2021 Summer Analysis on Metric Spaces Seminar
Professor Hiroyuki Chihara, University of the Ryukyus
The d-plane transform is defined by integrals of functions on the n-dimensional Euclidean space over all the d-dimensional planes. where 0<d<n. This maps functions on the Euclidean space to those on the affine Grassmannian G(d,n). This is said to be X-ray transform if d=1 and Radon transform if d=n-1. When n=2 the X-ray transform is thought to be measurements of CT scanners. In this talk we begin with the basic properties of the d-plane transform, and talk about concrete expression of the canonical relationof the d-plane transform and quantitative properties of the product of the image of the d-plane transforms. The latter one is related to the streaking artifact of CT image, and some generalization of recent results of Park-Choi-Seo (2017) and Palacios-Uhlmann-Wang (2018) for the X-ray transform on the plane.