Time reversal in photoacoustic tomography and levitation in a cavity
arXiv:1405.6283 · doi:10.1088/0266-5611/30/12/125006
Abstract
A class of photoacoustic acquisition geometries in n-space is considered such that the spherical mean transform admits an exact filtered back projection reconstruction formula. The reconstruction is interpreted as a time reversion mirror that reproduces exactly an arbitrary source distribution in the cavity. A series of examples of non-uniqueness of the inverse potential problem is constructed basing on the same geometrical technique.
References in corpus (4)
- Thermoacoustic tomography with variable sound speed
- Universal inversion formulas for recovering a function from spherical means
- A uniform reconstruction formula in integral geometry
- Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra