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Title: On Y. Nievergelt's Inversion Formula for the Radon Transform
Authors: Ournycheva, E.
Rubin, B.
Keywords: K-plane Radon Transform
Nievergelt's Inversion Formula
Convolution-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.
ISSN: 1311-0454
Appears in Collections:2010

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