Abstract
We propose the reconstruction of the solenoidal part of a vector field supported in the unit ball in 3 dimensions by using cone beam data from a curve surrounding it, and this curve satisfies the Tuy's condition of order 3. We use the quaternionic inversion formula to decompose the solenoidal part of a vector field into 2 parts. To recover the first one, which is the main part of the solenoidal component, another definition of a cone beam transform containing both Doppler and transverse data will be introduced. The second part will be reconstructed by using information from the first part as in Katsevich and Schuster's work with less data.
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