EVENTO
A noniterative reconstruction method based on higher-order topological derivatives for solving a class of inverse problems
Tipo de evento: Defesa de Tese de Doutorado
Several classes of inverse problems are written in the form of over-determined boundary value problems. This difficulty can be overcome by rewriting the inverse problem as an optimization problem. In particular, we are interested in the reconstruction of the support of a set of hidden anomalies embedded into a geometrical domain. The basic idea consists in minimizing a shape functional measuring the misfit of the solution obtained from the model and the data taken from the partial measurements with respect to the parameters of interest. This shape functional is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives. It means that the shape functional is expanded asymptotically and then truncated up to the desired order term. The resulting expression is trivially minimized with respect to the parameters under consideration, leading to a non-iterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to noisy data and independent of any initial guess.
Data Início: 01/04/2019 Hora: 14:00 Data Fim: 01/04/2019 Hora: 17:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Aluno: Lucas dos Santos Fernandes - LNCC - LNCC
Orientador: Antônio André Novotny - LNCC - LNCC Jan Sokolowski - Université de Lorraine, Institute Élie Cartan, France - CNRS,INRIA Ravi Prakash - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Antônio André Novotny - LNCC - LNCC Antoine Laurain - Technische Universität Berlin, Germany - Antonio Leitão - Universidade Federal de Santa Catarina - UFSC Frédéric Gerard Christian Valentin - Laboratório Nacional de Computação Científica - LNCC Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC
Suplente Banca Examinadora: Eduardo Alberto Fancello - Universidade Federal de Santa Catarina - UFSC
