Subspace-based coupled tensor decomposition for hyperspectral blind fusion

Fusing hyperspectral images (HSIs) and multispectral images (MSIs) is a widely employed technique for obtaining high spatial resolution HSIs (HR-HSIs). Many Tucker decomposition-based methods have been proposed and achieved commendable performance. However, the spatial-spectral correlation of HSIs may not be fully leveraged. To address this issue, we initially divide the HR-HSI into a coefficient tensor and a dictionary by utilizing its spectral correlation. Then, the coefficient tensor is further decomposed into three factor tensors through triple decomposition, which not only fully explores the spatial structure of the image, but also reduces the dimensionality of the problem. Meanwhile, a triple rank dynamic update scheme is proposed for avoiding cumbersome parameter tuning processes. Additionally, the degradation operators can be updated as dictionaries within the framework of triple decomposition, rendering our approach applicable in blind fusion scenarios. Furthermore, nonlocal self-similarity is utilized to cluster similar cubes together, reinforcing the low-rank prior of the data, then we minimize tensor average rank by developing an equivalent surrogate function with a difference of convex (DC) structure. An effective Gauss-Seidel difference of convex algorithm (GS-DCA) is presented to solve the proposed model. Finally, we provide a detailed convergence analysis of each algorithm based on Kurdyka-Lojasiewicz (KL) property. Extensive numerical experiments on hyperspectral datasets verify the effectiveness of our method.