  Measuring the error by an l^1-norm, we analyze under sparsity assumptions an
l^0-regularization approach, where the penalty in the Tikhonov functional is
complemented by a general stabilizing convex functional. In this context,
ill-posed operator equations Ax = y with an injective and bounded linear
operator A mapping between l^2 and a Banach space Y are regularized. For sparse
solutions, error estimates as well as linear and sublinear convergence rates
are derived based on a variational inequality approach, where the
regularization parameter can be chosen either a priori in an appropriate way or
a posteriori by the sequential discrepancy principle. To further illustrate the
balance between the l^0-term and the complementing convex penalty, the
important special case of the l^2-norm square penalty is investigated showing
explicit dependence between both terms. Finally, some numerical experiments
verify and illustrate the sparsity promoting properties of corresponding
regularized solutions.
