Alternating Direction Method of Multiplier for Tomography With Nonlocal Regularizers

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Title
Alternating Direction Method of Multiplier for Tomography With Nonlocal Regularizers
Author
Chun, Se YoungDewaraja, Yuni K.Fessler, Jeffrey A.
Issue Date
2014-10
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation
IEEE TRANSACTIONS ON MEDICAL IMAGING, v.33, no.10, pp.1960 - 1968
Abstract
The ordered subset expectation maximization (OSEM) algorithm approximates the gradient of a likelihood function using a subset of projections instead of using all projections so that fast image reconstruction is possible for emission and transmission tomography such as SPECT, PET, and CT. However, OSEM does not significantly accelerate reconstruction with computationally expensive regularizers such as patch-based nonlocal (NL) regularizers, because the regularizer gradient is evaluated for every subset. We propose to use variable splitting to separate the likelihood term and the regularizer term for penalized emission tomographic image reconstruction problem and to optimize it using the alternating direction method of multiplier (ADMM). We also propose a fast algorithm to optimize the ADMM parameter based on convergence rate analysis. This new scheme enables more sub-iterations related to the likelihood term. We evaluated our ADMM for 3-D SPECT image reconstruction with a patch-based NL regularizer that uses the Fair potential function. Our proposed ADMM improved the speed of convergence substantially compared to other existing methods such as gradient descent, EM, and OSEM using De Pierro's approach, and the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm.
URI
https://scholarworks.unist.ac.kr/handle/201301/9147
URL
http://ieeexplore.ieee.org/document/6825888/
DOI
10.1109/TMI.2014.2328660
ISSN
0278-0062
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ECE_Journal Papers
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