GEOMETRIC LOW-RANK TENSOR APPROXIMATION FOR REMOTELY SENSED HYPERSPECTRAL AND MULTISPECTRAL IMAGERY FUSION

Extracting complex spatial information from multispectral imagery (MSI) while maintaining abundant spectral information of hyperspectral imagery (HSI) and injecting them into the fused high-spatio-resolution HSI (HS$^2$I) is crucial for hyperspectral and multispectral (HS--MS) fusion. A common way is to learn low-rank/sparse representations from HSI and MSI, then reconstruct the fused HS$^2$I based on tensor/matrix decomposition or unmixing paradigms, which ignore the intrinsic geometry proximity inherited by low-rank property of the fused HS$^2$I. This study proposes to estimate the high-resolution HS$^2$I via low-rank tensor approximation with geometry proximity as side information learned from MSI and HSI by defined graph signals, which we name GLRTA. Row graph ${\cal G}_r$ and column graph ${\cal G}_c$ are defined on horizontal slice and lateral slice of MSI tensor $\cal M$ respectively, while spectral band graph ${\cal G}_b$ is defined on frontal slice of HSI tensor $\cal H$. By incorporating the learned graphs, the fused HS$^2$I is well estimated via low-rank tensor approximation without the need of the identity observations. Experimental results demonstrate that the proposed GLRTA can effectively improve the reconstruction results compared to other competitive works.