On Em - like Algorithms for Minimum Distance Estimation

We study minimum distance estimation problems related to maximum likelihood estimation in positron emission tomography (pet), which admit algorithms similar to the standard em algorithm for pet with the same type of monotonicity properties as does the em algorithm, see Vardi, Shepp, and Kaufman [25]. We derive the algorithms via the majorizing function approach of De Pierro [11], as well as via the alternating projections approach of Csiszár and Tusnády [7], and prove the monotonicity properties of these algorithms. The distances studied include the Hellinger distance and cross-entropy. The Pearson’s φ distance fits in, but does not seem to enjoy both monotonicity properties. For nonnegatively constrained least squares problems the two approaches lead to different algorithms, both of which enjoy the strong monotonicity properties. Corresponding author: Paul Eggermont Department of Mathematical Sciences University of Delaware Newark, Delaware 19716 telephone : (302) 831–1876 fax : (302) 831–4511 e-mail : [email protected]