  We consider the stable approximation of sparse solutions to non-linear
operator equations by means of Tikhonov regularization with a subquadratic
penalty term. Imposing certain assumptions, which for a linear operator are
equivalent to the standard range condition, we derive the usual convergence
rate $O(\sqrt{\delta})$ of the regularized solutions in dependence of the noise
level $\delta$. Particular emphasis lies on the case, where the true solution
is known to have a sparse representation in a given basis. In this case, if the
differential of the operator satisfies a certain injectivity condition, we can
show that the actual convergence rate improves up to $O(\delta)$.
