Single pixel X-ray transform and related inverse problems

2021/12/28 by Lai, Ru-Yu, Uhlmann, Gunther, Zhai, Jian +1
#35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.13978

Abstract

In this paper, we analyze the nonlinear single pixel X-ray transform K and study the reconstruction of f from the measurement Kf. Different from the well-known X-ray transform, the transform K is a nonlinear operator and uses a single detector that integrates all rays in the space. We derive stability estimates and an inversion formula of K. We also consider the case where we integrate along geodesics of a Riemannian metric. Moreover, we conduct several numerical experiments to corroborate the theoretical results.

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