Multi-resolution Analysis And Its Application On Image Processing

Multi-resolution analysis is local analysis in the time domain and frequency domain,and which represents the signal property using combination of the time domain and frequency domain.It is a useful tool to analyze the Non-stationary signals that implements multi-scale analysis to the signal by the translation and dilation of the mother function.It can effectively extract information from signal.Multi-resolution analysis is a booming hot research topic in recent years, which aims to obtain flexible,fast and effective signal processing algorithms through efficient approximation and characterization for the inherent geometric structures of high-dimensional data.Ridgelet,Curvelet and Contourlet,as their two-dimensional cases,represent a new type of harmonic transforms with multiresolution,locality,directionality,anisotropy and fixed basis elements.At present,Multi-resolution analysis is international acknowledged advanced technology in the domain of information and signal processing.Meanwhile it is the front question for discuss and study hotspot attached more and more importance to people in the domain such as signal filtering,image denoising, image edge detecting,image fusing etc.Multi-resolution analysis and its application in image processing are investigated in detail in this dissertation.The main work can be summarized on image denoising,image fusion,image edge detection.Firstly,the basic principles of the Wavelet,Ridgelet,Contourlet,Steerable Pyramid and their coefficients characteristics are discussed in the dissertation.Secondly,the finite Ridgelet transform and its application in image denoising are studied.Three denoising algorithms based on Finite Ridgelet Transform (FRIT) are proposed.They are adaptive denoising method based on cycle sample FRIT,block adaptive denoising method based on FRIT and the FRIT denoising method based on compact energy delaminating.To waken the Gibbs done by Wavelet and scratch by Contourlet,this paper theorizes uniform Hidden Markov Tree(HMT) denoising model both in Wavelet and Contourlet domain based on the multi-resolution principle.The method could both denoising and enhances the image efficiently.It is characterized by multi direction option,parallel information processing,high efficiency of information using,and fusing the enhanced on multi-resolution.By the simulation results,the effectiveness and superiority of the methods are proved.Thirdly,aiming at the limited direction of the Wavelet in the image fusion, the image fusion method based on Contourlet and the method based on Steerable Pyramid are proposed.The two methods for image fusion based on multi-resolution transform extract the edge and detail coefficients and fuse the information in high and low resolutions efficiently.The multi-directional and multi-resolution method fully extracting the fusion information,improves the image definition and information quantity by using different fusion methods in different frequency and directions,which comes over the directional limitation of Wavelet.By simulation experiment and comparison with other arithmetic,the validity and superiority of the method are proved.Finally,aiming at image fusion in the multi resolution domain,the edge detection methods based on Multi-resolution transform are carried out,which could extract the edge coefficients efficiently by Wavelet and Contourlet.A novel algorithm is presented for solving the "wrap" of the finite Ridgelet transform (FRIT) radically by the no wrap lines,and could advance the detection precision by using a trous Wavelet on the improved finite Radon transform instead of Mallat Wavelet.The method could choose and connect the lines,detect the points the length the width and the direction of the objects.The experimental results show that the method is precise to detect the edges of runways and harbor with the noise and comes over the FRIT defect.In conclusion,on the base of multi resolution analysis,this paper had researched on multi resolution analysis and its application on the image processing.Aiming at the shortcoming of the transforms,the improved algorithms were proposed.Experimental results indicated that the adopted intelligent optimization algorithms and the proposed methods could attain good results.