Kullback Proximal Algorithms for Maximum Likelihood Estimation
نویسنده
چکیده
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 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 sacri ce of monotonicity. We present an implementation of the algorithm using Mor e's Trust Region update strategy. For illustration the method is applied to a non-quadratic inverse problem with Poisson distributed data.
منابع مشابه
Noise Compensation by a Sequential Kullback Proximal Algorithm
We present sequential parameter estimation in the framework of the Hidden Markov Models. The sequential algorithm is a sequential Kullback proximal algorithm, which chooses the KullbackLiebler divergence as a penalty function for the maximum likelihood estimation. The scheme is implemented as £lters. In contrast to algorithms based on the sequential EM algorithm, the algorithm has faster conver...
متن کاملA comparison of algorithms for maximum likelihood estimation of Spatial GLM models
In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two n...
متن کاملSequential noise compensation by a sequential kullback proximal algorithm
We present a sequential noise compensation method based on the sequential Kullback proximal algorithm, which uses the Kullback-Leibler divergence as a regularization function for the maximum likelihood estimation. The method is implemented as filters. In contrast to sequential noise compensation method based on the sequential EM algorithm, the convergence rate of the method and estimation error...
متن کاملEvaluation of estimation methods for parameters of the probability functions in tree diameter distribution modeling
One of the most commonly used statistical models for characterizing the variations of tree diameter at breast height is Weibull distribution. The usual approach for estimating parameters of a statistical model is the maximum likelihood estimation (likelihood method). Usually, this works based on iterative algorithms such as Newton-Raphson. However, the efficiency of the likelihood method is not...
متن کامل