Method of analytic continuation for the inverse spherical mean transform in constant curvature spaces

DOI10.1007/s11854-012-0046-yzbMath1276.44002OpenAlexW2014174361MaRDI QIDQ355975

Boris Rubin, Ricardo Estrada, Yuri A. Antipov

Publication date: 25 July 2013

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-012-0046-y

zbMATH Keywords

inverse problemCauchy problemconstant curvatureanalytic continuationEuler-Poisson-Darboux equationinversion formulaespherical mean Radon transformspherical Radon transform

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Euler-Poisson-Darboux equations (35Q05) Analytic continuation of functions of one complex variable (30B40)

Related Items (12)

Generalized spherical mean value operators on Euclidean space ⋮ Range description for a spherical mean transform on spaces of constant curvature ⋮ Diagonal spherical means ⋮ Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data ⋮ Recovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonics ⋮ Support theorems for Funk-type isodistant Radon transforms on constant curvature spaces ⋮ Image reconstruction from radially incomplete spherical Radon data ⋮ The vertical slice transform on the unit sphere ⋮ Numerical inversion and uniqueness of a spherical Radon transform restricted with a fixed angular span ⋮ Recovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinates ⋮ Recovering finite parametric distributions and functions using the spherical mean transform ⋮ An efficient numerical algorithm for the inversion of an integral transform arising in ultrasound imaging

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