Exact Solutions of One-Dimensional TGV

L2-TGV-regularization has been introduced by Bredies, Kunisch, and Pock. This regularization method requires careful tuning of two regularization parameters. The focus of this paper is to derive analytical results, which allow for characterizing parameter settings, which make this method in fact different from L2-TV (the ROF-model) and L2-TV2 regularization, respectively. In this paper we also provide explicit solutions of TGV-denoising for particular one-dimensional function data.