Inversion of Spherical Means and the Wave Equation in Even Dimensions

By Markus Haltmeier, David V. Finch, Rakesh. SIAM Journal on Applied Mathematics, 2007

295 citations recorded by the source corpus.

We establish inversion formulas of the so-called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several formulas to recover initial data of the form $(f,0)$ (or $(0,g)$) for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball, provided that the initial data has support in the ball.

Subfields: Biomedical Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/96004471b65b0d9aba3e36e6849fe547382748fd

How researchers see this paper

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In Biomedical Engineering

1. Peter Kuchment
2. Leonid A. Kunyansky

In Mathematical Physics

1. Leonid A. Kunyansky
2. Peter Kuchment
3. Konstantin Pankrashkin
4. Nicolas Popoff

Citations in the corpus

• Mathematics of thermoacoustic tomography (2007, methodology): “Denoting by g, as before the spherical integrals (rather than averages) of f, the formulas of [37] in 2D look as follows:”