A unified regularization theory: the maximum non-extensive entropy principle

• Autor(a) principal: Velho,Haroldo F. de Campos
• Data de Publicação: 2006
• Outros Autores: Shiguemori,Elcio H., Ramos,Fernando M., Carvalho,João C.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Computational & Applied Mathematics
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022006000200011
• topic: Maximum non-extensive entropy pinciple; unified regularization theory; inverse problems

Tsallis' non-extensive entropy is used as a regularization operator. The parameter ''q'' (non-extensivity parameter) has a central role in the Tsallis' thermostatiscs formalism. Here, several values of q are investigated in inverse problems, using q < 1 and q > 1. Two standard regularization techniques are recovered for special q-values: (i) q = 2 is the well known Tikhonov regularization; (ii) q = 1 is the standard Boltzmann-Gibbs-Shannon formulation for entropy. The regularization feature is illustrated in an inverse test problem: the estimation of initial condition in heat conduction problem. Two methods are studied for determining the regularization parameter, the maximum curvature for the L-curve, and the Morozov's discrepancy principle. The new regularization of higher order is applied to the retrieval of the atmospheric vertical profile from satellite data.