A very popular algorithm for image processing and image reconstruction with non-differentiable priors is the primal-dual hybrid gradient (PDHG) algorithm proposed by Chambolle and Pock. In some scenarios it is beneficial to employ a stochastic version of this algorithm where not all of the dual updates are executed simultaneously. It turns out that the stochastic version has convergence rates along the same lines as the deterministic PDHG. Numerical results on clinical positron emission tomography (PET) data show a dramatic speed up by the proposed method and thereby the impact this may have on clinical applications. This is joint work with A. Chambolle, P. Markiewicz, P. Richtárik, J. Schott and C. Schoenlieb.