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Robust Low-Rank Tensor Minimization via a New Tensor Spectral k-Support Norm.
IEEE Transactions on Image Processing ( IF 10.6 ) Pub Date : 2019-10-15 , DOI: 10.1109/tip.2019.2946445 Jian Lou , Yiu-Ming Cheung
IEEE Transactions on Image Processing ( IF 10.6 ) Pub Date : 2019-10-15 , DOI: 10.1109/tip.2019.2946445 Jian Lou , Yiu-Ming Cheung
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.
中文翻译:
通过新的Tensor Spectral k-Support范数实现稳健的低秩张量最小化。
最近,基于用于三阶张量的新张量代数框架,张量奇异值分解(t-SVD)及其相关的输卵管等级定义为低等级张量建模提供了新的思路。由于其在跨通道/帧信息建模方面的卓越能力,其在强大的图像/视频恢复和背景建模中的应用显示出令人鼓舞的性能。在t-SVD框架下,我们提出了一种新的张量范数,称为张量谱k-支持范数(TSP-k)。作为现有张量核规范(TNN)和张量Frobenius规范(TFN)之间的插值,它能够同时将较小的奇异值驱动为零以引起低秩,并捕获更多全局信息以更好地保留固有结构。我们为TSP-k范数提供了近端算子和极点算子作为关键优化块,并为中型和大型张量提供了两种展示优化算法。在中型和大型尺寸的合成,图像和视频数据集上进行的实验均证明了TSP-k规范的优越性以及与现有同类软件相比这两种优化方法的有效性。
更新日期:2020-04-22
中文翻译:
通过新的Tensor Spectral k-Support范数实现稳健的低秩张量最小化。
最近,基于用于三阶张量的新张量代数框架,张量奇异值分解(t-SVD)及其相关的输卵管等级定义为低等级张量建模提供了新的思路。由于其在跨通道/帧信息建模方面的卓越能力,其在强大的图像/视频恢复和背景建模中的应用显示出令人鼓舞的性能。在t-SVD框架下,我们提出了一种新的张量范数,称为张量谱k-支持范数(TSP-k)。作为现有张量核规范(TNN)和张量Frobenius规范(TFN)之间的插值,它能够同时将较小的奇异值驱动为零以引起低秩,并捕获更多全局信息以更好地保留固有结构。我们为TSP-k范数提供了近端算子和极点算子作为关键优化块,并为中型和大型张量提供了两种展示优化算法。在中型和大型尺寸的合成,图像和视频数据集上进行的实验均证明了TSP-k规范的优越性以及与现有同类软件相比这两种优化方法的有效性。