In this paper we introduce a novel adaptive approach for solving l1-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 rened results under special conditions. In addition we discuss experimental observations in several numerical examples.

@TechReport{BMBO11,
  author       = {Burger, M. and Moeller, M. and Benning, M. and Osher, S.},
  title        = {An Adaptive Inverse Scale Space Method for Compressed Sensing},
  institution  = {UCLA},
  number       = {11-08},
  year         = {2011},
  type         = {CAM Report},
  url          = \{/2011/BMBO11},
}