Recovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonics

DOI10.1016/j.jmaa.2018.05.019zbMath1391.44003OpenAlexW2799987248MaRDI QIDQ1635595

Yehonatan Salman

Publication date: 31 May 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.05.019

zbMATH Keywords

inversion formulaFunk transformspherical transformlimited radii

Mathematics Subject Classification ID

Laplace transform (44A10) Volterra integral equations (45D05) Spherical harmonics (33C55)

Cites Work

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• Method of analytic continuation for the inverse spherical mean transform in constant curvature spaces
• A uniform reconstruction formula in integral geometry
• Inversion of the circular Radon transform on an annulus
• Explicit inversion formulae for the spherical mean Radon transform
• Mathematics of thermoacoustic tomography
• Conical Uniqueness Sets for the Spherical Radon Transform
• Image reconstruction from radially incomplete spherical Radon data
• Determining a Function from Its Mean Values Over a Family of Spheres
• On the injectivity of the circular Radon transform
• Inversion of Spherical Means and the Wave Equation in Even Dimensions
• Universal Inversion Formulas for Recovering a Function from Spherical Means
• Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors

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