CroDoSR: Tensor Cross-Domain Rank for Hyperspectral Image Super-Resolution

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.