In this talk, we will investigate a reconstruction problem that arises in limited data photoacoustic tomography with a flat observation surface. In the first part of this talk, we will explain which singularities of the original object can be reliably reconstructed and why artifacts can be generated when applying the classical FBP-type reconstruction operators to limited data. We will also provide precise characterizations of added artifacts and explain how they can be reduced. In the second part of this talk, we will present a stable reconstruction method, which is based on sparsity assumptions in the wavelet domain. In particular, we will present an easy to implement numerical algorithm for that problem. This is based on a joint work with Eric Todd Quinto (Tufts University) and Markus Haltmeier (University of Innsbruck).

This presentation is part of Minisymposium “MS7 - Limited data problems in imaging (2 parts)”
organized by: Bernadette Hahn (University of Würzburg) , Gaël Rigaud (Saarland University) , Jürgen Frikel (OTH Regensburg) .

Authors:

Jürgen Frikel (OTH Regensburg)

Keywords:

computed tomography, image reconstruction, incomplete data, inverse problems, microlocal analysis, photoacoustic tomography