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Inversion of the Radon transform with incomplete data

✍ Scribed by A. G. Ramm

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 297 KB
Volume: 15
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670150303

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✦ Synopsis

Abstract

The Radon transform R(p, θ), θ∈S^n−1^, p∈ℝ^1^, of a compactly supported function f(x) with support in a ball B~a~ of radius a centred at the origin is given for all \documentclass{article}\pagestyle{empty}\begin{document}$ \theta \in \mathop {S^{n - 1} }\limits^\tilde $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {S^{n - 1} }\limits^\tilde $\end{document} is an open set on S^n−1^, and all p∈(− ∞, ∞), n≥2. An approximate formula is given to calculate f(x) from the given data.

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