Fast-ion Dα (FIDA) and collective Thomson scattering (CTS) diagnostics provide indirect measurements of fastion velocity distribution functions in magnetically confined plasmas. Here we present the first prescription for
velocity-space tomographic inversion of CTS and FIDA measurements that can use CTS and FIDA measurements
together and that takes uncertainties in such measurements into account. Our prescription is general and could
be applied to other diagnostics. We demonstrate tomographic reconstructions of an ASDEX Upgrade beam ion
velocity distribution function. First, we compute synthetic measurements from two CTS views and two FIDA
views using a TRANSP/NUBEAM simulation, and then we compute joint tomographic inversions in velocity-space from these. The overall shape of the 2D velocity distribution function and the location of the maxima at full and half beam injection energy are well reproduced in velocity-space tomographic inversions, if the noise level in the measurements is below 10%. Our results suggest that 2D fast-ion velocity distribution functions can be directly inferred from fast-ion measurements and their uncertainties, even if the measurements are taken with different diagnostic methods