The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography
نویسندگان
چکیده
منابع مشابه
The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography
We describe an optimization problem arising in reconstructing 3D 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 millions variables over the standard simplex. To solve a problem of these characteristics, we develop and implement a new algorithm,...
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The ordered subsets EM (OSEM) algorithm has enjoyed considerable interest for emission image reconstruction due to its acceleration of the original EM algorithm and ease of programming. The transmission EM reconstruction algorithm converges very slowly and is not used in practice, particularly because there are faster simultaneous update algorithms that converge much faster. We introduce such a...
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The ordered subsets EM (OSEM) algorithm has enjoyed considerable interest for emission image reconstruction due to its acceleration of the original EM algorithm and ease of programming. The transmission EM reconstruction algorithm converges very slowly and is not used in practice. In this paper, we introduce a simultaneous update algorithm called separable paraboloidal surrogates (SPS) that con...
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In this paper we develop a framework of submodular optimization algorithms in line with the mirror-descent style of algorithms for convex optimization. We use the fact that a submodular function has both a subdifferential and a superdifferential, which enables us to formulate algorithms for both submodular minimization and maximization. This reveals a unifying framework for a number of submodul...
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We present new algorithms for penalized-likelihood image reconstruction: modified BSREM (block sequential regularized expectation maximization) and relaxed OS-SPS (ordered subsets separable paraboloidal surrogates). Both of them are globally convergent to the unique solution, easily incorporate convex penalty functions, and are parallelizable—updating all voxels (or pixels) simultaneously. They...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2001
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623499354564