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Please use this identifier to cite or link to this item: http://www.lib.ncsu.edu/resolver/1840.16/4300

Title: Nonlinear image denoising methodologies
Authors: Bao, Yufang
Advisors: Alexandra Duel-Hallen, Committee Member
Robert Cohen, Committee Member
Zhilin Li, Committee Member
Hamid Krim, Committee Chair
Arne A. Nilsson, Committee Member
Alexandra Duel-Hallen, Committee Member
Arne A. Nilsson, Committee Member
Hamid Krim, Committee Chair
Zhilin Li, Committee Member
Robert Cohen, Committee Member
Alexandra Duel-Hallen, Committee Member
Arne A. Nilsson, Committee Member
Hamid Krim, Committee Chair
Zhilin Li, Committee Member
Robert Cohen, Committee Member
Alexandra Duel-Hallen, Committee Member
Arne A. Nilsson, Committee Member
Hamid Krim, Committee Chair
Zhilin Li, Committee Member
Robert Cohen, Committee Member
Keywords: nonlinear image processing
diffusion
random walk
wavelet
information theory
nonlinear image processing
diffusion
random walk
wavelet
information theory
information theory
wavelet
random walk
diffusion
nonlinear image processing
diffusion
nonlinear image processing
information theory
wavelet
random walk
Issue Date: 24-Jun-2003
Degree: PhD
Discipline: Electrical Engineering
Abstract: In this thesis, we propose a theoretical as well as practical framework to combine geometric prior information to a statistical/probabilitstic methodology in the investigation of a denoising problem in its generic form together with its various applications in signal/image analysis. We are able in the process, to investigate, understand and mitigate existing limitations of so-called nonlinear diffusion techniques (such as the Perona-Malik equation) from a probabilistic view point, and propose a new nonlinear denoising method that is based on a random walk whose transition probabilities are selected by the information of a two-sided gradient. This results in a piecewise constant filtered image and lifts the long-standing problem of an unknown evolution stopping time. Our second contribution is in establishing a direct link between multi-resolution analysis techniques and so-called scale space analysis methods, which we in turn utilize to improve the performance of segmentation-optimized image analysis techniques. This is accomplished by using wavelets of higher order vanishing moments, specifically, we achieve a reduction in the typical "blocky" artifacts and a better preservation of texture information. Our third and final contribution is to propose a drastically different approach by isolating statistically independent components in a signal, which we later use as a basis for discrimination against noise, or potentially as plain features. This is related to the well known independent component analysis ( ICA ), for which we first propose Jensen-Rényi divergence as an information- theoretic criterion. In addition, we propose a Rényi mutual divergence as a better criterion to separate mixed signals along with a non-parametric estimation technique for such a measure for 1-D problems. A particle system simulation method is on our future plan of work and is currently ongoing to further investigate the stochastic properties of our diffusion framework.
URI: http://www.lib.ncsu.edu/resolver/1840.16/4300
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