Improved M-FOCUSS algorithm with overlapping blocks for locally smooth sparse signals

Rafal Zdunek, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)


The FOCal Underdetermined System Solver (FOCUSS) algorithm has already found many applications in signal processing and data analysis, whereas the regularized M-FOCUSS algorithm has been recently proposed by Cotter et al. for finding sparse solutions to an underdetermined system of linear equations with multiple measurement vectors. In this paper, we propose three modifications to the M-FOCUSS algorithm to make it more efficient for sparse and locally smooth solutions. First, motivated by the simultaneously autoregressive (SAR) model, we incorporate an additional weighting (smoothing) matrix into the Tikhonov regularization term. Next, the entire set of measurement vectors is divided into blocks, and the solution is updated sequentially, based on the overlapping of data blocks. The last modification is based on an alternating minimization technique to provide data-driven (simultaneous) estimation of the regularization parameter with the generalized cross-validation (GCV) approach. Finally, the simulation results demonstrating the benefits of the proposed modifications support the analysis.

Original languageEnglish
Pages (from-to)4752-4761
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number10 I
Publication statusPublished - 2008
Externally publishedYes


  • FOCal underdetermined system solver (FOCUSS)
  • Generalized cross-validation (GCV)
  • Smooth signals
  • sparse solutions
  • Underdetermined systems


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