The ‘Simultaneous Maximum-Likelihood Attenuation Correction Factors’ (sMLACF) algorithm presented here, is an iterative algorithm to calculate the maximum-likelihood (ML) estimate of the activity λ and the attenuation correction factors a in time-of-flight (TOF) positron emission tomography (PET), and this from emission data only. sMLACF is derived using the expectation-maximization (EM) princi...

We present an algorithm for color classification with explicit illuminant estimation and compensation. A Gaussian classifier is trained with color samples from just one training image. Then, using a simple diagonal illumination model, the illuminants in a new scene that contains some of the same surface classes are estimated in a Maximum Likelihood framework using the Expectation Maximization a...

The expectation-maximization (EM) algorithm aims to nd the maximum of a log-likelihood function, by alternating between conditional expectation (E) step and maximization (M) step. This survey rst introduces the general structure of the EM algorithm and the convergence guarantee. Then Gaussian Mixture Model (GMM) are employed to demonstrate how EM algorithm could be applied under Maximum-Likelih...

Advances in neonatal care have improved the survival of infants born prematurely although these infants remain at increased risk of adverse neurodevelopmental outcome. The measurement of white matter structure and features of the cortical surface can help define biomarkers that predict this risk. The measurement of these structures relies upon accurate automated segmentation routines, but these...

Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is co...

This work is focused on latent-variable graphical models for multivariate time series. We show how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of the inverse of spectral density matrix. When applied to a given time series, the algorithm produces a set of candidate models. Various i...

The asymptotic distribution of estimates that are based on a sub-optimal search for the maximum of the log-likelihood function is considered. In particular, estimation schemes that are based on a twostage approach, in which an initial estimate is used as the starting point of a subsequent iterative search, are analyzed. The analysis is relevant for cases where the log-likelihood function is kno...

We present an approximation algorithm for the maximization version of the two level uncapacitated facility location problem achieving a performance guarantee of 0.47. The main idea is to reduce the problem to a special case of MAX SAT, for which an approximation algorithm based on randomized rounding is presented.