Convergence analysis of the FOCUSS algorithm

Kan Xie, Zhaoshui He, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Focal Underdetermined System Solver (FOCUSS) is a powerful and easy to implement tool for basis selection and inverse problems. One of the fundamental problems regarding this method is its convergence, which remains unsolved until now. We investigate the convergence of the FOCUSS algorithm in this paper. We first give a rigorous derivation for the FOCUSS algorithm by exploiting the auxiliary function. Following this, we further prove its convergence by stability analysis.

Original languageEnglish
Article number6823752
Pages (from-to)601-613
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number3
Publication statusPublished - 1 Mar 2015
Externally publishedYes


  • Auxiliary function
  • convergence
  • Focal Underdetermined System Solver (FOCUSS) algorithm
  • global convergence theorem.


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