Kullback proximal algorithms for maximum-likelihood estimation
Chretien, S.; Hero, A.O., III
Information Theory, IEEE Transactions on
Volume 46, Issue 5, Aug 2000 Page(s):1800 - 1810
Digital Object Identifier 10.1109/18.857792
Summary:Accelerated algorithms for maximum-likelihood image reconstruction
are essential for emerging applications such as three-dimensional (3-D)
tomography, dynamic tomographic imaging, and other high-dimensional
inverse problems. In this paper, we introduce and analyze a class of
fast and stable sequential optimization methods for computing
maximum-likelihood estimates and study its convergence properties. These
methods are based on a proximal point algorithm implemented with the
Kullback-Liebler (KL) divergence between posterior densities of the
complete data as a proximal penalty function. When the proximal
relaxation parameter is set to unity, one obtains the classical
expectation-maximization (EM) algorithm. For a decreasing sequence of
relaxation parameters, relaxed versions of EM are obtained which can
have much faster asymptotic convergence without sacrifice of
monotonicity. We present an implementation of the algorithm using More's
(1983) trust region update strategy. For illustration, the method is
applied to a nonquadratic inverse problem with Poisson distributed data
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