Exact reconstruction filters to invert Radon transforms with finite elements
type: Item
instance of: scholarly article
title: Exact reconstruction filters to invert Radon transforms with finite elements
zbMATH Open document ID: 0613.65134
DOI: 10.1016/0022-247X(86)90217-9
author: Yves Nievergelt
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: Let R be the Radon transform and \(R^*\) its adjoint. It has been known for a long time that \((R*g)*f=R*(g*Rf)\). This formula is extensively used in computerized tomography to derive inversion algorithms. The idea is to prescribe R*g freely (e.g. as an approximate \(\delta\)-function), to determine g which defines the reconstruction filter. The author constructs pairs R*g, g for two and three dimensions. He suggests to use these functions as trial functions in a Ritz method for inverting R.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 45H05
Mathematics Subject Classification ID: 92C50
zbMATH DE Number: 3992893
zbMATH Keywords: Radon transform
zbMATH Keywords: computerized tomography
zbMATH Keywords: inversion algorithms
zbMATH Keywords: reconstruction filter
zbMATH Keywords: Ritz method
reviewed by: Frank Natterer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3992893