Probabilistic methods for data fusion

The main object of this paper is to show how we can use classical probabilistic methods such as Maximum Entropy (ME), maximum likelihood (ML) and/or Bayesian (BAYES) approaches to do microscopic and macroscopic data fusion. Actually ME can be used to assign a probability law to an unknown quantity when we have macroscopic data (expectations) on it. ML can be used to estimate the parameters of a probability law when we have microscopic data (direct observation). BAYES can be used to update a prior probability law when we have microscopic data through the likelihood. When we have both microscopic and macroscopic data we can use first ME to assign a prior and then use BAYES to update it to the posterior law thus doing the desired data fusion. However, in practical data fusion applications, we may still need some engineering feeling to propose realistic data fusion solutions. Some simple examples in sensor data fusion and image reconstruction using different kind of data are presented to illustrate these ideas. Keywords: Data fusion, Maximum entropy, Maximum likelihood, Bayesian data fusion, EM algorithm.