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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2006

Injectivity of Rotation invariant windowed Radon transforms.

Résumé

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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Dates et versions

hal-00271785 , version 1 (10-04-2008)

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  • HAL Id : hal-00271785 , version 1

Citer

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