A continuation log-barrier method for ℓ1-regularized least square

Abstract

Recently, there are increasing attention paid on compressed sensing which is distinct different from traditional signal processing and image reconstructed from indirect or incomplete measurement, especially ℓ1-norm problem which is transformed from compressive sensing. The idea of ℓ1-regularization, as the one of ℓ1-norm, has been receiving a lot of interest in signal processing, image recovery and statistic, etc. This paper will introduces a continuation log-barrier method for solving ℓ1-regularized least squares problem in the field of compressive sensing, which is a second-order method. Our work is inspired by the work in [4] and continuation idea, and the paper will introduce the continuation technique to increase the convergence rate. Therefore, Our continuation log-barrier method for ℓ1-regularized least square problem is accurate and fast in the sense. © 2011 Springer-Verlag Berlin Heidelberg.