Abstract
In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.
Highlights
In some problems coming from applied physics, a multidimensional function f taking values in Rp ought to be reconstructed given a set of observations
We study a reconstruction problem in which constraints are defined as integrals involving the unknown function f and the weight function λ against suitable measures Φ, see expressions (1.1) and (1.3)
We propose a global synthesis of the entropy maximisation methods for such reconstruction problems from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting
Summary
In some problems coming from applied physics, a multidimensional function f taking values in Rp ought to be reconstructed given a set of observations. We propose a global synthesis of the entropy maximisation methods for such reconstruction problems from the convex analysis point of view, as well as in the framework of the embedding into the MEM setting. It consists in the study of the entropy methods for the reconstruction of a multidimensional function submitted to very general constraints such as an integral inverse problem as in (1.3). We consider first some simple examples of single function reconstructions and a two-functions case study inspired by computational thermodynamics
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