CN103208098B - The Singularity spectrum function acquisition methods of high-definition picture restoration and system - Google Patents

Abstract

The invention provides a singular spectral function acquisition method and system for high-resolution image restoration. The method includes: obtaining the number of horizontal or vertical pixels of the high-resolution image and a low-resolution image, and obtaining low-frequency spectrum data of the high-resolution image according to the number of pixels and the low-resolution image; Obtain the zero-padding method spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image; perform Fourier transform on the zero-padding method spectral data to obtain the low-frequency spectral data of the high-resolution image. method image; obtain the best singularization operator according to the low frequency spectrum data zero padding method image, obtain the singular function according to the best singularization operator, obtain the singular spectrum function according to the singular function, and can obtain the singular spectrum function in the high frequency spectrum data In case of absence, the singular spectral function of high-resolution image restoration can be quickly and efficiently obtained for high-resolution image restoration.

Description

Singular spectral function acquisition method and system for high-resolution image restoration

technical field

The invention relates to a singular spectral function acquisition method and system for high-resolution image restoration.

Background technique

Satellite remote sensing has unique advantages such as large coverage, long duration, strong real-time performance, and is not restricted by national boundaries and regions. It is widely used in resource development, environmental monitoring, disaster research, and global change analysis. The spatial resolution of satellite imagery is a major index to measure satellite remote sensing capabilities, and it is also an important symbol to measure a country's space remote sensing level. Improving the spatial resolution of satellite observation has become a research hotspot in satellite engineering technology. There are many factors that will lead to the degradation of image quality in the process of satellite acquisition of images. Atmospheric disturbance, motion, defocus, transmission and noise will directly affect the degradation of image resolution, especially the limitation of satellite cut-off load, which makes the cut-off frequency of optical system limited and high. , and its CCD chip pixel size is limited and small, which limits the spatial high-frequency components of satellite images, making the image resolution not high enough.

According to the optical Fourier spectrum theory, the optical system has a cutoff frequency c _f =(Dl)/(2fλ), where D is the equivalent lens diameter, l is the CCD chip size, f is the lens focal length and λ is the light wavelength. If the pixel size of the CCD chip is w, then according to the sampling theorem, there is also a cutoff frequency u _w =1/(2w). Among the subjects, only the spatial frequency components smaller than u _w and c _f can be acquired and imaged. If c _f ≠ u _w , it will lead to waste of sampling resources or optical imaging resources. Assuming that the distance between the satellite and the subject is R, the resolvable distance of the satellite image is Δx=wR/f=λR/(Dl). If the pixel size of the CCD chip is reduced and u _w is increased, and the optical cut-off frequency is also increased c _f =u _w , the spatial resolution of the image can be improved (currently the minimum value is 50μm ² ), but the pixel size of the CCD chip w Too small and the signal-to-noise ratio is too low to be useful. Therefore, the lack of high-frequency components in satellite images is an unavoidable scientific problem. Traditional high resolution (reference 1: JLHarris, Diffraction and resolving power, J.Opt.Soc.Amer., 54(7):931-133, 1964 and literature 2: W.Lukosz, Optical systems with resolving power exceeding the classicallimit.J.Opt.Soc.Amer.,56(11):1463-1471,1966) refers to recovering the lost image high-frequency information beyond the cut-off frequency c _f of the optical system, this method is called high Resolution Restoration Technology. Most consider it impossible to accurately recover spectral information beyond the cutoff frequency and call this the high-resolution myth.

When multiple image sequences of the same scene can be obtained, a mathematical model can be established: g _i =Hs _i +n _i , i=1,2,...,k, where g _i , s _i , and _ni respectively represent the first i frames of low-resolution images, high-resolution images and noise images, H represents various factors that lead to low-resolution images. Through the multi-frame interpolation method (see Document 3: L. Zhang, X. Wu, An Edge-Guided Image Interpolation Algorithm via Directional Filtering and DataFusion, 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, Literature 5: A.Sánchez-Beato and G.Pajares, Non-iterative interpolation-based super-resolutionminimizing aliasing in the reconstructed image, IEEE Trans. Image Process., 17(10), pp.1817–1826, 2008, Document 6: S. Lertratanapanich, NKBOSE, High resolution image formation from low resolution frames using Delaunay triangulation, IEEE Transaction on Image Processing, 11(12):1427-1441, 2002 and literature 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), using prior knowledge to optimize the solution (see literature 8: X.Gao, K.Zhang, D.Tao and X.Li, Image Super-Resolution WithSparse Neighbor Embedding, I IEEE Trans.on Image Processing, Vol.21, No.7, pp.3194-3205, 2012, Document 9: Z MWang and WWWang, Fast and Adaptive Method for SAR Superresolution Imaging Based on Point Scattering Model and Optimal BasisSelection, IEEE Tran. on Image Processing, 18(7):1477-1486, 2009, Literature 10: A.Marquina and SJOsher, Image super- resolution by TV regularization and Bregman iteration, Journal of Scientific Computing, vol.37, no.3, pp.367–382, 2008 and literature 11: J.Yang, J.Wright, TSHuang and Y.Ma, "Image super-resolution viasparse representation, "IEEE Trans.Image Process., vol.19, no.11, pp.2861–2873, 2010), based on learning methods (see literature 11, literature 12: T.Goto, Y.Kawamoto, Y.Sakuta ,A.Tsutsui andM.Sakurai,Learning-based Super-resolution Image Reconstruction on Multi-coreProcessor,IEEE Transactions on Consumer Electronics,58(3):941～946,2012, Literature 13:P.Purkait and B.Chanda,Super Resolution Image Reconstruction Through Bregman Iteration Using Morphologic Regularization, IEEE Trans. on Image Processing, 21(9):4029～4040, 2012, Document 14: PPGajjar and MVJoshi, New learningbased super-resolution: Use of DWT and IGMR-F prior, IEEE Trans .on Image Processing, Vol.19, No.5, pp.120 1-1213, 2010, Literature 15: MS Crouse, RDNowak, R.GBaraniuk, Wavelet-based statistical signal processing using hidden Markovmodels, IEEE Transactions on Signal Processing, 46(4):886-902, 1998 and Literature 16: M NDo, M. Vetterli, The contourlet transform: An efficient directional multi-resolution image representation, IEEE Transactions on Image Processing, 14(12): 2091-2106, 2005) and so on (see literature 17: DD-Y Po and DO MNDo, Directional multi-scale modeling of images using the contourlet transform, IEEE Transactions on Image Processing, 15(6):1610-1620, 2006 and Literature 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) to obtain high-resolution images and improve image quality degradation caused by undersampling. However, in satellite observation and photography, multi-frame image acquisition in the same field of view is extremely wasteful of resources and difficult to achieve. Single-frame image super-resolution restoration technology is the key technology for remote sensing image super-resolution restoration, but there has been no substantial breakthrough so far. In order to study the high-resolution restoration of a single frame image, we consider the following mathematical model of the formation mechanism of a low-resolution image.

