A computation for tomographic reconstruction from projections
type: Item
instance of: scholarly article
title: A computation for tomographic reconstruction from projections
zbMATH Open document ID: 0807.65138
DOI: 10.1016/0096-3003(94)90054-X
author: Bui Doan Khanh
published in: Applied Mathematics and Computation
publication date: 1994-12-08T00:00:00Z
review text: The author proposes a numerical method for evaluating singular integrals (Hadamard finite part integrals) of the type \(\int^ b_ a f(x)(x- s)^{-2} dx\). He proposes to replace \(f\) by a piecewise quintic Hermite polynomial. Error estimates involving the fourth derivative of \(f\) are given. This type of integrals appears in some inversion formulae for the Radon transform.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 700381
zbMATH Keywords: tomographic reconstruction from projections
zbMATH Keywords: Hermite approximation
zbMATH Keywords: Hadamard finite part integrals
zbMATH Keywords: error estimates
zbMATH Keywords: singular integrals
zbMATH Keywords: inversion formulae
zbMATH Keywords: Radon transform
reviewed by: Peter Maass
MaRDI profile type: Publication
cites work: Q5186149
cites work: Q3325518
cites work: Q3754464
cites work: The circular harmonic Radon transform
cites work: A birth and death model of neuron firing
cites work: Q4113353
cites work: On the numerical integration of certain singular integrals
cites work: Spline approximations for Cauchy principal value integrals
full work available at URL: 0096-3003(94)90054-x
OpenAlex ID: W2088968669
description: scientific article; zbMATH DE number 700381