Alternating Direction Method of Multiplier for Tomography With Nonlocal Regularizers

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, O...

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Vydáno v:IEEE transactions on medical imaging Ročník 33; číslo 10; s. 1960 - 1968
Hlavní autoři: Se Young Chun, Dewaraja, Yuni K., Fessler, Jeffrey A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.10.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Alternating direction method of multiplier
Approximation algorithms
Approximation methods
Computer Simulation
Convergence
Emission
emission tomography
Image Processing, Computer-Assisted - methods
Image reconstruction
Mathematical analysis
Mathematical models
Multipliers
nonlocal (NL) regularizer
ordered-subset expectation maximization (OSEM)
Phantoms, Imaging
Projection
Single photon emission computed tomography
Tomography
Tomography, Emission-Computed - methods
Vectors
ISSN:0278-0062, 1558-254X, 1558-254X
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Popis
Shrnutí: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.
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ISSN:0278-0062
1558-254X
1558-254X
DOI:10.1109/TMI.2014.2328660