If the interference factors are not considered, the imaging process of an imaging system can be described as follows:

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

Here g(x, y), p(x, y), s(x, y) represent remote sensing image, field of view and point spread function of imaging system respectively, and * represents convolution operation. The spectrum function of the image is: G(u,v)=P(u,v)S(u,v), the spectrum function of the point spread function P(u,v)=1, |u|<c _f &|v |<c _f is a rectangular window with limited bandwidth. When the cut-off frequency c _s of the actual field of view is greater than the cut-off frequency c _f of the optical imaging system, the high-frequency components other than c _f of the field of view are lost and become a low-resolution image. It is traditionally believed that the c _f spectrum cannot be recovered outside the cutoff frequency of the optical imaging system. But according to the analytic continuation theorem: if the analytic is known on a certain finite interval, it can be uniquely extended to all regions. That is to say, "if two analytic functions are completely consistent in any given area", they must be completely consistent as a whole" that is, the same function (see text 19: EBSaff and A.D. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science, 2003, Pearson Education). The field of view can be regarded as a function on a bounded domain, and its spectral function is an analytic function. Therefore, according to the analytic continuation theorem, the image spectrum data G(u, v)=P(u,v)S(u,v),|u|<c _f &|v|<c _f , extended to the entire spectrum space, cut-off frequency c _f =∞. Early research from a single frame image The main method for high-resolution restoration is spectrum extrapolation (see literature 20: H.Greenspan, CHAnderson, S.Akber, Image enhancement by nonlinear extrapolation in frequency space, IEEE Trans. Image Processing, vol.9, no 6, pp. 1035—1048, 2000), prolate ellipsoid wave function method (see literature 21: HABrown, Effect of Truncation on Image Enhancement by Prolate Spheroidal Functions, Journal of the Optical Society of America, Vol.59, no 2, pp.228-229 , 1969), superposition sinusoidal template method (see literature 22: S.Wadaks, T.Sato, Superresolution in Incoherent Imaging System, Journal of the Optical Society of America, 65(3):354-355, 1975), interpolation method ( See document 3) and other super-resolution restoration techniques. However, these methods make full use of the high-resolution information hidden in the low-resolution image, and do not understand and apply the mathematical principle of the analytic continuation theorem, so they cannot or rarely study the image from the low-resolution image The method of obtaining high-frequency information, so the effect is very limited (see literature 23: SCPark, MKPark, MGKang, Super-resolution image reconstruction: a technical overview, IEEESignal Processing Magazine, Vol.2 0, no. 3, pp. 21-36, May 2003).

Contents of the invention

The object of the present invention is to provide a singular spectral function acquisition method and system for high-resolution image restoration, which can quickly and efficiently obtain singular spectral functions for high-resolution image restoration in the absence of high-frequency spectrum data for high-resolution image restoration. Restoration of high-rate images.

In order to solve the above problems, the present invention provides a singular spectral function acquisition method for high-resolution image restoration, including:

Obtain the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtain low-frequency spectrum data of the high-resolution image according to the number of pixels and the low-resolution image;

Acquiring the zero-padding method spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image;

performing Fourier transform on the zero-padding method spectral data to obtain the low-frequency spectral data zero-padding method image of the high-resolution image;

The optimal singularization operator is obtained according to the zero-padding image of the low-frequency spectrum data, the singular function is obtained according to the optimal singularization operator, and the singular spectral function is obtained according to the singular function.

Further, in the above method, the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image are obtained, and the high-resolution image is obtained according to the number of pixels and the low-resolution image In the step of image low-frequency spectral data,

A low-resolution image g _l (i,j), i,j=0,1,...,l needs to be restored to a high-resolution image g(i,j),i,j=0,1,. ..,N,N>>l, the spectral data of the g(i,j) image is expressed as G(k _x , _ky ), k _x ,ky _∈Ω , Ω is the spectral space of the high-resolution image , l represents the number of horizontal or vertical pixels of the low-resolution image, N represents the number of horizontal or vertical pixels of the high-resolution image to be restored, and the spectral data of the low-resolution image is expressed as G _l (k _x , k _y ), in, represents the Fourier transform of g _l (i, j), then the spectrum data of the low frequency range of g (i, j) image - l/2≤k _x , k _y <l/2 is expressed as

(N/l) ² G _l (k _x , k _y ).

Further, in the above method, in the step of obtaining the zero-padding spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image,

The zero-padding method spectral data of the high-resolution image is expressed as G(k _x , k _y )P(k _x , k _y ), where,

Further, in the above method, in the step of performing Fourier transform on the zero-padding method spectral data to obtain the low-frequency spectral data zero-padding method image of the high-resolution image,

The low-frequency spectral data zero-filling method image of the high-resolution image is expressed as in, Represents the inverse Fourier transform of G(k _x , _ky )P(k _x , _ky ).

