SPARSITY BASED REGULARIZATION FOR SIGNAL RECOVERY AND CLUSTERING

Abstract

In recent years, sparsity-base regularization has seen its usage in a wide range of signal/image recovery and clustering tasks. Sparsity-based regularization is about regularizing the unknowns by prompting its sparsity in a suitable domain. Most existing works focus on the linear inverse problem. This thesis aims at studying two challenging problems in signal recovery and signal clustering which both can be formulated as some non-convex and non-linear problems. One is the non-stationary blind defocus deblurring and the other is un-supervised data clustering. This thesis consists of two parts. The first part focuses on presenting a new computational framework for non-stationary blind defocus deblurring with state-of-the-art performance. The second part focuses on present a convex relaxation for k-means clustering method, together with a rigorous analysis on its theoretical soundness.