Convergence analysis of the FOCUSS algorithm

Zhaoshui He; Shengli Xie; Andrzej Cichocki

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arXiv · 1202.5470

Convergence analysis of the FOCUSS algorithm

Zhaoshui He·Shengli Xie·Andrzej Cichocki

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Abstract

FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems, which is extremely easy to implement. In this paper, we give a comprehensive convergence analysis on the FOCUSS algorithm towards establishing a systematic convergence theory by providing three primary contributions as follows. First, we give a rigorous derivation for this algorithm exploiting the auxiliary function. Then, we prove its convergence. Third, we systematically study its convergence rate with respect to the sparsity parameter p and demonstrate its convergence rate by numerical experiments.

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Zhaoshui He, Shengli Xie, Andrzej Cichocki. 2012-02-24. Convergence analysis of the FOCUSS algorithm. https://arxiv.org/abs/1202.5470

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