Space-alternating generalized expectation-maximization algorithm
Fessler, J.A.
Hero, A.O.
Div. of Nucl. Med., Michigan Univ., Ann Arbor, MI ;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Oct 1994
Volume: 42,
Issue: 10
On page(s): 2664-2677
ISSN: 1053-587X
References Cited: 43
CODEN: ITPRED
INSPEC Accession Number: 4798801
Digital Object Identifier: 10.1109/78.324732
Current Version Published: 2002-08-06
Abstract
The expectation-maximization (EM) method can facilitate maximizing
likelihood functions that arise in statistical estimation problems. In
the classical EM paradigm, one iteratively maximizes the conditional
log-likelihood of a single unobservable complete data space, rather than
maximizing the intractable likelihood function for the measured or
incomplete data. EM algorithms update all parameters simultaneously,
which has two drawbacks: 1) slow convergence, and 2) difficult
maximization steps due to coupling when smoothness penalties are used.
The paper describes the space-alternating generalized EM (SAGE) method,
which updates the parameters sequentially by alternating between several
small hidden-data spaces defined by the algorithm designer. The authors
prove that the sequence of estimates monotonically increases the
penalized-likelihood objective, derive asymptotic convergence rates, and
provide sufficient conditions for monotone convergence in norm. Two
signal processing applications illustrate the method: estimation of
superimposed signals in Gaussian noise, and image reconstruction from
Poisson measurements. In both applications, the SAGE algorithms easily
accommodate smoothness penalties and converge faster than the EM
algorithms
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