the recovery accuracy of SSIT method is better than Sinc and TV method.

Also can find out from image spectrum figure, the SSIT method has higher recovery accuracy than Sinc and TV method.Fig. 6 a, 6b, 6c and 6d are respectively under 10 grades of noises, add noise with reference to the spectrogram of image, the spectrogram of Sinc method restored image, the spectrogram of TV method restored image and the spectrogram of SSIT method restored image.Among Fig. 6 b, the spectrogram of Sinc method restored image is not observed the high fdrequency component beyond the cutoff frequency, illustrates that the Sinc interpolation resets into to be of a size of the 256X256 image, does not increase any high-frequency information, i.e. image detail to image.Among Fig. 6 c, the spectrogram of TV method restored image has the partial frequency spectrum component beyond cutoff frequency, seem seldom with external spectrum but compare cutoff frequency with the spectrogram of reference image, and error is very large.Among Fig. 6 d, the spectrogram that SSIT restores at cutoff frequency with external spectrum and cutoff frequency with interior frequency spectrum all and quite approaching with reference to the spectrogram of image illustrate that the image of correspondence is also approaching with the reference image.This has also illustrated that from the frequency spectrum angle precision of SSIT method is higher than TV and Sinc method.

Experiment three, image under consideration structure are on the impact of algorithm.

Be the impact on restoration algorithm of image under consideration structure, intensity profile characteristic, we select Fig. 7 a, 7b, 7c, 7d, 7e and 7f is with reference to image, size all is 256X256, respectively take cutoff frequency as 64, generate low resolution 128X128 image, then carry out high resolution restoration with sinc interpolation, TV regularization and SSIT method respectively, and will restore after image respectively with Fig. 7 a, 7b, 7c, 7d, 7e and 7f error of calculation Y-PSNR PSNR, the results are shown in following table:

Picture numbers	a	b	c	d	e	f
							Sinc	34.0	33.4	30.1	32.2	29.1	27.1
TV	34.4	34.3	29.9	32.8	29.3	27.8
							SSIT	34.7	35.5	31.4	33.6	29.7	28.2

According to upper table, can draw the ability that the Sinc method is not restored high fdrequency component, obtain the image of high PSNR with the Sinc method, the high fdrequency component of key diagram picture own is less.Six width of cloth are pressed 7a, 7b, 7d, 7c, 7e and 7f with reference to the high fdrequency component in the image as can be seen from the above table increases sequentially successively.The TV method has improved PSNR to 7a, 7b, 7d, 7e and 7f with reference to the recovery of image, has improved picture quality, but 7c has been reduced PSNR with reference to image restoration, illustrates that the TV method can lead not as the Sinc interpolation the image of some structure.The SSIT method has preferably restored image high fdrequency component in various picture structure situations.

Experiment four, the experiment of actual high resolution restoration

One, two and three emulation experiment has checked the SSIT method can restore high frequency spectrum by experiment.This experiment is directly got the lower left corner of two width of cloth such as Fig. 9 a and the 128X128 image of 8a from Fig. 3 a), is 64 low-frequency spectra data as the cutoff frequency of 256 restored images with its frequency spectrum, then resets into the 256X256 image with Sinc, TV and SSIT method respectively.The image that restores and spectrogram thereof respectively Fig. 9 except the lower left corner image and Fig. 8 with shown in.Such as Fig. 8 b, the image that the Sinc method is restored has pseudo-shadow, and such as Fig. 8 c, the image of TV method also has a little pseudo-shadow, and such as Fig. 8 d, the image of SSIT method does not almost have pseudo-shadow.The result of this and emulation experiment one is consistent.Spectrogram 8e, 8f and 8g from three kinds of methods, the image that also is the Sinc method only has the following low-frequency spectra of cutoff frequency, the image of TV method has a little frequency spectrum beyond cutoff frequency, only have the Frequency spectrum ratio of image beyond the cut-off frequency spectrum of SSIT method abundanter, cutoff frequency is with consistent on the interior spectrum distribution form, can find out on the form frequency spectrum beyond the cutoff frequency be cutoff frequency with the continuation of interior frequency spectrum, illustrate that the SSIT method just really restored in addition high fdrequency component of cutoff frequency.In Fig. 9, can find similar results equally.This experimental result shows that low resolution image frequency spectrum can be regarded as the low-frequency spectra of full resolution pricture, can continuation go out the high frequency spectrum of high-definition picture with these a little low-frequency spectras, thereby reach oversubscription image restoration.

