An adaptive inverse scale space method for compressed sensing

Abstract

In this paper we introduce a novel adaptive approach for solving $\ell ^1$-minimization problems as frequently arising in compressed sensing, which is based on the recently introduced inverse scale space method. The scheme allows to efficiently compute minimizers by solving a sequence of low-dimensional nonnegative least-squares problems. We provide a detailed convergence analysis in a general setup as well as refined results under special conditions. In addition, we discuss experimental observations in several numerical examples.