In the past few years, tensor robust principal component analysis (TRPCA) which is based on tensor singular value decomposition (t-SVD) has got a lot of attention in recovering low-rank tensor corrupted by sparse noise. However, most TRPCA methods only consider the global structure of the image, ignoring the local details and sharp edge information of the image, resulting in the unsatisfactory restoration results. In this paper, to fully preserve the local details and edge information of the image, we propose a new TRPCA method by introducing a total generalized variation (TGV) regularization. The proposed method can simultaneously explore the global and local prior information of high-dimensional data. Specifically, the tensor nuclear norm (TNN) is employed to develop the global structure feature. Moreover, we introduce the TGV, a higher-order generalization of total variation (TV), to preserve the local details and edges of the underlying image. Subsequently, the alternating direction method of multiplier (ADMM) algorithm is introduced to solve the proposed model. Sufficient experiments on color images and videos have demonstrated that our method is superior to other comparison methods.

中文翻译：

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用于高维数据恢复的具有总广义变分的张量鲁棒主成分分析


在过去的几年里，基于张量奇异值分解（t-SVD）的张量鲁棒主成分分析（TRPCA）在恢复被稀疏噪声破坏的低秩张量方面受到了广泛的关注。然而，大多数TRPCA方法只考虑图像的全局结构，忽略图像的局部细节和锐利边缘信息，导致恢复结果不理想。在本文中，为了充分保留图像的局部细节和边缘信息，我们通过引入总广义变分（TGV）正则化提出了一种新的TRPCA方法。该方法可以同时探索高维数据的全局和局部先验信息。具体来说，采用张量核范数（TNN）来开发全局结构特征。此外，我们引入了 TGV，即全变分（TV）的高阶概括，以保留底层图像的局部细节和边缘。随后，引入交替方向乘子法（ADMM）算法来求解所提出的模型。对彩色图像和视频的充分实验表明，我们的方法优于其他比较方法。