  The aim of this paper is to test and analyze a novel technique for image
reconstruction in positron emission tomography, which is based on (total
variation) regularization on both the image space and the projection space. We
formulate our variational problem considering both total variation penalty
terms on the image and on an idealized sinogram to be reconstructed from a
given Poisson distributed noisy sinogram. We prove existence, uniqueness and
stability results for the proposed model and provide some analytical insight
into the structures favoured by joint regularization.
  For the numerical solution of the corresponding discretized problem we employ
the split Bregman algorithm and extensively test the approach in comparison to
standard total variation regularization on the image. The numerical results
show that an additional penalty on the sinogram performs better on
reconstructing images with thin structures.
