A Comparison of Two Approaches: Maximum Entropy on the Mean (MEM) and Bayesian Estimation (BAYES) for Inverse Problems

TL;DR

This paper compares two probabilistic methods, MEM and BAYES, for solving inverse problems, analyzing their inference procedures and optimization criteria to understand their differences and applications.

Contribution

The paper provides a detailed comparison of MEM and BAYES approaches, highlighting their distinct inference procedures for inverse problems.

Findings

MEM and BAYES are two different inference procedures for inverse problems

The paper analyzes the optimization criteria used in both approaches

Comparison reveals differences in assumptions and solution strategies

Abstract

To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are in fact two different inference procedures to define the solution of an inverse problem as the optimizer of a compound criterion. Keywords: Inverse problems, Maximum Entropy on the Mean, Bayesian inference, Convex analysis.