Information Fusion in Signal and Image Processing: Major Probabilistic and Non-Probabilistic Numerical Approaches

Chapter 6

Probabilistic and Statistical Methods

6.1. Introduction and general concepts

Probabilistic methods essentially deal with the uncertainty of information. They rely on solid and well-mastered mathematical theories in signal and image processing, such as Bayesian decision theory, estimation theory, entropy measurements, etc., thus making it one of the preferred tools for fusion.

Information and its imperfections (mostly those whose nature can be expressed in terms of uncertainty) are modeled using probability distributions or statistical measurements. We will see in section 6.2 how this formalism can be used to measure information. We will then describe the different stages of the fusion process: modeling and estimation in section 6.3, Bayesian combination in section 6.4, then Bayesian combination seen as an estimation problem in section 6.5. The most common rules of decision making are presented in sections 6.6 and 6.7. The following sections give examples of applications and other theoretical tools are discussed, in the fields of multi-source classification in image processing in section 6.8, then of target motion analysis in signal processing in section 6.9.

6.2. Information measurements

If we have a set of l sources of information I_j, a first task often consists of transforming it into a smaller and therefore easier to process subset, without losing any information.

The approach in principal component analysis, which projects each source of information on the eigenvectors ...