A series solution and a fast algorithm for the inversion of the spherical mean Radon transform

Research output: Contribution to journalArticle

77 Citations (Scopus)

Abstract

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo-acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centres of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our approach results in an explicit series solution for any closed measuring surface surrounding a region for which the eigenfunctions of the Dirichlet Laplacian are explicitly known - such as, for example, cube, finite cylinder, half-sphere etc. In addition, we present a fast reconstruction algorithm applicable in the case when the detectors (the centres of the integration spheres) lie on a surface of a cube. This algorithm reconstructs 3D images thousands times faster than backprojection-type methods.

Original languageEnglish (US)
JournalInverse Problems
Volume23
Issue number6
DOIs
StatePublished - Dec 1 2007

Fingerprint

Spherical Means
Radon Transform
Radon
Series Solution
radon
Fast Algorithm
Inversion
inversions
Regular hexahedron
Photoacoustic Tomography
Dirichlet Laplacian
Inversion Formula
Reconstruction Algorithm
3D Image
Eigenvalues and eigenfunctions
Tomography
Eigenfunctions
eigenvectors
Closed-form
tomography

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A series solution and a fast algorithm for the inversion of the spherical mean Radon transform. / Kunyansky, Leonid.

In: Inverse Problems, Vol. 23, No. 6, 01.12.2007.

Research output: Contribution to journalArticle

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