Deterministic EM algorithms with penalties

Csiszar (1991) presented an axiomatic derivation of the use of the I-divergence as a discrepancy measure between nonnegative vectors. Snyder, Schulz, and O´Sullivan (see IEEE Trans. Signal Proc., vol.40, no.5, p.1143-50, 1992) then proposed the use of the I-divergence as an optimality criterion in deblurring problems, and introduced the deterministic version of the EM algorithm. Byrne (see IEEE Trans. Image Proc., vol.2, pp.96-103, Jan. 1993) used a similar scenario to Snyder et. al., but also looked at reverse entropy measures and included maximum entropy penalties. O´Sullivan introduced roughness penalties for use in stochastic problems where the use of Markov random fields may not arise naturally; these penalties are used inn this article for the deterministic problem