Reconstruction from limited data of arc means
type: Item
instance of: scholarly article
title: Reconstruction from limited data of arc means
zbMATH Open document ID: 0961.44004
DOI: 10.1007/BF02510116
author: V. P. Palamodov
published in: The Journal of Fourier Analysis and Applications
publication date: 2001-05-11T00:00:00Z
full work available at URL: https://eudml.org/doc/59629
review text: Let \(f\) be a function in a Euclidean plane with compact support in a half disk \(H\). The local arc problem, i.e. the problem of reconstruction of \(f\) from the data of its integrals over half circles \(A \subset H\) with centers at the diameter of \(H\) is studied: Reduction of the local arc problem to the limited angle problem for the Euclidean Radon transform. Explicit formulae for the reconstruction. Plancherel-type identity that equalizes a weighted \(L_2\)-norm of the original \(f\) with a Sobolev-type norm of its arc mean transform \(Mf\). Microlocal analysis of stability of the reconstruction.
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 86A22
zbMATH DE Number: 1445624
zbMATH Keywords: arc mean transform
zbMATH Keywords: reconstruction
zbMATH Keywords: factorization property
zbMATH Keywords: interpolation
zbMATH Keywords: Plancherel-type theorem
zbMATH Keywords: energy
zbMATH Keywords: audible zone
zbMATH Keywords: microlocal estimate
zbMATH Keywords: local arc problem
zbMATH Keywords: limited angle problem
zbMATH Keywords: Radon transform
zbMATH Keywords: stability
reviewed by: Eberhard Teufel
MaRDI profile type: Publication
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OpenAlex ID: W2071149174
Wikidata QID: Q125939627
description: scientific article; zbMATH DE number 1445624