Entropic Regularization of Higher Order¹

F. M. Ramos¹, - H. F. Campos Velho¹, - J. C. Carvalho¹ - N. J. Ferreira²

Instituto Nacional de Pesquisas Espaciais (INPE)
Caixa Postal 515
12201-970 São José dos Campos, SP - Brazil

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 the unknown parameters. Adopting the standard terminology, it is called 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.

 

Introduction
Entropic Regularization of Higher Order
    First-order Minimum Regularization
    Second-order Maximum Entropy Regularization
Conclusion
References
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