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：本文提出了一种新的二阶全广义变分（TGV）离散化方法，与现有离散模型相比具有若干独特性质。该模型基于与Condat离散全变分模型（《SIAM影像科学杂志》，10(3)，1258--1290，2017）相同的设计原则，并继承了其优势，特别是在成像问题求解质量方面的提升。我们提出了一种基于该新型离散化方案、采用二阶TGV的图像去噪算法。该算法的数值结果验证了所提离散化方案的优越性。此外，为比较新模型的旋转不变性，本文还给出了计算该离散化模型下TGV值的算法。