The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography

Authors:
Aharon Ben-Tal;Tamar Margalit;Arkadi Nemirovski
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2001

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Abstract

We describe an optimization problem arising in reconstructing three-dimensional medical images from positron emission tomography (PET). A mathematical model of the problem, based on the maximum likelihood principle, is posed as a problem of minimizing a convex function of several million variables over the standard simplex. To solve a problem of these characteristics, we develop and implement a new algorithm, ordered subsets mirror descent, and demonstrate, theoretically and computationally, that it is well suited for solving the PET reconstruction problem.