Regularization Approaches for Restoring Images Corrupted by Data Correlated Noise Models

Abstract

This thesis is dedicated to study the problem of restoring images corrupted by data correlated noise and linear blurring artifacts. Image restoration being an ill-posed problem, a closed form solution hardly exists, even if one exists, it does not continuously depend on the data. Therefore, in general, an iterative solution is being sought under a regularization framework. To this end, the image degradation process is modeled mathematically under a variational framework and it is solved using various computational methods to ensure the desired output. Three different noise distributions (viz. Chi, Rayleigh and Poisson) are being considered in this thesis. The reason for choosing these distributions are well justified by their presence in various practical imaging modalities such as Magnetic Resonance (MR), Synthetic Aperture Radar (SAR), Ultrasound(US) etc. Three different restoration models are proposed to handle these noise distributions and they are detailed in three chapters of this thesis. The Bayesian framework (which uses the statistical information of the noise present in an image to derive the energy functional) is being employed for designing the functional that corresponds to the model whose solution is being sought. The solutions (corresponding to the three restoration models proposed in this thesis) are provided using Non-Local Total Variational (NLTV), Non-Local Total Bounded Variational(NLTBV) and Non-Local p−norm total variation schemes as the regularization priors, since they ensure preservation of the details in the input data better compared to many other state-of-the art regularization priors. The numerical solution is provided using the split Bregman iterative scheme to improvise the convergence rate and reduce the parameter sensitivity of these models. Qualitative and quantitative analysis of these models are provided for various images from different imaging modalities (such as MR, SAR, US etc) to justify their performance and substantiate their relevance in the context of the current literature.