AU2020100275A4

AU2020100275A4 - Remote sensing image super-resolution based on multi-dictionary sparse representation with fractal classification

Info

Publication number: AU2020100275A4
Application number: AU2020100275A
Authority: AU
Inventors: Shuying Huang; Xin Wu; Yong Yang
Original assignee: Wu Xin Miss
Current assignee: Wu Xin Miss
Priority date: 2020-02-25
Filing date: 2020-02-25
Publication date: 2020-03-26
Anticipated expiration: 2028-02-25

Abstract

Image super resolution technology has a wide range of applications in military, medical and other aspects of important application prospects, but also faced with a variety of problems. This patent studies a super-resolution technology of single remote sensing image. Firstly, the input high-resolution remote sensing image is blurred and sampled down to obtain the corresponding low-resolution image. Secondly, the low-resolution of the image is divided into a few patches, and to assess each small patch of fractal dimension, and according to the value size of the fractal dimension, the image patches are divided into two categories, texture patches and smooth patches. Thirdly, using the existing trained dictionary pairs for low-resolution texture and smooth patches corresponding to high-resolution image reconstruction. Finally, high-resolution image is synthesized from these small patches of high resolution.

Description

BACKGROUND AND PURPOSE [0001] In image processing and pattern recognition, image super-resolution reconstruction technology USES a set of low-quality, low-resolution images (or moving sequences) to produce a single high-quality, high-resolution image. The application field of image super-resolution reconstruction is very wide, and it has important application prospect in military, medical, public security, computer vision and so on. Image super-resolution reconstruction technology can improve image recognition ability and accuracy. Image super-resolution reconstruction technology can realize the focused analysis of objects, so that higher spatial resolution images of the area of interest can be obtained, rather than directly using the configuration of high spatial resolution images with huge amount of data.

[0002] With the rapid development of science and technology, the original image processing methods can not meet the current needs. As a very important branch of image processing, super-resolution reconstruction technology is a technology to reconstruct one or more high-resolution images by processing several low-resolution images with complementary information. Super-resolution reconstruction technology is a hot topic in the field of image processing in recent years. By processing low-resolution images, images with better spatial resolution can be obtained to better meet the application requirements.

FRACTAL DIMENSION ALGORITHM DESCRIPTION [0001] Fractal dimension, known as the fractal theory of natural geometry, is a new branch of modern mathematics, but its essence is a new world outlook and methodology. Fractal dimension is a measure of the irregularity of complex form, which reflects the effectiveness of space occupied by complex form. It is combined with the chaos theory of dynamical system and complements each other. It acknowledges that the parts of the world may, under certain conditions or in certain processes, exhibit similarities with the whole in certain aspects (form, structure,

2020100275 25 Feb 2020 information, function, time, energy, etc.). It acknowledges that the variations in spatial dimensions can be discrete or continuous, thus expanding the field of vision.

[0002] The formula for calculating the fractal dimension is as follows:

d = lim £->0 loglV(g)|l . ^1ο^/ί J

Equation 1 where ε is the length of one side of the small cube, and A(g) is the number obtained by covering the measured body with the small cube. The dimension formula means that the dimension of the body can be determined by covering the measured body with the small cube with the side length of ε . For normal regular objects, the number of line segments required to cover a unit length is Ν(ε)= , a square with a unit side, > ^a cube with a unit side,

W)=(J^)^{3 can seen} f^rom these three expressions that the dimension formula also applies to the usual sense of dimension.

[0003] In general, fractal dimension usually represents the degree of irregularity of the image surface, while represents the roughness of the image surface. Therefore, the image can be divided into rough texture area and smooth flat area according to the size of fractal dimension.

JOINT DICTIONARY TRAINING ALGORITHM DESCRIPTION [0001 ] Given the sampled training image texture patch pairs P = {X¹’, Y¹},where

X^h ={x_l,x₂,...,x_n] are the set of high resolution image texture patches and

Y^l = {Τι , · · · ,y„} are the set of the corresponding low resolution image texture patches.

