Recently, tensor singular value decomposition (t-SVD) has emerged as a promising tool for hyperspectral image (HSI) processing. In the t-SVD, there are two key building blocks: (i) the low-rank enhanced transform and (ii) the accompanying low-rank characterization of transformed frontal slices. Previous t-SVD methods mainly focus on the developments of (i), while neglecting the other important aspect, i.e., the exact characterization of transformed frontal slices. In this letter, we exploit the potentiality in both building blocks by leveraging the \underline{\bf H}ierarchical nonlinear transform and the \underline{\bf H}ierarchical matrix factorization to establish a new \underline{\bf T}ensor \underline{\bf F}actorization (termed as H2TF). Compared to shallow counter partners, e.g., low-rank matrix factorization or its convex surrogates, H2TF can better capture complex structures of transformed frontal slices due to its hierarchical modeling abilities. We then suggest the H2TF-based HSI denoising model and develop an alternating direction method of multipliers-based algorithm to address the resultant model. Extensive experiments validate the superiority of our method over state-of-the-art HSI denoising methods.

翻译：近年来，张量奇异值分解（t-SVD）已成为高光谱图像（HSI）处理中一种有前景的工具。t-SVD包含两个关键组成部分：（i）低秩增强变换，以及（ii）变换后正面切片的伴随低秩表征。以往t-SVD方法主要关注（i）的发展，而忽视了另一重要方面，即变换后正面切片的精确表征。在本快报中，我们通过利用层次非线性变换和层次矩阵分解来挖掘两方面的潜力，建立了一种新的张量分解方法（称为H2TF）。与浅层对应方法（如低秩矩阵分解或其凸替代方法）相比，H2TF因其层次建模能力而能更好地捕捉变换后正面切片的复杂结构。随后，我们提出基于H2TF的HSI去噪模型，并开发了一种基于交替方向乘子法的算法来求解该模型。大量实验验证了我们的方法相对于最先进HSI去噪方法的优越性。