Nonlinear Image Denoising Methodologies

摘要

In this thesis, we propose a theoretical as well as practical framework to combine geometric prior information to a statistical/probabilistic 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.