Hyperspectral image super-resolution (HSI SR) aims to combine the detailed spectral information of hyperspectral images with the spatial resolution of multispectral images, thus enhancing the ability to extract valuable insights across various applications. Recently, the tensor singular value decomposition (t-SVD) has emerged as a powerful tool and has been introduced into the HSI SR field for exploring low-rank prior information. For t-SVD, the domain transform is crucial to acquiring more low-rank data characteristics. Nevertheless, previous efforts on domain transform have only involved the single transformed domain (i.e., single domain), while ignoring the potential pursuing the lower rankness in multiple successional transformed domains, termed cross-domain (CD). In this article, we propose a novel CD-based t-SVD and define the corresponding tensor CD rank based on a pivotal observation, i.e., the low-rank behavior of HSI in CD is more significant than that in single domain. More specifically, we first define a successional linear transform (SLT) to establish the CD concept, then develop a novel CD-based t-SVD and tensor CD rank, and theoretically deduce a new tensor CD-nuclear norm as the convex approximation of CD rank. Equipped with such a CD rank, we thus formulate a CD-rank-constrained minimization model for the HSI SR task, called CroDoSR, which is effectively solved by the alternating direction method of multipliers (ADMMs). Comprehensive experiments on several widely used datasets evidently demonstrate the superiority of the proposed CroDoSR method.

中文翻译：

---

CroDoSR：高光谱图像超分辨率的张量跨域排名


高光谱图像超分辨率（HSI SR）旨在将高光谱图像的详细光谱信息与多光谱图像的空间分辨率相结合，从而增强在各种应用中提取有价值的见解的能力。最近，张量奇异值分解（t-SVD）已成为一种强大的工具，并被引入 HSI SR 领域，用于探索低秩先验信息。对于 t-SVD，域变换对于获取更多低秩数据特征至关重要。然而，先前关于域变换的努力仅涉及单个变换域（即，单个域），而忽略了在多个连续变换域中追求较低等级的潜力，称为跨域（CD）。在本文中，我们提出了一种新颖的基于 CD 的 t-SVD，并根据一个关键观察定义了相应的张量 CD 秩，即 HSI 在 CD 中的低秩行为比在单域中更显着。更具体地说，我们首先定义连续线性变换（SLT）来建立 CD 概念，然后开发一种新颖的基于 CD 的 t-SVD 和张量 CD 秩，并从理论上推导出新的张量 CD-核范数作为 CD 的凸近似秩。配备这样的CD等级，我们因此为HSI SR任务制定了CD等级约束的最小化模型，称为CroDoSR，它可以通过乘子交替方向法（ADMM）有效地解决。对几个广泛使用的数据集的综合实验明显证明了所提出的 CroDoSR 方法的优越性。