A Second-Order TGV Discretization with $90^{\circ}$ Rotational Invariance Property

Abstract

In this work, we propose a new discretization for second-order total generalized variation (TGV) with some distinct properties compared to existing discrete formulations. The introduced model is based on same design principles as Condat's discrete total variation model (\textit{SIAM J. Imaging Sci}., 10(3), 1258--1290, 2017) and shares its benefits, in particular, improved quality for the solution of imaging problems. An algorithm for image denoising with second-order TGV using the new discretization is proposed. Numerical results obtained with this algorithm demonstrate the discretization's advantages. Moreover, in order to compare invariance properties of the new model, an algorithm for calculating the TGV value with respect to the new discretization model is given.