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

Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/46450

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Title: Multiplicative algorithms for maximum penalized likelihood inversion with non negative constraints and generalized error distributions
Related: Communications in statistics : theory and methods, Vol. 35, Issue 5, p.831-848
DOI: 10.1080/03610920500501478
Publisher: Taylor and Francis
Date: 2006
Author/Creator: Ma, Jun
Description: In many linear inverse problems the unknown function f (or its discrete approximation θpₓ₁), 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.
Description: 18 page(s)
Subject Keyword: maximum penalized likelihood
Subject Keyword: multiplicative iterative algorithms
Subject Keyword: non negative linear inverse problems
Subject Keyword: primary inverse problems
Subject Keyword: secondary inversion method
Resource Type: journal article
Organisation: Macquarie University. Dept. of Statistics

Identifier: http://hdl.handle.net/1959.14/46450
Identifier: ISSN:0361-0926
Identifier: mq-rm-2006003689
Language: eng
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