Fast EM-like methods for maximum "a posteriori" estimates in emission tomography

The maximum-likelihood (ML) approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. The expectation-maximization (EM) algorithm is an iterative algorithm for maximizing the Poisson likelihood in emission c...

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Vydané v:IEEE transactions on medical imaging Ročník 20; číslo 4; s. 280 - 288
Hlavní autori: De Pierro, A.R., Yamagishi, M.E.B.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY IEEE 01.04.2001
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Acceleration
Algorithms
Biological and medical sciences
Computed tomography
Computerized tomography
Convergence
Electrical capacitance tomography
Image Processing, Computer-Assisted - methods
Image reconstruction
Investigative techniques, diagnostic techniques (general aspects)
Iterative algorithms
Iterative methods
Likelihood Functions
Mathematical Computing
Maximum a posteriori estimation
Maximum likelihood estimation
Medical imaging
Medical sciences
Miscellaneous. Technology
Phantoms, Imaging
Poisson Distribution
Positron emission tomography
Radionuclide investigations
Single photon emission computed tomography
Spurious signal noise
Studies
Tomography, Emission-Computed
Radionuclide study
Regularization method
Simulation
Ordered set
A posteriori estimation
Maximum likelihood
EM algorithm
Comparative study
Implementation
Test object
Emission tomography
ISSN:0278-0062, 1558-254X
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Popis
Shrnutí:The maximum-likelihood (ML) approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. The expectation-maximization (EM) algorithm is an iterative algorithm for maximizing the Poisson likelihood in emission computed tomography that became very popular for solving the ML problem because of its attractive theoretical and practical properties. Recently, (Browne and DePierro, 1996 and Hudson and Larkin, 1991) block sequential versions of the EM algorithm that take advantage of the scanner's geometry have been proposed in order to accelerate its convergence. In Hudson and Larkin, 1991, the ordered subsets EM (OS-EM) method was applied to the hit problem and a modification (OS-GP) to the maximum a posteriori (MAP) regularized approach without showing convergence. In Browne and DePierro, 1996, we presented a relaxed version of OS-EM. (RAMLA) that converges to an ML solution. In this paper, we present an extension of RAMLA for MAP reconstruction. We show that, if the sequence generated by this method converges, then it must converge to the true MAP solution. Experimental evidence of this convergence is also shown. To illustrate this behavior we apply the algorithm to positron emission tomography simulated data comparing its performance to OS-GP.
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ISSN:0278-0062
1558-254X
DOI:10.1109/42.921477