[0002] Solve the following two functions:

2020100275 25 Feb 2020 and

Z)_A=^arg minjl^-zvllkzllzll,

Z)_;=^arg min||y'-Z)_;z[ +2||ζ||,

Equation 2

Equation 3 respectively. Formula and formula can be combined to share the same codes as following:

arg min -’-IM _ n ζ|Γ ₊ J_||y^z _ nz||² +z(J-+ J-)||z|| ^s {Dh,D„z} tv II Ik _M\\ ‘ Ik (_N m J ¹¹¹

Equation 4 where M and N are the dimensions of the low-resolution and high-resolution image texture patches in vector form. In addition, 1/M and 1/V are balance coefficient. Formula (4) can be rewritten as

Equation 5 where min ||V -D Z\\²+Λ ίο,,,ο,,ζ!^{11 c c 112}

Equation 6

THE PROCEDURES OF QUALITY REDUCTION OF SIMULATED HR IMAGES

ARE AS FOLLOWS:

[0001] Gaussian fuzzy matrix H is generated by gaussian fuzzy kernel function.

[0002] First, the fuzzy kernel matrix convolved with the HR image, and then the result of convolution is sampled down to obtain the low-resolution blur images +.

Y = DHX Equation?

where D represents the down-sampling operator which can make large image smaller.

X represents high-resolution image. Image super-resolution (SR) is a technology of recovering the high-resolution (HR) image X from the low-resolution (LR) images Y.

2020100275 25 Feb 2020

THE CALCULATION PROCEDURES OF FRACTAL DIMENSION OF

LOW-RESOLUTION IMAGE PATCHES ARE AS FOLLOWS:

[0001] Divide image Y into several 5x5 blocks F = , where y,.(z = 1,2,...TV) is 5x 5 image patch. Scan from top to bottom, left to right, one pixel at a time.

[0002] The box-counting dimension 5 of the image patch surface is calculated, in which the image patch is a rational fractal surface.

Equation 8 where r(uj = (i-l)xiV+j represents the enumeration of set {(/,7):/,7 = 1,2,---77}.

[0003] Calculate the corresponding fractal dimension D according to the box-counting dimension 5 .

Σ/,Σ',ΚΚ others

Equation 9

THE PROCEDURES OF IMAGE BLOCK CLASSIFICATION BASED ON

FRACTAL DIMENSION D ARE AS FOLLOWS:

[0001] Determine whether the image is magnified by two, three or four.

[0002] Select the trained dictionary pairs (Z\, D, ) according to the magnification of the image.

2020100275 25 Feb 2020 [0003] Assuming that the magnification is two, image patches are divided into two categories according to threshold value of fractal dimension D , texture patches Y_T ⁼ {ΥπΎτ2’···Υτ„} and smooth patches = (^,,^2,---^,,,} · Each image patch has to be judged, when D is greater than the threshold value, this image patch such as y_n is classified as texture areas Y_T, otherwise, this image patch such as y_s belongs in the smooth zone .

[0004] After getting two kinds of low-resolution image patches, the corresponding dictionary pairs (D_n, D_TI) and (D_Sh, D_SI) are used to reconstruct the high-resolution image patches corresponding to the low-resolution image patches tj and K_s .Solve the optimization problem with ^d_t,d/ and (y_T,y_s) defined as following:

min ||.D_riz - y_T ||^ + λ ||α_Γ ||₍ Equation 10 min ||z)_va-y_v||₂+ Equation 11 [0005] Then generate the optimal sparse coefficient a'_T and a_s of the high-resolution image patches. So the high-resolution image patch x_T = D_na’_T and ^xs = ^Dsh^as _are expressed.

[0006] Finally, put each HR image patch back to its corresponding position to restore the final full high-resolution image X*. Other magnification ratios follow a similar procedure.

Claims

1. The procedures of quality reduction of simulated HR images are as follows:

[0001] Gaussian fuzzy matrix H is generated by Gaussian fuzzy kernel function.

