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.