Rate of Convergence of the FOCUSS Algorithm

Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the ℓ p -norm with p ∈ (0, 2) to measure the sparsity of solutions. In this paper, we give a systematical analysis on the rate of convergence of the FOCUSS algorithm with...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2017-06, Vol.28 (6), p.1276-1289
Main Authors: Kan Xie, Zhaoshui He, Cichocki, Andrzej, Xiaozhao Fang
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Automation
Convergence
Electronic mail
focal underdetermined system solver (FOCUSS) algorithm
Indexes
Learning systems
linear convergence
Matching pursuit algorithms
rate of convergence
superlinear convergence
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Summary:Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the ℓ p -norm with p ∈ (0, 2) to measure the sparsity of solutions. In this paper, we give a systematical analysis on the rate of convergence of the FOCUSS algorithm with respect to p ∈ (0, 2). We prove that the FOCUSS algorithm converges superlinearly for 0
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2016.2532358