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Robust Low-Rank Tensor Minimization via a New Tensor Spectral k -Support Norm

机译:通过新的张光谱k -support规范稳健的低秩张力最小化

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Recently, based on a new tensor algebraic framework for third-order tensors, the tensor singular value decomposition (t-SVD) and its associated tubal rank definition have shed new light on low-rank tensor modeling. Its applications to robust image/video recovery and background modeling show promising performance due to its superior capability in modeling cross-channel/frame information. Under the t-SVD framework, we propose a new tensor norm called tensor spectral k-support norm (TSP-k) by an alternative convex relaxation. As an interpolation between the existing tensor nuclear norm (TNN) and tensor Frobenius norm (TFN), it is able to simultaneously drive minor singular values to zero to induce low-rankness, and to capture more global information for better preserving intrinsic structure. We provide the proximal operator and the polar operator for the TSP-k norm as key optimization blocks, along with two showcase optimization algorithms for medium- and large-size tensors. Experiments on synthetic, image and video datasets in medium and large sizes, all verify the superiority of the TSP-k norm and the effectiveness of both optimization methods in comparison with the existing counterparts.
机译:最近,基于新的张量代数框架用于三阶张量,张量奇异值分解(T-SVD)及其相关的管腿级定义在低级张量模型上具有新的光。它的应用于强大的图像/视频恢复和后台建模显示出的性能,因为它在建模交叉通道/帧信息中的卓越能力。在T-SVD框架下,我们通过替代凸松弛提出称为张量谱k载体标准(TSP-K)的新张量标量。作为现有张量核标准(TNN)和张量Frobenius规范(TFN)之间的插值,能够同时驱动较小的奇异值以归零以诱导低秩率,并捕获更好的全局信息以更好地保持内在结构。我们为TSP-K标准提供了近端运算符和极性运算符作为键优化块,以及两个展示优化算法,用于中型和大尺寸张量。中等尺寸合成,图像和视频数据集的实验,均验证了TSP-K标准的优越性以及与现有对应物相比的优化方法的有效性。

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