2014/01/24 by Sunghwan Moon, Sung‐Hwan Moon, Moon, Sunghwan
Engineering · Mathematics · Medicine · #Advanced X-ray and CT Imaging #Medical Imaging Techniques and Applications #Photoacoustic and Ultrasonic Imaging #math.FA #msc:44A12 #msc:65R10 #msc:92C55
paper · pdf · doi:10.48550/arxiv.1401.6266
16 pages, 3 figures
arxiv created 2014/12/07 · arxiv updated 2014/12/09
PAT is the best-known example of a hybrid imaging method. In this article, we define a Radon-type transform arising in a version of PAT that uses integrating circle detectors and describe how the Radon transform integrating over all circles with a fixed radius is determined from this Radon-type transform. Also, the inversion of the Radon transform integrating over all circles is provided. Various configuration of detectors have their own geometry problems. Here we consider three situations: when the centers of the detectors are located on a cylinder, on a plan, and on a sphere. This transform is similar to a toroidal transform, which maps a given function to its integrals over a set of tori. We also study this mathematically similar object.