On the convergence of FOCUSS algorithm for sparse representation

Details On the convergence of FOCUSS algorithm for sparse representation On the convergence of FOCUSS algorithm for sparse representation

2012-02-24

arxiv.org/abs/1202.5470v2

Computer Science

Information Theory

Scientific paper

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 provide a comprehensive convergence analysis on the FOCUSS algorithm towards establishing a systematic convergence theory for it. First, we give a rigorous derivation for this algorithm exploiting the auxiliary function. Then, we prove its convergence. In particular, we systematically analyze its convergence rate for different sparsity parameter $p$ and demonstrate its convergence rate by numerical experiments.

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