Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double-layer potentials for the wave equation, for domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.

Original languageEnglish (US)
Article number025012
JournalInverse Problems
Volume27
Issue number2
DOIs
StatePublished - Feb 2011

Fingerprint

Wave equations
Prisms
Polyhedron
Polygon
Right prism
Double Layer Potential
Cuboid
Inversion Formula
Pyramid
Rectangle
Filtration
Wave equation
Triangle
Inversion
Valid
Transform
Symmetry

ASJC Scopus subject areas

  • Signal Processing
  • Computer Science Applications
  • Applied Mathematics
  • Mathematical Physics
  • Theoretical Computer Science

Cite this

@article{7f17dbd655664dd8b5848f908768490a,
title = "Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra",
abstract = "We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double-layer potentials for the wave equation, for domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.",
author = "Leonid Kunyansky",
year = "2011",
month = "2",
doi = "10.1088/0266-5611/27/2/025012",
language = "English (US)",
volume = "27",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "2",

}

TY - JOUR

T1 - Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

AU - Kunyansky, Leonid

PY - 2011/2

Y1 - 2011/2

N2 - We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double-layer potentials for the wave equation, for domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.

AB - We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double-layer potentials for the wave equation, for domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.

UR - http://www.scopus.com/inward/record.url?scp=79551655845&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551655845&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/27/2/025012

DO - 10.1088/0266-5611/27/2/025012

M3 - Article

AN - SCOPUS:79551655845

VL - 27

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 2

M1 - 025012

ER -