  Accelerated algorithms for maximum likelihood image reconstruction are
essential for emerging applications such as 3D tomography, dynamic tomographic
imaging, and other high dimensional inverse problems. In this paper, we
introduce and analyze a class of fast and stable sequential optimization
methods for computing maximum likelihood estimates and study its convergence
properties. These methods are based on a {\it proximal point algorithm}
implemented with the Kullback-Liebler (KL) divergence between posterior
densities of the complete data as a proximal penalty function. When the
proximal relaxation parameter is set to unity one obtains the classical
expectation maximization (EM) algorithm. For a decreasing sequence of
relaxation parameters, relaxed versions of EM are obtained which can have much
faster asymptotic convergence without sacrifice of monotonicity. We present an
implementation of the algorithm using Mor\'{e}'s {\it Trust Region} update
strategy. For illustration the method is applied to a non-quadratic inverse
problem with Poisson distributed data.