Further, in the above method, the step of obtaining the best singularization operator according to the zero-padding image of the low-frequency spectrum data includes:

initialization: φ(i,j)=δ(i,j), where, Among them, "*" means convolution, and δ(i, j) is a two-dimensional Dirac function;

The four basic singularization operators are recorded as:

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);

implement judge whether

If so, will assigned to After assigning φ(i,j)*φ _I (i,j) to φ(i,j), repeat the execution and judge whether A step of;

If not, output the best singularization operator φ(i,j).

Further, in the above method, the step of obtaining the singular function according to the optimal singularization operator includes:

The singular function h(i,j) is obtained from the solution of the zero state of the difference equation φ(i,j)*h(i,j)=δ(i,j).

Further, in the above method, in the step of obtaining the singular spectrum function according to the singular function, the singular spectrum function is

According to another aspect of the present invention, a singular spectral function acquisition system for high-resolution image restoration is provided, including:

The low-frequency spectrum data module is used to obtain the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtain the high-resolution image according to the number of pixels and the low-resolution image The low-frequency spectrum data of

A zero-padding spectral data module, configured to obtain the zero-padding spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image;

A zero-padding method image module is used to perform Fourier transform on the zero-padding method spectral data to obtain a low-frequency spectral data zero-padding method image of a high-resolution image;

The singular spectrum function module is configured to obtain an optimal singularization operator according to the zero-padding method image of the low-frequency spectrum data, obtain a singular function according to the optimal singularization operator, and obtain a singular spectral function according to the singular function.

Further, in the above system, the low-frequency spectrum data module is used to represent a low-resolution image as g _l (i,j), i,j=0,1,...,l, to be restored to The high-resolution image is expressed as g(i,j), i,j=0,1,...,N,N>>l, and the spectral data of the g(i,j) image is expressed as G(k _x ,k _y ), k _x , k _y ∈ Ω, Ω is the spectral space of the high-resolution image, l represents the horizontal or vertical pixel number of the low-resolution image, N represents the horizontal or vertical pixel number of the high-resolution image to be restored The number of vertical pixels, the spectrum data of the low-resolution image is expressed as G _l (k _x , k _y ), in, represents the Fourier transform of g _l (i, j), then the spectrum data of the low frequency range of g (i, j) image - l/2≤k _x , k _y <l/2 is expressed as

(N/l) ² G _l (k _x , k _y ).

Further, in the above system, the zero-padding spectral data module expresses the zero-padding spectral data of the high-resolution image as G(k _x , _ky )P(k _x , _ky ), wherein,

Further, in the above system, the zero-padding image module represents the low-frequency spectral data zero-padding image of the high-resolution image as in, Represents the inverse Fourier transform of G(k _x , _ky )P(k _x , _ky ).

Further, in the above system, the singular spectrum function module is used for

initialization: φ(i,j)=δ(i,j), Among them, "*" means convolution, and δ(i, j) is a two-dimensional Dirac function;

The four basic singularization operators are recorded as:

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);

implement judge whether

If so, will assigned to After assigning φ(i,j)*φ _I (i,j) to φ(i,j), repeat the execution and judge whether A step of;

If not, output the best singularization operator φ(i,j).

Further, in the above system, the singular spectrum function module obtains the singular function h(i,j) according to the solution of the zero state of the differential equation φ(i,j)*h(i,j)=δ(i,j) ).

Further, in the above system, the singular spectrum function module is based on Get the singular spectral function.

Compared with the prior art, the present invention obtains the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtains the high-resolution image according to the number of pixels and the low-resolution image. Low-frequency spectral data of the high-resolution image; obtaining zero-padding method spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image; performing Fourier transform on the zero-padding method spectral data to obtain high-resolution Low-frequency spectral data zero-padding method image of low-frequency spectral data; According to the low-frequency spectral data zero-padding method image, the best singularization operator is obtained, and the singular function is obtained according to the best singularization operator, and the singular spectrum is obtained according to the singular function The function can quickly and efficiently obtain the singular spectral function of high-resolution image restoration for high-resolution image restoration in the absence of high-frequency spectral data.

Description of drawings

Fig. 1a is a flowchart of high resolution image restoration according to an embodiment of the present invention;

Fig. 1b is a detailed flowchart of step S4 in Fig. 1a;

Fig. 1c is a detailed flowchart of step S5 in Fig. 1a;

Fig. 2 is a schematic diagram of a 256X256 low-resolution image restored to a 512X512 high-resolution image according to an embodiment of the present invention;

Figure 3a is a reference image for simulation according to an embodiment of the present invention;

Fig. 3b is a low-resolution image with a cutoff frequency of 32-96 according to an embodiment of the present invention, and the error peak signal-to-noise ratio of the image restored by Sinc interpolation, TV regularization and SSIT method;

Fig. 4 is a schematic diagram of a high-resolution image restoration experiment with a cutoff frequency of 64 according to an embodiment of the present invention;

Fig. 5a takes Fig. 3a as the reference image, and the peak signal-to-noise ratio of the restoration error changes with the noise size

Figure 5b takes the image after the noise is added as the reference image, and the peak signal-to-noise ratio of the restoration error varies with the size of the noise;

Fig. 6a is a spectrogram of a noise-added reference image according to an embodiment of the present invention;

Fig. 6 b is the spectrogram of the image restored by the Sinc method of an embodiment of the present invention;

Fig. 6c is a spectrum diagram of an image restored by the TV method according to an embodiment of the present invention;

Fig. 6d is a spectrum diagram of an image restored by the SSIT method according to an embodiment of the present invention;

Fig. 7a is the first reference image used for testing according to an embodiment of the present invention;

