When

Start: 10/31/2012 - 1:15pm

End : 10/31/2012 - 2:15pm

End : 10/31/2012 - 2:15pm

Category

Applied Math Seminar

Speaker

Jurgen Frikel (Helmholtz Zentrum in Munich)

Abstract

In various models of photoacoustic tomography, the reconstruction problem amounts to the inversion of the spherical

mean Radon transform. For this purpose, many different exact inversion formulas have been developed. However, in practice only

an approximate reconstruction can be computed. In this talk, we present two approximate reconstruction techniques.

In the first part of the talk, a summability approach will be introduced as method for approximate inversion of the spherical mean

Radon transform. In the second part, we investigate the discretization of series expansion methods for the inversion

of the spherical mean Radon transform in an approximation theoretic setting. In particular, we will show that by applying

spectral methods to discretization of series expansions, optimal convergence rates can be achieved. Moreover, we shall

also outline that these discretization schemes may also be applied in situations where the spherical mean data is

available on scattered points.

Where

KRV164

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