Broken ray tomography in the disk

Abstract

Given a bounded $C^1$ domain $\Omega \subset {\mathbb{R}}^n$ and a nonempty subset $E$ of its boundary (set of tomography), we consider broken rays which start and end at points of $E$. We ask: If the integrals of a function over all such broken rays are known, can the function be reconstructed? We give positive answers when $\Omega$ is a ball and the unknown function is required to be uniformly quasianalytic in the angular variable and the set of tomography is open. We also analyze the situation when the set of tomography is a singleton.

18 pages, 2 figures; final version

References in corpus (2)

• Inversion formulas for the broken-ray Radon transform
• Detecting small low emission radiating sources

Cited by in corpus (6)

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• Exact inversion of the conical Radon transform with a fixed opening angle
• Inversion of the star transform
• Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
• The Broken Ray Transform in $n$ Dimensions with Flat Reflecting Boundary
• Survey on Broken Ray Transforms