Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1641

 Title: On Y. Nievergelt's Inversion Formula for the Radon Transform Authors: Ournycheva, E.Rubin, B. Keywords: K-plane Radon TransformNievergelt's Inversion FormulaConvolution-Backprojection Method Issue Date: 2010 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Fractional Calculus and Applied Analysis, Vol. 13, No 1, (2010), 43p-56p Abstract: In 1986 Y. Nievergelt suggested a simple formula which allows to reconstruct a continuous compactly supported function on the 2-plane from its Radon transform. This formula falls into the scope of the classical convolution-backprojection method. We show that elementary tools of fractional calculus can be used to obtain more general inversion formulas for the k-plane Radon transform of continuous and L^p functions on R^n for all 1 ≤ k < n. Further generalizations and open problems are discussed. Description: Mathematics Subject Classification 2010: 42C40, 44A12. URI: http://hdl.handle.net/10525/1641 ISSN: 1311-0454 Appears in Collections: 2010

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