K-plane Radon Transform Nievergelt's Inversion Formula Convolution-Backprojection Method
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 13, No 1, (2010), 43p-56p
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.