On Y. Nievergelt's Inversion Formula for the Radon Transform

Ournycheva, E., and Rubin, B.. "On Y. Nievergelt's Inversion Formula for the Radon Transform." Fractional Calculus and Applied Analysis 13.1 (2010): 43-56. <http://eudml.org/doc/219576>.

@article{Ournycheva2010,
abstract = {Mathematics Subject Classification 2010: 42C40, 44A12.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.},
author = {Ournycheva, E., Rubin, B.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {K-plane Radon Transform; Nievergelt's Inversion Formula; Convolution-Backprojection Method; -plane Radon transform; Nievergelt's inversion formula; convolution-backprojection method},
language = {eng},
number = {1},
pages = {43-56},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On Y. Nievergelt's Inversion Formula for the Radon Transform},
url = {http://eudml.org/doc/219576},
volume = {13},
year = {2010},
}

TY - JOUR
AU - Ournycheva, E.
AU - Rubin, B.
TI - On Y. Nievergelt's Inversion Formula for the Radon Transform
JO - Fractional Calculus and Applied Analysis
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 13
IS - 1
SP - 43
EP - 56
AB - Mathematics Subject Classification 2010: 42C40, 44A12.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.
LA - eng
KW - K-plane Radon Transform; Nievergelt's Inversion Formula; Convolution-Backprojection Method; -plane Radon transform; Nievergelt's inversion formula; convolution-backprojection method
UR - http://eudml.org/doc/219576
ER -