The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography
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A new algorithm, ordered subsets mirror descent, is developed and implemented, and it is demonstrated that it is well suited for solving the PET reconstruction problem.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.read more
Citations
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References
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TL;DR: Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm, applicable in both single photon (SPECT) and positron emission tomography (PET).
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