Multiplicative algorithms for maximum penalized likelihood inversion with non negative constraints and generalized error distributions

Jun Ma*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    In many linear inverse problems the unknown function f (or its discrete approximation Θ p ×1 ), which needs to be reconstructed, is subject to the non negative constraint(s); we call these problems the non negative linear inverse problems (NNLIPs). This article considers NNLIPs. However, the error distribution is not confined to the traditional Gaussian or Poisson distributions. We adopt the exponential family of distributions where Gaussian and Poisson are special cases. We search for the non negative maximum penalized likelihood (NNMPL) estimate of Θ. The size of Θ often prohibits direct implementation of the traditional methods for constrained optimization. Given that the measurements and point-spread-function (PSF) values are all non negative, we propose a simple multiplicative iterative algorithm. We show that if there is no penalty, then this algorithm is almost sure to converge; otherwise a relaxation or line search is necessitated to assure its convergence.

    Original languageEnglish
    Pages (from-to)831-848
    Number of pages18
    JournalCommunications in Statistics - Theory and Methods
    Volume35
    Issue number5
    DOIs
    Publication statusPublished - 2006

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