Improved FOCUSS Method With Conjugate Gradient Iterations

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 paramete...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2009-01, Vol.57 (1), p.399-404
Main Authors: Zhaoshui He, Cichocki, A., Zdunek, R., Shengli Xie
Format: Article
Language:English
Subjects:
Applied sciences
Availability
Basis pursuit (BP)
Biomedical signal processing
Character generation
Computational efficiency
conjugate gradient (CG)
Conjugate gradients
Derivation
Exact sciences and technology
Focusing
FOCUSS
Information, signal and communications theory
Inverse problems
Laboratories
Large-scale systems
matching pursuit (MP)
Matching pursuit algorithms
Miscellaneous
nonlinear transform
orthogonal matching pursuit (OMP)
preconditioned conjugate gradient (PCG)
preconditioner
Representations
Signal processing
Solvers
Telecommunications and information theory
Vectors
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.2007605