Recently, tensors are widely used to represent higher-order data with internal spatial or temporal relations, e.g. images, videos, hyperspectral images (HSIs). While the true signals are usually corrupted by noises, it is of interest to study tensor recovery problems. To this end, many models have been established based on tensor decompositions. Traditional tensor decomposition models, such as the CP and Tucker factorization, treat every mode of tensors equally. However, in many real applications, some modes of the data act differently from the other modes, e.g. channel mode of images, time mode of videos, band mode of HSIs. The recently proposed model called t-SVD aims to tackle such problems. In this paper, we focus on tensor denoising problems. Specifically, in order to obtain low-rank estimators of true signals, we propose to use different shrinkage functions to shrink the tensor singular values based on the t-SVD. We derive Stein’s unbiased risk estimate (SURE) of the proposed model and develop adaptive SURE-based tuning parameter selection procedure, which is totally data-driven and simultaneous with the estimation process. The whole modeling procedure requires only one round of t-SVD. To demonstrate our model, we conduct experiments on simulation data, images, videos and HSIs. The results show that the proposed SURE approximates the true risk function accurately. Moreover, the proposed model selection procedure picks good tuning parameters out. We show the superiority of our model by comparing with state-of-the-art denoising models. The experiments manifest that our model outperforms in both quantitative metrics (e.g. RSE, PSNR) and visualizing results.

最近，张量被广泛用于表示具有内部空间或时间关系的高阶数据，例如图像、视频、高光谱图像 (HSI)。虽然真实信号通常会被噪声破坏，但研究张量恢复问题是很有趣的。为此，已经建立了许多基于张量分解的模型。传统的张量分解模型，例如 CP 和 Tucker 分解，平等地对待每种张量模式。然而，在许多实际应用中，数据的某些模式与其他模式的行为不同，例如图像的通道模式、视频的时间模式、HSI 的波段模式。最近提出的称为 t-SVD 的模型旨在解决这些问题。在本文中，我们专注于张量去噪问题。具体来说，为了获得真实信号的低秩估计，我们建议使用不同的收缩函数来收缩基于 t-SVD 的张量奇异值。我们推导出所提出模型的 Stein 无偏风险估计 (SURE)，并开发了基于自适应 SURE 的调整参数选择程序，该程序完全由数据驱动并与估计过程同步。整个建模过程只需要一轮 t-SVD。为了演示我们的模型，我们对模拟数据、图像、视频和 HSI 进行了实验。结果表明，所提出的 SURE 准确地逼近了真实的风险函数。此外，所提出的模型选择过程会挑选出好的调整参数。我们通过与最先进的去噪模型进行比较来展示我们模型的优越性。实验表明，我们的模型在两个定量指标（例如 RSE、