Iterative thresholding algorithms

This article provides a variational formulation for hard and firm thresholding. A related functional can be used to regularize inverse problems by sparsity constraints. We show that a damped hard or firm thresholded Landweber iteration converges to its minimizer. This provides an alternative to an algorithm recently studied by the authors. We prove stability of minimizers with respect to the parameters of the functional by means of Γ-convergence. All investigations are done in the general setting of vector-valued (multi-channel) data.