EVENTO
Dynamic regularization, level set shape optimization and computed myography
Tipo de evento: Seminário LNCC
We consider inverse problems of surface recovery from noisy boundary data, where the forward problem involves the inversion of elliptic PDEs. Instances arise in electromagnetic data inversion, impedance tomography, potential problems and computed myography. Two unrelated applications are described, both giving rise to a situation where the usual ikhonov-type approach leads to numerical difficulty which a dynamic regularization scheme alleviates. In computed myography the challenge is to determine electric activity of individual muscles in a human limb using surface electromyography. To obtain meaningful solutions a regularization reflecting a priori information is chosen and the reconstructed source is represented in terms of tripole basis functions. The latter gives rise to additional numerical sensitivity upon using an inexact conjugate gradient iteration. This affects a Tikhonov regularization approach, where a small correction is blended with a singular matrix. Using iterative, or dynamic, egularization instead gives much better results. Special challenges arise when the surface has discontinuities, and in our second application we then consider reduced problems of shape recovery. The piecewise constant solution, a scaling and translation of characteristic functions, is described in terms of a smoother level set function. However, again the usual approach fails, often not converging in a consistent fashion when employing direct linear algebra solvers. We propose a fast and robust dynamic regularization method for this purpose. For larger problems of this sort, especially in 3D, iterative methods are required. Preconditioned conjugate gradient variants are investigated for the inner iteration of a Gauss-Newton outer loop and the efficacy of the obtained scheme is demonstrated.
Data Início: 04/04/2011 Hora: 14:00 Data Fim: Hora: 15:30
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Uri Ascher - - Un. British Columbia -
