Geodesic
On Y. Nievergelt's Inversion Formula for the Radon Transform
Fractional calculus and applied analysis, Tome 13 (2010) no. 1, pp. 43-56.

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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.
Keywords: K-plane Radon Transform, Nievergelt's Inversion Formula, Convolution-Backprojection Method 
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Ournycheva, E.; Rubin, B. On Y. Nievergelt's Inversion Formula for the Radon Transform. Fractional calculus and applied analysis, Tome 13 (2010) no. 1, pp. 43-56. http://geodesic.mathdoc.fr/item/FCAA_2010_13_1_a3/