H.F. de Campos Velho (2006): Entropic Regularization for Inverse Problems, 2nd LNCC Meeting on Computational Modelling, August 8-11, Petropolis (RJ), Brazil.

Abstract: Regularized solutions is a standard procedure to deal with inverse problems. Similar to the other standard regularization techniques, such as Tikhonov’s regularization, entropic regularization searches to incorporate some a priori information from the physical phenomena. Thus, for a suitable choice of the penalty or regularization parameter, the entropic regularization yields good reconstructions which are consistent with the available data. Here, a generalization of the standard MaxEnt regularization method is treated [8], 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. One technique is based on the minimization of the entropy of the vector of first-differences of unknown parameters, the minimum first-order entropy method (MinEnt-1). MinEnt-1 is applied to geophysics reconstructions using magnetotelluric and gravimetric data [1, 3, 8, 9]. 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 identify turbulent properties and the pollutant sources in the atmospheric flow [2, 5-7]. Finally, a higher order for non-extensive entropic regularization is employed to the retrieval of vertical profiles of temperature in the atmosphere from remote sensing data [4].

References:

[1] H.F. de Campos Velho, F.M. Ramos (1997): Numerical Inversion of Two-Dimensional Geoelectric Conductivity Distributions from Eletromagnetic Ground Data, Brazilian Journal of Geophysics, 15(2), 133-143.

[2] H.F. de Campos Velho, M.R. de Moraes, F.M. Ramos, G.A. Degrazia, D. Anfossi (2000): An Automatic Methodology for Estimating Eddy Diffusivity from Experimental Data, Il Nuovo Cimento, 23 C(1), 65-84.

[3] H.F. de Campos Velho, V.C.F. Barbosa, D.R. Roberti, R.P. Souto, E.H. Shiguemori (2005): Inverse Analysis in Geoscience Problems, XXVI Iberian Latin American Congress on Computational Methods in Engineering (CILAMCE-2005), October 19-21, Guarapari (ES), Brazil, Abstract Book page 237, Proceedings in CD-Rom paper code CIL1013 (12 pages).

[4] H.F. de Campos Velho, F.M. Ramos, E.H. Shiguemori, J.C. Carvalho, J.D.S. da Silva (2006): A Unified Regularization Theory: The Maximum Non-extensive Entropy Principle, to be submitted.

[5] D.R. Roberti, H.F. de Campos Velho, G.A. Degrazia (2004): Identifing Counter-gradient Term in Atmospheric Convective Boundary Layer, Inverse Problems in Science and Engineering, 12(3), 329-339.

[6] D.R. Roberti, D. Anfossi, H.F. de Campos Velho, G.A. Degrazia (2005): Estimation of Horizontal Dimensions of an Area Source, Ciencia e Natura - ISSN 0100-8307 (Special issue: Proceedings of IV Brazilian Workshop on Micrometeorology, 14-16 December, 2005, Santa Maria (RS), Brasil), pp. 147-150. (in Portuguese)

[7] D.R. Roberti, D. Anfossi, H.F. de Campos Velho, G.A. Degrazia (2005): Estimation of Emission Rate of Pollutant Atmospheric Source, 5th International Conference on Inverse Problems in Engineering: Theory and Practice (ICIPE-2005), July 11-15, Cambridge, UK, Vol. III, R03 (7 pages).

[8] F.M. Ramos, H.F. de Campos Velho, J.C. Carvalho, N.J. Ferreira (1999): Novel Approaches on Entropic Regularization, Inverse Problems, 15(5), 1139-1148.

[9] J.B.C. Silva, F.S. Oliveira, V.C.F. Barbosa, H.F. de Campos Velho (2006): Gravity Inversion Using Entropic Regularization, Society of Exploration Geophysicists - Sixth Annual Meeting, 1-6 October, New Orleans, Louisiana, USA.