SSIT is a kind of effective high resolution restoration new method.Experimental result shows: the recovery accuracy of SSIT is under various cutoff frequencys, and under the various noise situations and under the various picture structures, the SSIT method all has higher precision than the restored image of Sinc and TV method.But SSIT and Sinc, TV method are the same, and its recovery accuracy increases with the loss of low-resolution image high-frequency information and reduces, and increase with the noise of low-resolution image and fall.The former be because cutoff frequency beyond high-frequency information lose too much, the latter be because of noise corrupted the high-frequency information of image so that the unusual information of image is difficult to accurate detection, thereby cause SSIT method restored image precise decreasing.Experimental result shows that low resolution image frequency spectrum can be regarded as the low-frequency spectra of full resolution pricture, can continuation go out the high frequency spectrum of high-definition picture with these a little low-frequency spectras, thereby reach oversubscription image restoration.

Embodiment two

As shown in figure 10, the present invention also provides another kind of low-frequency spectra data padding method image-taking system, comprises low-frequency spectra data module 1, zero padding method frequency spectrum data module 2, zero padding method image module 3.

Low-frequency spectra data module 1 is used for obtaining horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtains the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image.

Preferably, described low-frequency spectra data module 1 is used for a width of cloth low-resolution image is expressed as g _l(i, j), i, j=0,1 ..., l will reset into high-definition picture and be expressed as g (i, j), i, and j=0,1 ..., N, N＞＞l, the frequency spectrum data of g (i, j) image is expressed as G (k _x, k _y), k _x, k _y∈ Ω, Ω are the spectrum space of described high-definition picture, and l represents horizontal or vertical pixel number of low-resolution image, and N represents horizontal or vertical pixel number of the high-definition picture of parked, and the frequency spectrum data of low-resolution image is expressed as G _l(k _x, k _y), Then the low-frequency spectra data of g (i, j) image are expressed as

G(k _x,k _y)=(N/l) ²G _l(k _x,k _y)，-l/2≤k _x,k _y<l/2。

Preferably, zero padding method frequency spectrum data module 2 is used for the zero padding method frequency spectrum data according to the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture.

Described zero padding method frequency spectrum data module is expressed as G (k with the zero padding method frequency spectrum data of described high-definition picture _x, k _y) P (k _x, k _y), wherein,

Zero padding method image module 3 is used for described zero padding method frequency spectrum data is made Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture.

Preferably, described zero padding method image module 3 with the low-frequency spectra data padding method image representation of described high-definition picture is

A follow-up Singularity spectrum function module 4, can utilize that zero padding method image module 3 generates according to the best unusualization operator of described low-frequency spectra data padding method Image Acquisition, obtain singular function according to described unusualization of the best operator, obtain Singularity spectrum function according to described singular function.

Preferably, described Singularity spectrum function module 4 is used for

Initialization:

Wherein, " * " represents convolution, and δ (i, j) is two-dimentional Dirac function;

Remember four substantially unusualization operator be:

φ ₁(i,j)=φ _i,j-(i,j)=δ(i,j)-δ(i,j-1),φ ₂(i,j)=φ _i-,j-(i,j)=δ(i,j)-δ(i-1,j-1)，

φ ₃(i,j)=φ _i+,j-(i,j)=δ(i,j)-δ(i+1,j-1),φ ₄(i,j)=φ _i-,j(i,j)=δ(i,j)-δ(i-1,j)；

Carry out $I=\underset{i=\mathrm{1,2,3,4}}{\arg \max }\left\{{|{\mathrm{\&phi;}}_i(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)|}_1\right\},$ Judge whether ${|{\mathrm{\&phi;}}_I(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)|}_1<\mathrm{mx},$

If then will Assignment is given ${\tilde{g}}_{\mathrm{\&phi;}}(i,j),\mathrm{mx}={\left|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)\right|}_1,$ And with φ (i, j) * φ _I(i, j) assignment to φ (i, j) after, repeat described execution $I=\underset{i=\mathrm{1,2,3,4}}{\arg \max }\left\{{|{\mathrm{\&phi;}}_i(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)|}_1\right\}$ With judge whether ${|{\mathrm{\&phi;}}_I(i,j)*{\tilde{g}}_{\mathrm{\&phi;}}(i,j)|}_1<\mathrm{mx}$ Step;

If not, then export best unusualization operator φ (i, j).

