Abstract
Recovery of image data from photoacoustic measurements asks for the inversion of the spherical mean value operator. In contrast to direct inversion methods for specific geometries, we consider a semismooth Newton scheme to solve a total variation regularized least squares problem. During the iteration, each matrix vector multiplication is realized in an efficient way using a recently proposed spectral discretization of the spherical mean value operator. All theoretical results are illustrated by numerical experiments.
Original language | English |
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Journal | Advances in Computational Mathematics |
Volume | 41 |
Issue number | 2 |
Pages (from-to) | 423-438 |
ISSN | 1019-7168 |
DOIs | |
Publication status | Published - 2014 |
Keywords
- Spherical mean operator
- Fast Fourier transform
- Total variation regularization
- Photoacoustic imaging