Convolution-backprojection method for the k-plane transform, and calderón's identity for ridgelet transforms

Boris Rubin

doi:10.1016/j.acha.2004.03.003

Convolution-backprojection method for the k-plane transform, and calderón's identity for ridgelet transforms

Boris Rubin^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Letter › peer-review

19 Scopus citations

Abstract

We develop a convolution-backprojection method for the k-plane Radon transform f → f, f ∈ L^p (ℝ). A slight modification of this method gives an explicit inversion formula for f̂ in terms of the corresponding wavelet-like transforms (or the k-plane ridgelet transforms), and a generalization of Calderlón's reproducing formula.

Original language	English
Pages (from-to)	231-242
Number of pages	12
Journal	Applied and Computational Harmonic Analysis
Volume	16
Issue number	3
DOIs	https://doi.org/10.1016/j.acha.2004.03.003
State	Published - May 2004

Keywords

Convolution-backprojection method
K-plane Radon transform
Ridgelet transforms
Wavelet transforms

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10.1016/j.acha.2004.03.003

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title = "Convolution-backprojection method for the k-plane transform, and calder{\'o}n's identity for ridgelet transforms",

abstract = "We develop a convolution-backprojection method for the k-plane Radon transform f → f, f ∈ Lp (ℝ). A slight modification of this method gives an explicit inversion formula for {\^f} in terms of the corresponding wavelet-like transforms (or the k-plane ridgelet transforms), and a generalization of Calderl{\'o}n's reproducing formula.",

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AB - We develop a convolution-backprojection method for the k-plane Radon transform f → f, f ∈ Lp (ℝ). A slight modification of this method gives an explicit inversion formula for f̂ in terms of the corresponding wavelet-like transforms (or the k-plane ridgelet transforms), and a generalization of Calderlón's reproducing formula.

KW - Convolution-backprojection method

KW - K-plane Radon transform

KW - Ridgelet transforms

KW - Wavelet transforms

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SN - 1063-5203

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JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 3

ER -

Convolution-backprojection method for the k-plane transform, and calderón's identity for ridgelet transforms

Abstract

Keywords

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