Support Theorems for the Radon Transform and Cramér-Wold Theorems
By Jan Boman, Filip Lindskog. 2008
61 citations recorded by the source corpus.
This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980s and 1990s.
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Finance
View Paper: https://www.semanticscholar.org/paper/ea09231244bfdcd03aff6370c0117626cb4a362a
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In Artificial Intelligence
- Lorenzo Rosasco
- Tomaso A. Poggio
- Fabio Anselmi
- Stefano Soatto
- Ding-Xuan Zhou
- Ernesto De Vito
- Alessandro Achille
- Andrea Caponnetto
In Computer Vision and Pattern Recognition
- Fabio Anselmi
- Lorenzo Rosasco
- Tomaso A. Poggio
- Luc Van Gool
- Andrew Zisserman
- Bernt Schiele
- Jitendra Malik
- Xiaogang Wang
Citations in the corpus
- On Invariance and Selectivity in Representation Learning (2015, background): “Interestingly, R can be shown to be a generalization of the Radon Transform to probability distributions [17].”
- Sliced and Radon Wasserstein Barycenters of Measures (2014, unknown): “One can however show that for ) is a measure, as detailed in the following proposition, see [7] for more details and connections with the celebrated Cram`er-Wold Theorem.”