Fig. 7b is a second reference image used for testing according to an embodiment of the present invention;

Fig. 7c is a third reference image used for testing according to an embodiment of the present invention;

Fig. 7d is a fourth reference image used for testing according to an embodiment of the present invention;

Fig. 7e is a fifth reference image used for testing according to an embodiment of the present invention;

Fig. 7f is a sixth reference image used for testing according to an embodiment of the present invention;

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

Fig. 8b is a 256X256 image after high-resolution restoration by the Sinc method of an embodiment of the present invention;

Fig. 8c is a 256X256 image restored by the TV method in an embodiment of the present invention with high resolution;

Figure 8d is a 256X256 image restored by the SSIT method in an embodiment of the present invention with high resolution;

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

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

Figure 8g is a spectrogram of 8d;

Fig. 9 is a 512X512 image restored with a high resolution of a 128X128 low-resolution image in the lower left corner by the SSTI method according to an embodiment of the present invention;

FIG. 10 is a block diagram of an image acquisition system for low-frequency spectral data zero-padding method according to an embodiment of the present invention.

detailed description

In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, the present invention provides a singular spectral function acquisition method for high-resolution image restoration, including:

Embodiment one

As shown in Figure 1a, the present invention provides a singular spectral function acquisition method for high-resolution image restoration including:

Step S1, obtain the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtain the low-frequency spectrum data of the high-resolution image according to the number of pixels and the low-resolution image .

Preferably, in the step S1, a low-resolution image g _l (i,j), i,j=0,1,...,l is to be restored to a high-resolution image g(i,j), i,j=0,1,...,N,N>>l, the spectrum data of g(i,j) image is expressed as G(k _x , _ky ), the specific G(k _x , _ky ) can be Including low-frequency spectral data and high-frequency spectral data, k _x , _ky ∈ Ω, Ω is the spectral space of the high-resolution image, l represents the number of horizontal or vertical pixels of the low-resolution image, N represents the number of pixels to be restored The number of horizontal or vertical pixels of the high-resolution image, and the spectral data of the low-resolution image is expressed as G _l (k _x , k _y ), in, represents the Fourier transform of g _l (i, j), then the spectrum data of the low frequency range of g (i, j) image - l/2≤k _x , k _y <l/2 is expressed as

(N/l) ² G _l (k _x , k _y ), specifically, the number of horizontal or vertical pixels of each image is equal, and the number of pixels of each image is the number of horizontal pixels multiplied by the vertical pixels Number of points, such as 256 X 256, 512X512, namely l ² or N ² .

Step S2, acquiring zero-padding spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image.

Preferably, in step S2, the zero-padding spectral data of the high-resolution image is expressed as G(k _x , _ky )P(k _x , _ky ), where,

Specifically, as shown in Figure 2, the low-frequency spectrum data in the zero-padding method spectral data of the 512X512 high-resolution image to be restored in (b) comes from the low-resolution image of 256X256 in (a) in Figure 2 Spectral data, the zero-padding spectral data of the high-resolution image is the zero-padding spectral data in which the high-frequency spectral data part is filled with zeros.

Step S3, perform Fourier transform on the zero-padding method spectral data to obtain the zero-padding method image of the low-frequency spectral data of the high-resolution image.

Preferably, in step S3, the low-frequency spectral data zero-filling method image of the high-resolution image is expressed as in, Represents the inverse Fourier transform of G(k _x , _ky )P(k _x , _ky ).

Step S4, obtaining an optimal singularization operator according to the zero-padding image of the low-frequency spectrum data, obtaining a singular function according to the optimal singularization operator, and obtaining a singular spectral function according to the singular function. Specifically, each image has its optimal singularization operator, even if it becomes a low-resolution image, the optimal singularization operator will not change. The singularization operator determines the singular spectral function, and the optimal singularization operator can obtain the simplest singular information mathematical model of the image.

Preferably, as shown in Figure 1b, in step S4, the step of obtaining the best singularization operator according to the zero-padding image of the low-frequency spectrum data includes:

Step S41, initialization:

φ(i,j)=δ(i,j), Among them, "*" means convolution, and δ(i, j) is a two-dimensional Dirac function. Specifically, as shown in Figure 2, (c) is the zero-padding method for the low-frequency spectrum data. The image after the operator convolution

Step S42, record the four basic singularization operators as:

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, execute judge whether If so, then go to step S44, if not, that is Then go to step S45.

Step S44, will assigned to which is And assign φ(i,j)*φ _I (i,j) to φ(i,j) namely After that, go to step S43.

Step S45, outputting the best singularization operator φ(i,j).

Preferably, in step S4, the step of obtaining a singular function according to the optimal singularization operator includes:

Obtain the singular function h(i,j) according to the solution of the zero state of the differential equation φ(i,j)*h(i,j)=δ(i,j), specifically, "*" means convolution, δ( i,j) is a two-dimensional Dirac function, if the optimal singularization operator is regarded as a system, then the singular function h(i,j) is the unit impulse response of the optimal singularization operator φ(i,j) .

Preferably, in step S4, in the step of obtaining the singular spectrum function according to the singular function, the singular spectrum function is Specifically, according to the singular spectral function H(k _x , k _y ) generated by the optimal singularization operator φ(i,j), the parameters of the singular information mathematical model should be as few as possible

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>\sqrt{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}<span\; class="notranslate">\; ,</span>$

Among them, H(k _x , _ky ) is called singular spectral function, (a _c , i _c , j _c ), c=1,2,...,q are undetermined model parameters, and q<<N ² is the amount of information , which is required to be as small as possible; Ω is the high-resolution image spectrum space, and the singular function h(i,j) is the original function of the singular spectrum function,

In the subsequent high-resolution image restoration method (singular information theory spectrum extension method, SSIT), step S5 to step S7 may be performed according to the results obtained by the singular spectral function acquisition method of high-resolution image restoration.

