Local singularity reconstruction from integrals over curves in \(\mathbb{R}^3\)
type: Item
instance of: scholarly article
title: Local singularity reconstruction from integrals over curves in \(\mathbb{R}^3\)
zbMATH Open document ID: 1270.44005
author: Eric Todd Quinto
author: Hans Rullgård
published in: Inverse Problems and Imaging
publication date: 2013-06-05T00:00:00Z
review text: The present paper deals with the representation of the microlocal analysis to understand a tomographic transform that can be integrated over curves in space. Microlocal properties of general curvilinear Radon transform in \(\mathbb R^3\) are developed, which are shown to be used to develop a local back projection reconstruction algorithm that decreases the effect of the added singularities and reconstruct the shape of object. This research tracks through electron microscopy. In Section 4, the reconstruction for a specific transform by the electron microscope tomography problem is presented, where the electrons travel over curves such as helices or spirals.
reviewed by: Deshna Loonker
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 6170746
zbMATH Keywords: curvilinear Radon transform
zbMATH Keywords: microlocal analysis
zbMATH Keywords: electron microscopy
zbMATH Keywords: Fourier integral operator
zbMATH Keywords: back projection reconstruction algorithm
MaRDI profile type: Publication
full work available at URL: ipi.2013.7.585
OpenAlex ID: W2080540092
DOI: 10.3934/IPI.2013.7.585
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description: scientific article; zbMATH DE number 6170746