Display Abstract

Title Exact reconstructions and parametrices in photoacoustic tomography

Name Victor P Palamodov
Country Israel
Email palamodo@post.tau.ac.il
Submit Time 2014-02-27 11:12:26
Special Session 45: Hybrid imaging methods
Several closed exact formulae are known for reconstruction of a function from data of spherecal means for spheres centered at a (hyper)surface. The central sets are spheres, ellipsoids or paraboloids. There is an infinite series of unknown algebraic hypersurfaces that can serve as central sets for a reconstruction formula of the same analytical form. These surfaces look exotic but have a simple algebraic definition. It is much easier to construct a parametrix for this problem. A parametrix is a left inverse for a spherical mean operator modulo a smoothing operator in the Sobolev scale of spaces. Application of a parametrix to the integral data correctly reproduces up to a continuous function simple discontinuities like jumps or delta inclusion.