An inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions
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Publication:2252091
DOI10.1016/j.jmaa.2014.05.007zbMath1302.44002arXiv1208.5739OpenAlexW2022489810MaRDI QIDQ2252091
Publication date: 16 July 2014
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1208.5739
Related Items (16)
Range description for a spherical mean transform on spaces of constant curvature ⋮ The spherical Radon transform with centers on cylindrical surfaces ⋮ Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data ⋮ Image reconstruction from radially incomplete spherical Radon data ⋮ Photoacoustic inversion formulas using mixed data on finite time intervals* ⋮ Explicit Inversion Formulas for the Two-Dimensional Wave Equation from Neumann Traces ⋮ Iterative methods for photoacoustic tomography in attenuating acoustic media ⋮ A Galerkin Least Squares Approach for Photoacoustic Tomography ⋮ Microlocal analysis for spherical Radon transform: two nonstandard problems ⋮ 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 ⋮ On artifacts in limited data spherical Radon transform: curved observation surface ⋮ Recovering the Initial Data of the Wave Equation from Neumann Traces ⋮ Recovering a Function from Circular Means or Wave Data on the Boundary of Parabolic Domains ⋮ The universal back-projection formula for spherical means and the wave equation on certain quadric hypersurfaces ⋮ On the exactness of the universal backprojection formula for the spherical means Radon transform
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- Synthetic aperture inversion
- Determining a Function from Its Mean Values Over a Family of Spheres
- Inversion of Spherical Means and the Wave Equation in Even Dimensions
- Universal Inversion Formulas for Recovering a Function from Spherical Means
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