Abstract
Localized basis set functions related to spherical wave functions are constructed for scalar and vector 3D tomography. The functions are truncated in a spherical domain of radius $r_0$, so that these vanish outside the domain. The analytical form of the respective scalar and vector ray transforms are obtained. So, the inversion algorithm can be reduced to solving the linear system of equations because of orthogonality and completeness of the basis functions.
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