Abstract
The objective of reconstructive integral geometry is to recover a function from its integrals over a set of subvarieties. A parametrix is a method of reconstruction of a function from its integral data up to a smoothing operator. In the simplest case, a parametrix recovers a function with a jump singularity along a curve (surface) up to a continuous function, which can be quite informative in medical imaging. We provide an explicit construction for a wide class of acquisition geometries. The case of photo-acoustic geometry is of special interest.
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Palamodov, V.P. A parametrix method in integral geometry. JAMA 125, 353–370 (2015). https://doi.org/10.1007/s11854-015-0011-7
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DOI: https://doi.org/10.1007/s11854-015-0011-7