English

Convergence analysis of the FOCUSS algorithm

Information Theory 2013-04-19 v4 math.IT

Abstract

FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems, which is extremely easy to implement. In this paper, we give a comprehensive convergence analysis on the FOCUSS algorithm towards establishing a systematic convergence theory by providing three primary contributions as follows. First, we give a rigorous derivation for this algorithm exploiting the auxiliary function. Then, we prove its convergence. Third, we systematically study its convergence rate with respect to the sparsity parameter p and demonstrate its convergence rate by numerical experiments.

Keywords

Cite

@article{arxiv.1202.5470,
  title  = {Convergence analysis of the FOCUSS algorithm},
  author = {Zhaoshui He and Shengli Xie and Andrzej Cichocki},
  journal= {arXiv preprint arXiv:1202.5470},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author due to a crucial error

R2 v1 2026-06-21T20:24:37.111Z