Space-alternating generalized expectation-maximization algorithm
Fessler, J.A.; Hero, A.O.
Signal Processing, IEEE Transactions on
Volume 42, Issue 10, Oct 1994 Page(s):2664 - 2677
Digital Object Identifier 10.1109/78.324732
Summary: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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