Research On Single-image Super-resolution Reconstruction Based On Rational Fractal Interpolation

The purpose of single-image super-resolution(SR)is to reconstruct a latent high-resolution(HR)image using a single low-resolution(LR)input.SR is a classic method of image processing which has value in both academic and industrial applications.SR has a wide range of practical applications,such as video surveillance,criminal investigation,remote sensing,medical image processing,and consumer electronics.It is a difficult problem that maintains the image texture details and edge structure simultaneously in image SR technology.In this paper,we study interpolation-based SR method through constructing interpolation function.We use a simple mathematical scheme to recover a high-quality HR image from one LR image by applying surf interpolation in image interpolation.By analyzing the parameters and its effects,some adaptive image interpolation algorithms are proposed.The main contributions are bas following:First,a new type ofC~2 continuous rational interpolation with adjustable parameters is proposed,and the error estimates are given.A new type of bivariate rational fractal interpolation model is constructed,and its analytical properties such as error analysis,stability analysis and quasi-locality are investigated.In addition,we provide the method for calculating the fractal dimension.Second,in order to make up for the deficiency of the traditional interpolation algorithm in texture detail preservation,a new method of image interpolation based on parameter optimization is proposed.Based on the convergence analysis of interpolation,objective function of parameter optimization is constructed by using the mapping between region sampling and point sampling.Finally,optimal parameters are obtained by iterative method which aims to reduce error for image interpolation.Third,in order to compensate the deficiency of rational function on the boundary preserving,a new method of region adaptive image interpolation based on NSCT(nonsubsampled contourlet transform)is proposed.Image is divided into different regions and interpolated by using different methods respectively.Image edge contour information is captured by the NSCT,and the image is divided into edge region and non-edge region adaptively according to preset threshold.As for edge region,edge-directed interpolation technique is used to get high resolution image,similarly,rational function interpolation algorithm is used in non-edge region.The objective image with high resolution ratio than the input image is obtained by adaptive interpolation.Forth,as for the disadvantage of single scale of fractal dimension in texture analysis,a single-image SR method based on rational fractal interpolation is proposed.The proposed model has different forms of expression with various values of the scaling factors and shape parameters;thus,it can be employed to better describe image features than current interpolation schemes.Furthermore,this model combines the advantages of rational interpolation and fractal interpolation,and its effectiveness is validated through theoretical analysis.We propose a single-image SR method by applying the fractal analysis method in the interpolation model.The LR input image is divided into texture and non-texture regions,and then the image is interpolated according to the characteristics of the local structure.Specifically,in the texture region,the scaling factor calculation is the critical step.We present a method to accurately calculate scaling factors based on local fractal analysis.