Step S5, according to the optimal singularization operator and using the point spread function tomography method to obtain the coordinate parameters of the high-resolution image restoration. Specifically, the point spread function is defined as in, Here k _x , _ky denote spectral space points that can be estimated from said low resolution image.

Preferably, as shown in Figure 1c, step S5 includes:

Step S51, initialization: c=1,

Step S52, calculate: Will assigned to which is c=c+1, wherein, (i _c , j _c ) represent the coordinate parameters, c=1,2,...,q, the coordinate parameters are non-zero coordinates, and the set of the coordinate parameters is χ ={(i ₁ ,j ₁ ),(i ₂ ,j ₂ )...,(i _q ,j _q )};

Step S53, judging whether Wherein, ||·|| ₂ represents the quadratic norm, if so, then go to step S52, if not, namely Then go to step S54;

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

Step S6, obtaining weighted parameters for high-resolution image restoration according to the singular spectrum function and the coordinate parameters.

Preferably, in step S6, a singular information mathematical model is constructed according to the analytic continuation theorem

Among them, e=2.718281828459;

Obtain the weighted parameters a _c , c=1,2,...,q of high-resolution image restoration by using the pseudo-inverse matrix method. Specifically, the weighted parameters a _c , c=1,2,...,q are functions A non-zero value in .

Step S7, obtain the high-frequency spectrum data of the high-resolution image according to the weighting parameters and the singular spectrum function, obtain complete spectrum data according to the low-frequency spectrum data and high-frequency spectrum data of the high-resolution image, and obtain the complete spectrum data according to the The full spectral data outputs the high resolution image.

Preferably, in step S7, the high-frequency spectrum data of the high-resolution image is obtained according to the weighting parameter and the singular spectrum function, and the complete spectrum data of the high-resolution image is obtained according to the low-frequency spectrum data and high-frequency spectrum data of the high-resolution image Steps include:

According to the singular information mathematical model Continuation of the high-frequency spectrum data of the high-resolution image, specifically, (d) in Figure 2 is to use the point spread function tomography to obtain the singular information coordinate parameters ( _{ic, j c )} , and solve the singular information mathematical model The singular information map obtained;

The complete spectrum data G(k _x , _ky ) is obtained according to the low-frequency spectrum data and high-frequency spectrum data of the high-resolution image. Specifically, (e) in FIG. 2 is an image of complete spectrum data.

Preferably, in step S7, in the step of outputting the high-resolution image according to the complete spectral data, the high-resolution image g(i,j) is output according to the complete spectral data G(k _x , _ky ) ), Specifically, (f) in FIG. 2 is a restored 512×512 high-resolution image.

In more detail, in order to verify the effectiveness of the high-resolution image restoration method of the present invention, that is, the singular information theory spectrum continuation method (SSIT), a simulation experiment is firstly conducted to determine the effectiveness of the method. The simulation experiment plan is: according to the mechanism of losing high-frequency spectral components that lead to low-resolution images, remove the high-frequency spectral data other than the cut-off frequency of high-resolution images to obtain low-resolution images, and then use the sinc interpolation method and TV regularization Method and method of the present invention (SSIT) for high resolution image restoration. The simulation experiment is as follows:

Experiment 1. Investigate the influence of the cut-off frequency on the algorithm.

Using the 256X256 size of the Shanghai Hongqiao Airport in China as shown in Figure 3a, the remote sensing image in the gray range (0-255) is used as a reference image, and the cut-off frequency range is (32-96) to generate a low-resolution image with a size of 64x64-192x192, respectively High-resolution restoration is performed with sinc interpolation method, TV regularization method and SSIT method. The error peak signal-to-noise ratio of each restored image and the reference image is shown in Fig. 3b. In general, the error peak signal-to-noise ratio (PSNR) of various methods increases with the increase of the cut frequency (Cut Frequency). The SSIT method has higher super-resolution restoration image accuracy than the sinc and TV methods at various cut-off frequencies. . The SSIT method has a cutoff frequency of about 45, and the PSNR value has reached above 30dB.

Fig. 4 is a schematic diagram of a high-resolution image restoration experiment with a cutoff frequency of 64 in an embodiment of the present invention. When the cutoff frequency is 64, the 128X128 low-resolution image is shown in (a) in Fig. 4, which is a 128X128 low-resolution image. The images restored by the Sinc, TV and SSIT methods are shown in Figure 4 (b) is the image restored by the Sinc method, (c) is the image restored by the TV method and (d) is the image restored by the SSIT method, Their error peak signal-to-noise ratios are PSNR=32.2dB, 32.8dB and 33.6dB, respectively. Although the PSNR is similar, the image difference is more obvious. The Sinc method image is blurry, with truncation artifacts clearly visible next to the two aircraft. The image of the TV method has a small amount of artifacts. The image of the SSIT method is the closest to the reference image, with almost no artifacts. It is easier to see the difference between the images of the three methods and the error images of the reference image, as shown in Figure 4 (e) is the error map of Figure 4 (b) and Figure 3a, (f) is The error diagrams and (g) of (c) in Figure 4 and Figure 3a are shown in the error diagrams of (d) in Figure 4 and Figure 3a. The Sinc method has significant artifacts, followed by the TV method, and the SSIT method has the least artifacts , the displayed error range is -31% to 31%.

