Single Pixel X-ray Transform and Related Inverse Problems

Ru Yu Lai, Gunther Uhlmann, Jian Zhai, Hanming Zhou

Research output: Contribution to journalArticlepeer-review

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 of the linearization at zero. 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.

Original languageEnglish (US)
Pages (from-to)1894-1909
Number of pages16
JournalSIAM Journal on Imaging Sciences
Volume15
Issue number4
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.

Keywords

  • X-ray transform
  • inverse problems
  • single pixel X-ray transform

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