SPECT/CT registration with the DCC and MC simulations for SPECT imaging

We want to perform the attenuation correction in the case of 3D attenuated ray transform with a parallel geometry. We suppose that the attenuation function is available but not registered with the data. We use the sum on each slice of the 2D data consistency conditions of the attenuated Radon transform to register the attenuation function with the data. We then correct for the attenuation using the Novikov formula. We show numerical experiments indicating the feasibility of the approach and propose a scheme including the diffusion correction for the registration of CT to SPECT for SPECT imaging improvement.