On PDE based and Statistical Approaches for Image Restoration

Abstract

This thesis describes and focuses on an ill-posed inverse problem of image restoration which is a fundamental requirement for various high level computer vision applications. Various image denoising approaches based on deterministic and statistical arguments are investigated and new modifications are proposed to further enhance the performance of these approaches significantly. First section of the thesis provides the preliminaries of the basic mathematical concepts used in image restoration problem. Middle section of the thesis presents multiscale implementation of deterministic and statistical approaches using wavelet transform. The last section is related to a Low rank approximations for image denoising problem where we investigate residual noise estimation strategy used in WNNM algorithm. We propose non-trivial improvements to residual noise estimation by exploiting various geometrical and statistical properties of a given noisy image. By considering these modifications, we succeeded to improve the denoising results beyond WNNM.