  Focus of this work is solving a non-smooth constraint minimization problem by
a primal-dual splitting algorithm involving proximity operators. The problem is
penalized by the Bregman divergence associated with the non-smooth total
variation (TV) functional.
  We analyse two aspects: Firstly, the convergence of the regularized solution
of the minimization problem to the minimum norm solution. Second, the
convergence of the iteratively regularized minimizer to the minimum norm
solution by a primal-dual algorithm. For both aspects, we use the assumption of
a variational source condition (VSC). This work emphasizes the impact of the
choice of the parameters in stabilization of a primal-dual algorithm. Rates of
convergence are obtained in terms of some concave, positive definite index
function.
  The algorithm is applied to a simple two dimensional image processing
problem. Sufficient error analysis profiles are provided based on the size of
the forward operator and the noise level in the measurement.
