A new approach to constrained expectation-maximization for density estimation

In this paper, we present two density estimation methods based on constrained expectation-maximization (EM) algorithm. We propose a penalty-based maximum-entropy expectation-maximization (MEEM) algorithm to obtain a smooth estimate of the density function. We further propose an attraction-repulsion expectation-maximization (AREM) algorithm for density estimation in order to determine equilibrium between over-smoothing and over-fitting of the estimated density function. Computer simulation results are used to show the effectiveness of the proposed constrained expectation-maximization algorithms in image reconstruction and sensor field estimation from randomly scattered samples.