Nonlinear Image Denoising Methodologies
NORTH CAROLINA STATE UNIV AT RALEIGH DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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In this thesis, we propose a theoretical as well as practical framework to combine geometric prior information to a statisticalprobabilistic methodology in the investigation of a denoising problem in its generic form together with its various applications in signalimage 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.
- Theoretical Mathematics
- Operations Research