Experiment 2. Investigate the influence of noise on the restoration algorithm

In order to investigate the impact of noise on the high-resolution restoration accuracy of the method of the present invention, Gaussian white noise with zero mean is added to the reference image 3a, the mean square error is 1-10 respectively, and the low-resolution 128X128 image with a cut-off frequency of 64 is taken, and Sinc Interpolation, TV regularization, and SSIT methods were used for high-resolution restoration, and the peak-to-noise ratio of the restoration error was calculated using (a) in Figure 2 and the image after adding noise as reference images, respectively. The results are shown in Figures 5a and 5b. With the increase of the noise (Noise Level), the PSNR values of the three methods all decrease. Compared with the PSNR of the reference image (a) in Figure 2, the PSNR declines slowly, that is to say, the restored image is closer to that before the noise is added. The image shows that all three methods have denoising effect. PSNR decreases with the increase of noise, which means that the noise destroys the details of the image and affects the restoration accuracy of the three methods. In the case of various levels of noise, the PSNR of the SSIT method is always higher than that of the Sinc and TV methods. From the quantitative index PSNR, the restoration accuracy of the SSIT method is better than that of the Sinc and TV methods.

It can also be seen from the image spectrogram that the SSIT method has higher restoration accuracy than the Sinc and TV methods. Figures 6a, 6b, 6c, and 6d are the spectrograms of the noise-added reference image, the image restored by the Sinc method, the image restored by the TV method, and the image restored by the SSIT method, respectively, under 10 levels of noise. In Figure 6b, no high-frequency components other than the cut-off frequency are observed in the spectrum diagram of the image restored by the Sinc method, indicating that the Sinc interpolation restores an image with a size of 256X256, and does not add any high-frequency information to the image, that is, image details. In Fig. 6c, the spectrogram of the image restored by the TV method has some spectral components outside the cutoff frequency, but compared with the spectrogram of the reference image, the spectrum outside the cutoff frequency appears to be very small, and the error is large. In Fig. 6d, the spectrogram restored by SSIT is quite close to the spectrogram of the reference image outside the cutoff frequency and within the cutoff frequency, indicating that the corresponding image is also close to the reference image. This also shows that the accuracy of the SSIT method is higher than that of the TV and Sinc methods from the spectrum point of view.

Experiment 3. Investigate the influence of image structure on the algorithm.

In order to investigate the influence of image structure and gray distribution characteristics on the restoration algorithm, we choose Figures 7a, 7b, 7c, 7d, 7e and 7f as reference images, all of which are 256X256 in size, respectively, with a cutoff frequency of 64 to generate low-resolution 128X128 Image, and then use sinc interpolation, TV regularization and SSIT methods to perform high-resolution restoration, and calculate the peak signal-to-noise ratio PSNR of the restored image with Fig. 7a, 7b, 7c, 7d, 7e and 7f respectively. The results are shown below surface:

image number 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 the above table, it can be concluded that the Sinc method has no ability to restore high-frequency components. Using the Sinc method to obtain an image with high PSNR indicates that the image itself has less high-frequency components. It can be seen from the above table that the high frequency components in the six reference images increase sequentially according to 7a, 7b, 7d, 7c, 7e and 7f. The restoration of the reference images 7a, 7b, 7d, 7e and 7f by the TV method improves the PSNR and improves the image quality, but the restoration of the 7c reference image reduces the PSNR, indicating that the TV method will not be as good as the Sinc for certain structures. interpolation. The SSIT method can restore the high-frequency components of the image well under various image structures.

Experiment 4. Actual high-resolution restoration experiment

Through the simulation experiments of experiments 1, 2 and 3, it is verified that the SSIT method can restore high-frequency spectrum. In this experiment, two 128X128 images in the lower left corner of Figure 9 and 8a are taken directly from Figure 3a), and their spectra are used as low-frequency spectrum data with a cutoff frequency of 64 for 256 restored images, and then restored by Sinc, TV and SSIT methods respectively to a 256X256 image. The restored images and their spectrograms are shown in the images except the lower left corner of Figure 9 and Figures 8b, 8c, 8d, 8e, 8f, and 8g, respectively. As shown in Figure 8b, the image restored by the Sinc method has artifacts, as shown in Figure 8c, the image by the TV method also has a little artifact, and as shown in Figure 8d, the image by the SSIT method has almost no artifacts. This is consistent with the result of simulation experiment 1. From the spectrograms 8e, 8f and 8g of the three methods, the image of the Sinc method also has only low-frequency spectrum below the cutoff frequency, the image of the TV method has a little spectrum outside the cutoff frequency, and only the image of the SSIT method has a spectrum outside the cutoff frequency It is relatively rich, and the spectrum distribution within the cutoff frequency is consistent in form. From the morphology, it can be seen that the spectrum outside the cutoff frequency is an extension of the spectrum within the cutoff frequency, which shows that the SSIT method really restores the high frequency components outside the cutoff frequency. Similar results can also be found in Figure 9. This experimental result shows that the low-resolution image spectrum can be regarded as the low-frequency spectrum of the high-resolution image, and the high-frequency spectrum of the high-resolution image can be extended by using these low-frequency spectra, so as to achieve super-resolution image restoration.

SSIT is an effective new method for high-resolution restoration. The experimental results show that: the restoration accuracy of SSIT is higher than that of Sinc and TV methods under various cut-off frequencies, various noise conditions and various image structures. However, SSIT is the same as Sinc and TV methods, its restoration accuracy decreases with the increase of high-frequency information loss in low-resolution images, and decreases with the increase of noise in low-resolution images. The former is because too much high-frequency information is lost outside the cutoff frequency, and the latter is because the noise destroys the high-frequency information of the image, making it difficult to accurately detect the singular information of the image, which leads to a decrease in the accuracy of the image restored by the SSIT method. The experimental results show that the low-resolution image spectrum can be regarded as the low-frequency spectrum of the high-resolution image, and the high-frequency spectrum of the high-resolution image can be extended by using these low-frequency spectra, so as to achieve super-resolution image restoration.

Embodiment two

As shown in Figure 10, the present invention also provides another singular spectrum function acquisition system for high-resolution image restoration, including a low-frequency spectrum data module 1, a zero-padding method spectrum data module 2, a zero-padding method image module 3, and a singular spectrum function Module 4.

