The ordered subsets mirror descent optimization method with applications to tomography

被引：85

作者：

Ben-Tal, A ^{[1
]}

Margalit, T ^{[1
]}

Nemirovski, A ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Fac Ind Engn & Management, MINERVA Optimizat Ctr, IL-32000 Haifa, Israel

来源：

SIAM JOURNAL ON OPTIMIZATION | 2001年 / 12卷 / 01期

关键词：

positron emission tomography; maximum likelihood; image reconstruction; convex optimization; mirror descent;

D O I：

10.1137/S1052623499354564

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：79 / 108

页数：30

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