Penalized maximum-likelihood image reconstruction usingspace-alternating generalized EM algorithms
Fessler, J.A.; Hero, A.O., III
Image Processing, IEEE Transactions on
Volume 4, Issue 10, Oct 1995 Page(s):1417 - 1429
Digital Object Identifier 10.1109/83.465106
Summary:Most expectation-maximization (EM) type algorithms for penalized
maximum-likelihood image reconstruction converge slowly, particularly
when one incorporates additive background effects such as scatter,
random coincidences, dark current, or cosmic radiation. In addition,
regularizing smoothness penalties (or priors) introduce parameter
coupling, rendering intractable the M-steps of most EM-type algorithms.
This paper presents space-alternating generalized EM (SAGE) algorithms
for image reconstruction, which update the parameters sequentially using
a sequence of small “hidden” data spaces, rather than
simultaneously using one large complete-data space. The sequential
update decouples the M-step, so the maximization can typically be
performed analytically. We introduce new hidden-data spaces that are
less informative than the conventional complete-data space for Poisson
data and that yield significant improvements in convergence rate. This
acceleration is due to statistical considerations, not numerical
overrelaxation methods, so monotonic increases in the objective function
are guaranteed. We provide a general global convergence proof for SAGE
methods with nonnegativity constraints
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