The low-frequency spectrum data module 1 is used to obtain the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtain the high-resolution image according to the number of pixels and the low-resolution image The low-frequency spectral data of the image.

Preferably, the low-frequency spectrum data module 1 is used to represent a low-resolution image as g _l (i, j), i, j=0, 1,..., l, to be restored to a high-resolution image Expressed as g(i,j), i,j=0,1,...,N,N>>l, the spectral data of g(i,j) image is expressed as G(k _x , _ky ), k _x , _ky ∈ Ω, Ω is the spectral space of the high-resolution image, l represents the number of horizontal or vertical pixels of the low-resolution image, and N represents the number of horizontal or vertical pixels of the high-resolution image to be restored number, the spectrum data of the low-resolution image is expressed as G _l (k _x , k _y ), in, represents the Fourier transform of g _l (i, j), then the spectrum data of the low frequency range of g (i, j) image - l/2≤k _x , k _y <l/2 is expressed as

(N/l) ² G _l (k _x , k _y ).

Preferably, the zero-padding spectral data module 2 is configured to acquire the zero-padding spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image.

The zero-padding spectral data module expresses the zero-padding spectral data of the high-resolution image as G(k _x , _ky )P(k _x , _ky ), wherein,

The zero-padding method image module 3 is configured to perform Fourier transform on the zero-padding method spectral data to obtain a zero-padding method image of low-frequency spectral data of a high-resolution image.

Preferably, the zero-padding method image module 3 represents the low-frequency spectral data zero-padding method image of the high-resolution image as in, Represents the inverse Fourier transform of G(k _x , _ky )P(k _x , _ky ).

The singular spectrum function module 4 is configured to obtain an optimal singularization operator according to the zero-padding method image of the low-frequency spectrum data, obtain a singular function according to the optimal singularization operator, and obtain a singular spectral function according to the singular function.

Preferably, the singular spectrum function module 4 is used for

initialization: φ(i,j)=δ(i,j), Among them, "*" means convolution, and δ(i, j) is a two-dimensional Dirac function;

The four basic singularization operators are recorded as:

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);

implement judge whether

If so, will assigned to After assigning φ(i,j)*φ _I (i,j) to φ(i,j), repeat the execution and judge whether A step of;

If not, output the best singularization operator φ(i,j).

Preferably, the singular spectral function module 4 obtains the singular function h(i,j) according to the solution of the zero state of the differential equation φ(i,j)*h(i,j)=δ(i,j).

Preferably, the singular spectral function module 4 is based on Get the singular spectral function.

A subsequent coordinate parameter module 5 can obtain the coordinate parameters of high-resolution image restoration according to the optimal singularization operator obtained by the singular spectrum function module 4 and by using point spread function tomography.

Preferably, the coordinate parameter module 5 is used for

initialization: c=1,

calculate: Will assigned to c=c+1, where ( _{ic,j c )} represents the coordinate parameter, c=1,2,...,q, the coordinate parameter is a non-zero coordinate;

judge whether Among them, ||·|| ₂ represents the quadratic norm,

If so, then repeat the steps of the calculation;

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

A weighting parameter module 6, configured to obtain weighting parameters for high-resolution image restoration according to the singular spectrum function and the coordinate parameters.

Preferably, the weighted parameter module 6 is used to construct a singular information mathematical model according to the analytic continuation theorem Among them, e=2.718281828459;

The weighted parameters a _c of high resolution image restoration are obtained by pseudo-inverse matrix method, c=1,2,...,q.

A restoration module 7, configured to obtain high-frequency spectrum data of the high-resolution image according to the weighting parameters and the singular spectrum function, obtain complete spectrum data according to the low-frequency spectrum data and high-frequency spectrum data of the high-resolution image, and Outputting the high resolution image based on the complete spectrum data.

Preferably, the restoration module 7 is configured to use the singular information mathematical model

extending the high frequency spectral data of the high resolution image;

Acquiring the complete spectrum data G(k _x , _ky ) according to the low frequency spectrum data and high frequency spectrum data of the high resolution image;

outputting the high-resolution image g(i,j) according to the complete spectral data G(k _x , _ky ),

For details of the second embodiment, please refer to the corresponding part in the first embodiment.

Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and for relevant information, please refer to the description of the method part.

Professionals can further realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software or a combination of the two. In order to clearly illustrate the possible For interchangeability, in the above description, the composition and steps of each example have been generally described according to their functions. Whether these functions are executed by hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may use different methods to implement the described functions for each specific application, but such implementation should not be regarded as exceeding the scope of the present invention.

Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and equivalent technologies thereof, the present invention also intends to include these modifications and variations.

Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and for relevant information, please refer to the description of the method part.

Professionals can further realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software or a combination of the two. In order to clearly illustrate the possible For interchangeability, in the above description, the composition and steps of each example have been generally described according to their functions. Whether these functions are executed by hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may use different methods to implement the described functions for each specific application, but such implementation should not be regarded as exceeding the scope of the present invention.

Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and equivalent technologies thereof, the present invention also intends to include these modifications and variations.

