The Vertical Slice Transform in Spherical Tomography

Abstract

The vertical slice transform takes a function on the n-dimensional unit sphere to integrals of that function over spherical slices parallel to the last coordinate axis. This transform arises in thermoacoustic tomography. We obtain new inversion formulas for the vertical slice transform and its singular value decomposition. The results can be applied to the inverse problem for the Euler-Poisson-Darboux equation associated to the corresponding spherical means.

19 pages

Cited by in corpus (2)

• The Funk-Radon transform for hyperplane sections through a common point
• Reconstruction of functions on the sphere from their integrals over hyperplane sections