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Injectivity of Rotation invariant windowed Radon transforms.

Abstract : We consider rotation invariant windowed Radon transforms that integrate a function over hyperplanes by using a radial weight (called window). T. Quinto proved their injectivity for square integrable functions of compact support. This cannot be extended in general. Actually, when the Laplace transform of the window has a zero with positive real part , the windowed Radon transform is not injective on functions with a Gaussian decay at infinity, depending on . Nevertheless, we give conditions on the window that imply injectivity of the windowed Radon transform on functions with a more rapid decay than any Gaussian function.
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https://hal.archives-ouvertes.fr/hal-00271785
Contributor : Hermine Biermé <>
Submitted on : Thursday, April 10, 2008 - 12:02:54 PM
Last modification on : Friday, April 10, 2020 - 5:12:13 PM

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  • HAL Id : hal-00271785, version 1

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Hermine Biermé. Injectivity of Rotation invariant windowed Radon transforms.. Journal of Mathematical Analysis and Applications, Elsevier, 2006, 316 (2), pp.383--396. ⟨hal-00271785⟩

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