Kernel based methods for image reconstruction from spherical means

Start: 10/31/2012 - 1:15pm
End  : 10/31/2012 - 2:15pm

Applied Math Seminar

Jurgen Frikel (Helmholtz Zentrum in Munich)


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.


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