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.

翻译：本文提出一种二阶全广义变分（TGV）的新型离散化方法，该方法相较于现有离散公式具有若干显著特性。该模型基于Condat离散全变分模型（《SIAM影像科学杂志》，10(3)，1258–1290，2017）相同的设计原理构建，并继承其优势，尤其在成像问题求解中展现出更优的质量。针对采用新离散化方案的二阶TGV图像去噪问题，本文提出相应算法。数值实验验证了该离散化方案的优越性。此外，为比较新模型的旋转不变性，本文给出了基于该离散化模型的TGV值计算算法。