Iterative regularization with a general penalty term-theory and application to L1 and TV regularization

In this paper, we consider an iterative regularization scheme for linear ill-posed equations in Banach spaces. As opposed to other iterative approaches, we deal with a general penalty functional from Tikhonov regularization and take advantage of the properties of the regularized solutions which where supported by the choice of the specific penalty term. We present convergence and stability results for the presented algorithm. Additionally, we demonstrate how these theoretical results can be applied to L-1- and TV-regularization approaches and close the paper with a short numerical example.