[0002] First, the fuzzy kernel matrix convolved with the HR image, and then the result of convolution is sampled down to obtain the low-resolution blur images Y.

Y = DHX Equation 1 where D represents the down-sampling operator which can make large image smaller.

X represents high-resolution image. Image super-resolution (ST?) is a technology of recovering the high-resolution (HR) image X from the low-resolution (LR) images Y.

2. The calculation procedures of fractal dimension of low-resolution image patches are as follows:

[0001] Step 1: Divide image Y into several 5x5 blocks Y = {y_t,y₂,...y_N}, where yfi = 1,2,...A) is 5x 5 image patch. Scan from top to bottom, left to right, one pixel at a time.

[0002] Step 2: The box-counting dimension S of the image patch surface is calculated, in which the image patch is a rational fractal surface.

Equation 2

2020100275 25 Feb 2020

Equation 3 where r(i,/) = (i-l)xlV+j represents the enumeration of set {(z,y): i,j = 1.2.,¥}.

[0003] Step 3: Calculate the corresponding fractal dimension D according to the box-counting dimension S' .

ι^ςςκι. ς:.ς;ι^ '=1 7=1 [2, others

3. The procedures of image block classification based on fractal dimension ^D are as follows:

[0001] Step 1: Determine whether the image is magnified by two, three or four.

[0002] Step 2: Select the trained dictionary pairs (D_h, D,) according to the magnification of the image.

[0003] Step 3: Assuming that the magnification is two, image patches are divided into two categories according to threshold value of fractal dimension D , texture patches U = {y_ri,y_T2,...y_T„} and smooth patches r_x ={j\i As₂>···>&,>} · Each image patch has to be judged, when D is greater than the threshold value, this image patch such as y_Ti is classified as texture areas K,, otherwise, this image patch such as y_Sj belongs in the smooth zone 7_X.

[0004] Step 4: After getting two kinds of low-resolution image patches, the corresponding dictionary pairs (D_n, D_TI) and (D_Sh, D_SI) are used to reconstruct the high-resolution image patches corresponding to the low-resolution image patches Y_Tand 7_X .Solve the optimization problem with (d_t,D_s( and (y_T,y_s) defined as following:

2020100275 25 Feb 2020 mm\\D_Ta -υ[+2||α_Γ||ι

Equation 4

Equation 5 [0005] Then generate the optimal sparse coefficient a_T and a* of the high-resolution image patches. So the high-resolution image patch x_T = D_na’_T and ^xs = ^Dsh^as _are expressed.

[0006] Step 5: Finally, put each HR image patch back to its corresponding position to restore the final full high-resolution image X*. Other magnification ratios follow a similar procedure.

4. The procedures of dictionary pairs training and acquisition are as follows:

[0001] Step 1: Given the sampled training image texture patch pairs p = {x^h, Y¹}, where X^h = {x_l,x₂,...,x_n] are the set of high resolution image texture patches and Y^l ={y_t,y₂,...,y„} are the set of the corresponding low resolution image texture patches.

[0002] Step 2: Solve the following two functions:

Z>„=^arg min ||ύ*-Z)_Az||^+ 2HZ]], and

Z)_;=arg min ||y'-Z)_;z[+21)2^

Equation 6

Equation 7 respectively. Formula and formula can be combined to share the same codes as following:

arg min Flfy* _ _{D Z}l|² + _L||y' _ D Zl|² +f[—+ —ΊΐΙζΙΙ ^s {D,„_Dl,z}_NW ^h Ik _M\\ 'IL· (N M J ¹¹¹

Equation 8

2020100275 25 Feb 2020 where M and N are the dimensions of the low-resolution and high-resolution image texture patches in vector form. In addition, 1/M and 1/7V are balance coefficient. Formula (8) can be rewritten as where min ||Y -D Z||²+2fk₊ J-kll λ,β,.4^{11 c c} ² LY Mf ¹¹¹

-/= x Ί yjN ,D_C = -/= D, _y/M J

Equation 9

Equation 10