In this paper, we propose an attraction-repulsion expectation-maximization (AREM) algorithm for image reconstruction and sensor field estimation. We rely on a new method for density estimation to address the problems of image reconstruction from limited samples and sensor field estimation from randomly scattered sensors. Density estimation methods often suffer from undesirable phenomena such as over-fitting and over-smoothing. Specifically, various density estimation techniques based on a Gaussian mixture model (GMM) tend to cluster the Gaussian functions together, thus resulting in over-fitting. On the other hand, other approaches repel the Gaussian functions and yield over-smooth density estimates. We propose a method that seeks an equilibrium between over-fitting and over-smoothing in density estimation by incorporating attraction and repulsion forces among the Gaussian functions and determining the optimal balance between the competing forces experimentally. We model the attractive and repulsive forces by introducing the Gibbs and inverse Gibbs distributions, respectively. The maximization of the likelihood function augmented by the Gibbs density mixture is solved under the expectation-maximization (EM) method. Computer simulation results are provided to demonstrate the effectiveness of the proposed AREM algorithm in image reconstruction and sensor field 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.

In this paper, we propose a maximum-entropy expectation-maximization (MEEM) algorithm. We use the proposed algorithm for density estimation. The maximum-entropy constraint is imposed for smoothness of the estimated density function. The derivation of the MEEM algorithm requires determination of the covariance matrix in the framework of the maximum-entropy likelihood function, which is difficult to solve analytically. We, therefore, derive the MEEM algorithm by optimizing a lower-bound of the maximum-entropy likelihood function. We note that the classical expectation-maximization (EM) algorithm has been employed previously for 2-D density estimation. We propose to extend the use of the classical EM algorithm for image recovery from randomly sampled data and sensor field estimation from randomly scattered sensor networks. We further propose to use our approach in density estimation, image recovery and sensor field estimation. Computer simulation experiments are used to demonstrate the superior performance of the proposed MEEM algorithm in comparison to existing methods.

In this paper, we propose a maximum-entropy expectation-maximization algorithm. We use the proposed algorithm for density estimation. The maximum-entropy constraint is imposed in order to ensure smoothness of the estimated density function. The exact derivation of the maximum-entropy expectation-maximization algorithm requires determination of the covariance matrix combined with the maximum entropy likelihood function, which is difficult to solve directly. We therefore introduce a new lower-bound for the EM algorithm derived by using the Cauchy-Schwartz inequality to obtain a suboptimal solution. We use the proposed algorithm for function interpolation and image segmentation. We propose the use of the EM algorithm for image recovery from randomly sampled data and signal reconstruction from randomly scattered sensors. We further propose to use our approach to maximum-entropy expectation-maximization (MEEM) in all of these applications. Computer simulation experiments are used to demonstrate the performance of our algorithm in comparison to existing methods.