Preferably, described Singularity spectrum function module 4 is obtained singular function h (i, j) according to the solution of the zero condition of difference equation φ (i, j) * h (i, j)=δ (i, j).

Preferably, described Singularity spectrum function module 4 bases

Obtain Singularity spectrum function.

One coordinate parameters module 5 is used for obtaining the coordinate parameters that high-definition picture restores according to described unusualization of the best operator and operating point spread function chromatography.

Preferably, described coordinate parameters module 5 is used for

Initialization: c=1,

Calculate: $(i_c,j_c)=\arg \underset{i,j\&Element;\mathrm{1,2},...,N}{\max }\left\{\right|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)\left|\right\},b={\tilde{g}}_{\mathrm{\&phi;}}(i_c,j_c)/p\left(\mathrm{0,0}\right),$ Will ${\tilde{g}}_{\mathrm{\&phi;}}(i,j)-\mathrm{bp}(i-i_c,j-j_c)$ Assignment is given

(i wherein _c, j _c) represent described coordinate parameters, c=1,2 ..., q, described coordinate parameters are nonzero coordinates;

Judge whether ${\left|\right|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)\left|\right|}_2\&NotEqual;{\left|\right|{\tilde{g}}_{\mathrm{\&phi;}}(i,j)-\mathrm{bp}(i-i_c,j-j_c)\left|\right|}_2,$ Wherein, || || ₂Expression secondary norm,

If then repeat the step of described calculating;

If not, q=c then, output coordinate parameter { (i _c, j _c), c=1,2 ..., q }.

One weighting parameters module 6 is used for obtaining the weighting parameters that high-definition picture restores according to described Singularity spectrum function and described coordinate parameters.

Preferably, described weighting parameters module 6 is used for constructing unusual information mathematical model according to the analytical continuation theorem $G(k_x,k_y)=\underset{c=1}{\overset{q}{\mathrm{\&Sigma;}}}{a}_c{e}^{-\frac{2\mathrm{\&pi;}}{N}(k_x{i}_c+k_y{j}_c)\sqrt{-1}}H(k_x,k_y),P(k_x,k_y)=0,$ Wherein,

e=2.718281828459；

Obtain the weighting parameters a that high-definition picture restores with the pseudo inverse matrix method _c, c=1,2 ..., q.

One restoration module 7, be used for obtaining according to described weighting parameters and Singularity spectrum function the high frequency spectrum data of described high-definition picture, according to low-frequency spectra data and the high frequency spectrum data acquisition complete frequency spectrum data of described high-definition picture, and export described high-definition picture according to described complete frequency spectrum data.

Preferably, described restoration module 7 is used for according to unusual information mathematical model $G(k_x,k_y)=\underset{c=1}{\overset{q}{\mathrm{\&Sigma;}}}{a}_c{e}^{-\frac{2\mathrm{\&pi;}}{N}(k_x{i}_c+k_y{j}_c)\sqrt{-1}}H(k_x,k_y),P(k_x,k_y)=0$ The high frequency spectrum data of the described high-definition picture of continuation;

Low-frequency spectra data and the described complete frequency spectrum data of high frequency spectrum data acquisition G (k according to described high-definition picture _x, k _y);

According to described complete frequency spectrum data G (k _x, k _y) output described high-definition picture g (i, j),

The detailed content of embodiment two specifically can be with reference to the counterpart among the embodiment one.

Each embodiment adopts the mode of going forward one by one to describe in this instructions, and what each embodiment stressed is and the difference of other embodiment that identical similar part is mutually referring to getting final product between each embodiment.For the disclosed system of embodiment, because corresponding with the disclosed method of embodiment, so description is fairly simple, relevant part partly illustrates referring to method and gets final product.

