Preprint A551/2007
The EM algorithm for ill-posed integral equations: a convergence analysis

Alfredo N. Iusem | Resmerita, Elena | Engl, Heinz W.

**Keywords: **
EXpectation-maximization | integral equations | iill-posed problems

The EM algorithm is a convenient tool for approximating maximum likelihood estimators in situation where available data are incomplete, as it is the case for many inverse problems. Our focus here is in the continuous version of the EM algorithm for a Poisson model, which is known to perform unstably when applied to ill-posed integral equations. We interprete and analize the EM algorithm as a regularization procedure: we show weak convergence of the iterates to a solution of the equation when exact data are considered. In the case of perturbed data, similar results are established by employing a stopping rule of discrepancy type under
boundedness assumptions on the problem data.