A key task of tomography lies in the reconstruction of a three-dimensional object given information about projections to two-dimensional manifolds. An additional challenge comes in when not only the object but also its motion needs to be estimated from the data. In this extended abstract, we review the well-known common line method for motion detection in the parallel beam computed tomography and its counterpart for the diffraction tomography of scattering objects, the common circle method. For the latter, we present numerical simulations with noisy data.