Modeling and estimation using maximum entropy and minimum mean squared criteria based on partial and noisy observations.

Abstract

Modeling a process, based on fully or partially corrupted observations, is of great interest in areas of signal reconstruction and compression. It is particularly of interest to ensure that the quality of the model is solely based on observed data and no other implicit assumptions. To this end firstly, we propose a globally convergent algorithm, Modified Equation Error Output Error (MEEOE), for modeling Infinite Impulse Response (HR) filters, where we have assumed full observation. Secondly, we offer another modeling scheme, Maximum Entropy Kalman Filter (MEKF), based on partial observations and a given set of constraints, that ensures the construction of the most appropriate model, i.e. solely based on observed data and the a priori constraints. In both cases we have assumed corrupted observations. The optimality of MEEOE under conditions of insufficient modeling and colored input is shown. Application of MEKF to image compression and reconstruction is also demonstrated.