Rate of Convergence of the FOCUSS Algorithm

Kan Xie, Zhaoshui He, Andrzej Cichocki, Xiaozhao Fang

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)


    Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the ℓ-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 < p < 1 and linearly for 1 ≤ p < 2 usually, but may superlinearly in some very special scenarios. In addition, we verify its rates of convergence with respect to p by numerical experiments.

    Original languageEnglish
    Article number7423792
    Pages (from-to)1276-1289
    Number of pages14
    JournalIEEE Transactions on Neural Networks and Learning Systems
    Issue number6
    Publication statusPublished - Jun 2017


    • Convergence
    • focal underdetermined system solver (FOCUSS) algorithm
    • linear convergence
    • rate of convergence
    • superlinear convergence


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