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

Fractional Calculus and Applied Analysis (2010)

- Volume: 13, Issue: 1, page 43-56
- ISSN: 1311-0454

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topOurnycheva, 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 -

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