Microlocal analysis of 𝑑-plane transform on the Euclidean space

Abstract

This is a short summary of our recently published paper [l] (SIAM J. Math. Anal., 2022). We study the basic properties of 𝒹-plane transform on the Euclidean space as a Fourier integral operator, and its application to the microlocal analysis of streaking artifacts in its filtered back projection. The 𝒹-plane transform is defined by integrals of functions on the 𝓃-dimensional Euclidean space over all the 𝒹-dimensional planes, where O < 𝒹 < 𝓃. Our results are related to the metal streaking artifacts of CT images, and some generalization of recent results of Park-Choi-Seo [15] (Comm. Pure Appl. Math., 2017) and Palacios-Uhlmann-Wang [14] (SIAM J.Math. Anal., 2018) for the X-ray transform on the plane.