Stanley Osher

Title: Fast Bregman Iteration for Compressive Sensing and Sparse Denoising

Abstract: We propose, analyze and show results of extremely fast, efficient and simple methods for solving the convex optimization problem:min_u{|u|_L1 /Au=f, u in R^n, A mXn, m<n}. The linearized method was first devised with J. Darbon, then the realization that it is relevant to this problem was done in more generality and with theoretical and computational results with W. Yin, D. Goldfarb and J. Darbon, convergence results for the linearized method with J. Cai and Z. Shen, and an improvement with Y. Mao, B.Dong and W. Yin, with sparse denoising added. Bregman iteration, introduced to image science with M. Burger, D. Goldfarb, J-J Xu, and W. Yin, is the key idea.