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The Vertical Slice Transform in Spherical Tomography
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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.
Forward citations
Cited by 2 Pith papers
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On Two Families of Funk-Type Transforms
For centers outside the sphere, the shifted Funk transform reduces, via a Möbius change of variables, to a parallel slice transform, yielding exact injectivity and inversion results.
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Towards Better Spherical Sliced-Wasserstein Distance Learning with Data-Adaptive Discriminative Projection Direction
DSSW applies data-adaptive weights to spherical projection directions and outperforms unweighted spherical sliced-Wasserstein baselines on several learning tasks.
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