An Accelerated Penalized Maximum Likelihood Algorithm for Positron Emission Tomography

We develop a "fast" algorithm for obtaining regularized estimates of emission means in positron emission tomography (PET). The algorithm, which iteratively minimizes a penalized maximum likelihood (PML) objective function (i.e., negative log likelihood function plus a scaled penalty functi...

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Bibliographic Details
Published in:IEEE transactions on nuclear science 2007-10, Vol.54 (5), p.1648-1659
Main Authors: Ji-Ho Chang, Anderson, J.M.M., Mair, B.A.
Format: Article
Language:English
Subjects:
Accelerated penalized maximum likelihood (APML) method
Acceleration
Algorithms
Bayesian methods
Convergence
Emission
Estimates
Image converters
Image reconstruction
Imaging phantoms
Iterative algorithms
Maximum likelihood estimation
Pattern search
Penalty function
Positron emission
Positron emission tomography
positron emission tomography (PET)
regularized image reconstruction
Thorax
Tomography
Utilities
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Description
Summary:We develop a "fast" algorithm for obtaining regularized estimates of emission means in positron emission tomography (PET). The algorithm, which iteratively minimizes a penalized maximum likelihood (PML) objective function (i.e., negative log likelihood function plus a scaled penalty function), is based on a "pattern search" and a previously developed PML algorithm. As desired, the proposed accelerated PML (APML) algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations. For the case where the PML objective function is strictly convex, which is true for the class of penalty functions under consideration, we prove that the APML algorithm converges to the unique minimizer of the PML objective function. To demonstrate the utility of the APML algorithm, we applied it to real thorax phantom data and compared it to two existing PML algorithms.
ISSN:0018-9499
1558-1578
DOI:10.1109/TNS.2007.901226