Introduction to Radon Transforms (Encyclopedia . Rubin<|
Introduction to Radon TransformsWith Elements of Fractional Calculus and Harmonic Analysis\nAuthor(s): Boris Rubin\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521854597, 978-0521854597\nSynopsis\nThe Radon transform represents a function on a manifold by its integrals over certain submanifolds. Integral transformations of this kind have a wide range of applications in modern analysis, integral and convex geometry, medical imaging, and many other areas. Reconstruction of functions from their Radon transforms requires tools from harmonic analysis and fractional differentiation. This comprehensive introduction contains a thorough exploration of Radon transforms and related operators when the basic manifolds are the real Euclidean space, the unit sphere, and the real hyperbolic space. Radon-like transforms are discussed not only on smooth functions but also in the general context of Lebesgue spaces. Applicati.
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