We propose a new way to treat the exponential/relative entropy cone using symmetric cone solvers. Our approach is based on highly accurate rational (Padé) approximations of the logarithm function. The key to this approach is that our rational approximations, by construction, inherit the (operator) concavity of the logarithm. Importantly, our method extends to the matrix logarithm and other deri...

Suppose we have a posterior density for a parameter given a sample and we form a second posterior density for the same parameter, based on a different model and a different data set. Then we can evaluate the relative entropy distance between the two posteriors. Minimizing the relative entropy over the second sample gives the virtual sample that would make the second posterior as close as possib...

How do macroscopic systems react to imposed external forces? Attempts to answer this question by a general principle have a long history. The general feeling is that the macroscopic systems in their reaction to imposed external forces follow some kind of optimization strategy in which their internal structure is changed so that they offer the least possible resistance. What is the potential inv...

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. The...

Edge detection is an important task in image processing. Edge is defined as the boundary between two regions separated by two relatively distinct gray level properties. Traditional edge detection methods give rise to the exponential increment of computational time. In this paper, edge detection in gray level images is done by using Renyi entropy and particle swarm optimization (PSO) algorithm. ...

Multiple-target tracking (MTT) in the presence of spurious measurements poses difficult computational challenges related to the measurement-to-track data association problem. Different approaches have been proposed to tackle this problem, including various approximations and heuristic optimization tools. The Cross Entropy (CE) and the related Parametric MinxEnt (PME) methods are recent optimiza...

Multiple-target tracking (MTT) in the presence of spurious measurements poses difficult computational challenges related to the measurement-to-track data association problem. Different approaches have been proposed to tackle this problem, including various approximations and heuristic optimization tools. The Cross Entropy (CE) and the related Parametric MinxEnt (PME) methods are recent optimiza...

The recent developments of the Wireless Sensor Network (WSN) with low power cameras have made the possibility of transferring the raw images to the remote areas at any time. As a result, the energy consumption during computation is more. To alleviate this problem, a mechanism called image fusion using histogram-based multi-thresholding with entropy and optimization technique is proposed in this...