Maximum Entropy and Linear Inverse Problems. A Short Review

Abstract

In this paper we give a short review of the Maximum Entropy (ME) principle used to solve inverse problems. We distinguish three fundamentally different approaches for solving inverse problems when using the ME principle: a) Classical ME in which the unknown function is considered to be or to have the properties of a probability density function, b) ME in mean in which the unknown function is assumed to be a random function and the data are assumed to be the expected values of some finite number of known constraints on the unknown function, and finally, c) Bayesian approach with ME priors. In this case the ME principle is used only for assigning a probability distribution to the unknown function to translate our prior knowledge about it. In each approach, we describe the main ideas and give explicitly the hypothesis, the practical and the theoretical limitations.