  We propose and analyze an accelerated iterative dual diagonal descent
algorithm for the solution of linear inverse problems with general
regularization and data-fit functions. In particular, we develop an inertial
approach of which we analyze both convergence and stability. Using tools from
inexact proximal calculus, we prove early stopping results with optimal
convergence rates for additive data-fit terms as well as more general cases,
such as the Kullback-Leibler divergence, for which different type of proximal
point approximations hold.