Claims (14)

1. A singular spectral function acquisition method for high-resolution image restoration, characterized in that, comprising: Obtain the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtain low-frequency spectrum data of the high-resolution image according to the number of pixels and the low-resolution image; Acquiring the zero-padding method spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image; performing Fourier transform on the zero-padding method spectral data to obtain the low-frequency spectral data zero-padding method image of the high-resolution image; The optimal singularization operator is obtained according to the zero-padding image of the low-frequency spectrum data, the singular function is obtained according to the optimal singularization operator, and the singular spectral function is obtained according to the singular function. 2. the singular spectral function acquisition method of high-resolution image restoration as claimed in claim 1, is characterized in that, obtains the horizontal or vertical pixel number of the high-resolution image to be restored and a low-resolution image, according to In the step of obtaining the low-frequency spectrum data of the high-resolution image and the number of pixels and the low-resolution image, A low-resolution image g _l (i,j), i,j=0,1,...,l needs to be restored to a high-resolution image g(i,j),i,j=0,1,. ..,N,N>>l, the spectral data of g(i,j) image is expressed as G(k _x , _ky ), k _x ,ky _∈Ω , Ω is the spectral space of the high-resolution image , l represents the number of horizontal or vertical pixels of the low-resolution image, N represents the number of horizontal or vertical pixels of the high-resolution image to be restored, and the spectral data of the low-resolution image is expressed as G _l (k _x , k _y ), in, Represents the Fourier transform of g _l (i, j), then the spectrum data of the low-frequency range of the g (i, j) image - l/2≤k _x , k _y <l/2 is expressed as (N/l) ² G _l (k _x , k _y ). 3. the singular spectral function obtaining method of high-resolution image restoration as claimed in claim 2 is characterized in that, according to the low-frequency spectral data of described high-resolution image, obtains the zero-padding method spectral data of described high-resolution image step, The zero-padding method spectral data of the high-resolution image is expressed as G(k _x , k _y )P(k _x , k _y ), where, 4. the singular spectral function acquisition method of high-resolution image restoration as claimed in claim 3, is characterized in that, do Fourier transform to the low-frequency spectral data zero-filling of described zero padding method spectral data to obtain high-resolution image In the step of law image, The low-frequency spectral data zero-filling method image of the high-resolution image is expressed as in, Represents the inverse Fourier transform of G(k _x , _ky )P(k _x , _ky ). 5. the singular spectral function obtaining method of high-resolution image restoration as claimed in claim 4, is characterized in that, according to described low-frequency spectrum data zero padding method image, obtains the step of optimal singularization operator comprising: initialization: φ(i,j)=δ(i,j), where, Among them, "*" means convolution, and δ(i, j) is a two-dimensional Dirac function; The four basic singularization operators are recorded as: 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); implement judge whether If so, will assigned to After assigning φ(i,j)*φ _I (i,j) to φ(i,j), repeat the execution and judge whether A step of; If not, output the best singularization operator φ(i,j). 6. the singular spectral function acquisition method of high-resolution image restoration as claimed in claim 5, is characterized in that, according to described optimal singularization operator, obtains the step of singular function comprising: The singular function h(i,j) is obtained from the solution of the zero state of the difference equation φ(i,j)*h(i,j)=δ(i,j). 7. the singular spectrum function obtaining method of high-resolution image restoration as claimed in claim 6 is characterized in that, in the step of obtaining singular spectrum function according to described singular function, singular spectrum function is 8. A singular spectral function acquisition system for high-resolution image restoration, characterized in that it comprises: The low-frequency spectrum data module is used to obtain the number of horizontal or vertical pixels of the high-resolution image to be restored and a low-resolution image, and obtain the high-resolution image according to the number of pixels and the low-resolution image The low-frequency spectrum data of A zero-padding spectral data module, configured to obtain the zero-padding spectral data of the high-resolution image according to the low-frequency spectral data of the high-resolution image; A zero-padding method image module is used to perform Fourier transform on the zero-padding method spectral data to obtain a low-frequency spectral data zero-padding method image of a high-resolution image; The singular spectrum function module is configured to obtain an optimal singularization operator according to the zero-padding method image of the low-frequency spectrum data, obtain a singular function according to the optimal singularization operator, and obtain a singular spectral function according to the singular function. 9. the singular spectral function acquisition system of high-resolution image restoration as claimed in claim 8, is characterized in that, described low-frequency spectrum data module is used for representing a low-resolution image as g _l (i, j), i,j=0,1,...,l, express the high-resolution image to be restored as g(i,j),i,j=0,1,...,N,N>>l, The spectral data of the g(i, j) image is expressed as G(k _x , _ky ), k _x , _ky ∈ Ω, Ω is the spectral space of the high-resolution image, and l represents the horizontal or horizontal direction of the low-resolution image The number of vertical pixels, N represents the number of horizontal or vertical pixels of the high-resolution image to be restored, and the spectrum data of the low-resolution image is expressed as G _l (k _x , k _y ), in, Represents the Fourier transform of g _l (i, j), then the spectrum data of the low-frequency range of the g (i, j) image - l/2≤k _x , k _y <l/2 is expressed as (N/l) ² G _l (k _x , k _y ). 10. the singular spectral function acquisition system of high-resolution image restoration as claimed in claim 9, is characterized in that, described zero-padding method spectral data module represents the zero-padding method spectral data of described high-resolution image as G( k _x ,k _y )P(k _x ,k _y ), where, 11. The singular spectral function acquisition system of high-resolution image restoration as claimed in claim 10, is characterized in that, described zero-padding method image module represents the low-frequency spectrum data zero-padding method image of described high-resolution image as in, Represents the inverse Fourier transform of G(k _x , _ky )P(k _x , _ky ). 12. The singular spectrum function acquisition system of high resolution image restoration as claimed in claim 11, is characterized in that, described singular spectrum function module is used for initialization: φ(i,j)=δ(i,j), Among them, "*" means convolution, and δ(i, j) is a two-dimensional Dirac function; The four basic singularization operators are recorded as: 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); implement judge whether If so, will assigned to After assigning φ(i,j)*φ _I (i,j) to φ(i,j), repeat the execution and judge whether If not, output the best singularization operator φ(i,j). 13. The singular spectrum function acquisition system of high-resolution image restoration as claimed in claim 12, is characterized in that, described singular spectrum function module according to differential equation φ (i, j)*h (i, j)=δ( The solution of the zero state of i,j) obtains the singular function h(i,j). 14. The singular spectrum function acquisition system of high resolution image restoration as claimed in claim 13, is characterized in that, described singular spectrum function module according to Get the singular spectral function.