The professional can also further recognize, unit and the algorithm steps of each example of describing in conjunction with embodiment disclosed herein, can realize with electronic hardware, computer software or the combination of the two, for the interchangeability of hardware and software clearly is described, composition and the step of each example described in general manner according to function in the above description.These functions are carried out with hardware or software mode actually, depend on application-specific and the design constraint of technical scheme.The professional and technical personnel can specifically should be used for realizing described function with distinct methods to each, but this realization should not thought and exceeds scope of the present invention.

Obviously, those skilled in the art can carry out various changes and modification to invention and not break away from the spirit and scope of the present invention.Like this, if of the present invention these revise and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these change and modification.

Claims (8)

1. a low-frequency spectra data padding method image acquiring method is characterized in that, comprising:

Obtain horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtain the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image;

Zero padding method frequency spectrum data according to the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture;

Described zero padding method frequency spectrum data is made Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture.

2. low-frequency spectra data padding method image acquiring method as claimed in claim 1, it is characterized in that, obtain horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtain according to described pixel number and low-resolution image in the step of low-frequency spectra data of described high-definition picture

One width of cloth low-resolution image g _l(i, j), i, j=0,1 ..., l will reset into high-definition picture g (i, j), i, and j=0,1 ..., N, N＞＞l, the frequency spectrum data of g (i, j) image is expressed as G (k _x, k _y), k _x, k _y∈ Ω, Ω are the spectrum space of described high-definition picture, and l represents horizontal or vertical pixel number of low-resolution image, and N represents horizontal or vertical pixel number of the high-definition picture of parked, and the frequency spectrum data of low-resolution image is expressed as G _l(k _x, k _y),

Then the low-frequency spectra data of g (i, j) image are expressed as

G(k _x,k _y)=(N/l) ²G _l(k _x,k _y)，-l/2≤k _x,k _y<l/2。

3. low-frequency spectra data padding method image acquiring method as claimed in claim 2 is characterized in that, in the step according to the zero padding method frequency spectrum data of the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture,

The zero padding method frequency spectrum data of described high-definition picture is expressed as G (k _x, k _y) P (k _x, k _y), wherein,

4. low-frequency spectra data padding method image acquiring method as claimed in claim 3 is characterized in that, described zero padding method frequency spectrum data is done in the step of Fourier transform with the low-frequency spectra data padding method image that obtains high-definition picture,

The low-frequency spectra data padding method image representation of described high-definition picture is

5. a low-frequency spectra data padding method image-taking system is characterized in that, comprising:

The low-frequency spectra data module is used for obtaining horizontal or vertical pixel number and a width of cloth low-resolution image of the high-definition picture of parked, obtains the low-frequency spectra data of described high-definition picture according to described pixel number and low-resolution image;

Zero padding method frequency spectrum data module is used for the zero padding method frequency spectrum data according to the described high-definition picture of low-frequency spectra data acquisition of described high-definition picture;

Zero padding method image module is used for described zero padding method frequency spectrum data is made Fourier transform to obtain the low-frequency spectra data padding method image of high-definition picture.

6. low-frequency spectra data padding method image-taking system as claimed in claim 5 is characterized in that, described low-frequency spectra data module is used for a width of cloth low-resolution image is expressed as g _l(i, j), i, j=0,1 ..., l will reset into high-definition picture and be expressed as g (i, j), i, and j=0,1 ..., N, N＞＞l, the frequency spectrum data of g (i, j) image is expressed as G (k _x, k _y), k _x, k _y∈ Ω, Ω are the spectrum space of described high-definition picture, l ²Horizontal or vertical pixel number of expression low-resolution image, N ²Horizontal or vertical pixel number of the high-definition picture of expression parked, the frequency spectrum data of low-resolution image is expressed as

Then the low-frequency spectra data of g (i, j) image are expressed as

G(k _x,k _y)=(N/l) ²G _l(k _x,k _y)，-l/2≤k _x,k _y<l/2。

7. low-frequency spectra data padding method image-taking system as claimed in claim 6 is characterized in that, described zero padding method frequency spectrum data module is expressed as G (k with the zero padding method frequency spectrum data of described high-definition picture _x, k _y) P (k _x, k _y), wherein,

8. low-frequency spectra data padding method image-taking system as claimed in claim 7 is characterized in that, described zero padding method image module with the low-frequency spectra data padding method image representation of described high-definition picture is

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