Inverting the spherical Radon transform for physi- cally meaningful functions
نویسنده
چکیده
Abstract In this paper we refer to the reconstruction formulas given in Andersson’s On the determination of a function from spherical averages, which are often used in applications such as SAR1 and SONAR2. We demonstrate that the first one of these formulas does not converge given physically reasonable assumptions. An alternative is proposed and it is shown that the second reconstruction formula is well-defined but might be difficult to compute numerically.
منابع مشابه
Inversion of noisy Radon transform by SVD based needlets
Article history: Received 29 July 2008 Revised 29 May 2009 Accepted 3 June 2009 Available online 12 June 2009 Communicated by W.R. Madych A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established i...
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