This talk will give a brief overview of the sparse optimization applied to compressive sensing and image restoration. Recently, sparsity related regularization has been extensively exploited to solve various imaging problems and often results in large scale highly nonlinear or even non-convex optimization problems. Subsequently our research is devoted to developing appropriate sparsity regularization and devising corresponding efficient numerical algorithms for these optimization problems. In this talk, we will focus on: 1) efficient sparse recovery via iterative support detection in compressive sensing; 2) fast optimization algorithms for total variation regularized image restoration.

This is joint work with Prof. Wotao Yin (Rice), Prof. Yin Zhang (Rice), Dr. Junfeng Yang (Nanjing University), during my stay in Rice University.