Computational solutions of Nonlinear
University of Helsinki.
Fecha: 24-26 de febrero de 2016
Aula 420, módulo 17,
Horario: Miércoles, Jueves y Viernes de 10:30-12:30
This course introduces mathematical inverse problems arising from various
practical measurements. Application areas include medical imaging,
underground prospecting, nondestructive testing and speech signal
inversion. Special emphasis is reserved for nonlinear inverse problems
related to partial differential equation (PDE) coefficient recovery. The key
example is Electrical Impedance Tomography (EIT), whose mathematical
model is the infamous Calderon Problem. The central methodology for
noise-robust inversion is nonlinear Fourier transform based on exponentially
behaving Complex Geometric Optics (CGO) solutions. Presented are
several different computational inversion methods making use of CGO
solutions, including the regularized D-bar method. Numerical computation of
CGO solutions is explained for Schrodinger and Beltrami equations, and the
Matlab codes will be made available for participants. Most of the course
material follows the book Mueller-Siltanen: “Linear and nonlinear inverse
problems with practical applications," SIAM 2012.
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