Improved FOCUSS method with conjugate gradient iterations

Zhaoshui He, Andrzej Cichocki, Rafal Zdunek, Shengli Xie

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53 Citations (SciVal)


FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems. In this correspondence, we strengthen the FOCUSS method with the following main contributions: 1) we give a more rigorous derivation of the FOCUSS for the sparsity parameter 0 < p < 1 by a nonlinear transform and 2) we develop the CG-FOCUSS by incorporating the conjugate gradient (CG) method to the FOCUSS, which significantly reduces a computational cost with respect to the standard FOCUSS and extends its availability for large scale problems. We justify the CG-FOCUSS based on a probability theory. Furthermore, the high performance of the CG-FOCUSS is demonstrated with experiments.

Original languageEnglish
Pages (from-to)399-404
Number of pages6
JournalIEEE Transactions on Signal Processing
Issue number1
Publication statusPublished - 2009
Externally publishedYes


  • Basis pursuit (BP)
  • Conjugate gradient (CG)
  • Matching pursuit (MP)
  • Nonlinear transform
  • Orthogonal matching pursuit (OMP)
  • Preconditioned conjugate gradient (PCG)
  • Preconditioner


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