Novel approaches to entropic regularization

Abstract

In this work, two new entropic regularization techniques are introduced. They represent a generalization of the standard MaxEnt regularization method, and allow for a greater flexibility for introducing any prior information about the expected structure of the true physical model, or its derivatives, into the inversion procedure. The first technique is based on the minimization of the entropy of the vector of first-differences of unknown parameters. Adopting standard terminology, it is known as the minimum first-order entropy method (MinEnt-1). To illustrate the essential feature of the method, MinEnt-1 is applied to the reconstruction of two-dimensional geoelectric conductivity distributions from magnetotelluric data. The second technique is based on the maximization of the entropy of the vector of second-differences of the unknown parameters, and is denoted as the MaxEnt-2 method. The MaxEnt-2 method is applied to the retrieval of vertical profiles of temperature in the atmosphere from remote sensing data.