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arXiv · 2112.13978

Single pixel X-ray transform and related inverse problems

Ru-Yu Lai·Gunther Uhlmann·Jian Zhai·Hanming Zhou
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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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Ru-Yu Lai, Gunther Uhlmann, Jian Zhai, Hanming Zhou. 2021-12-28. Single pixel X-ray transform and related inverse problems. https://arxiv.org/abs/2112.13978

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