Hyperspectral and Multispectral Image Fusion Based on Local Low Rank and Coupled Spectral Unmixing

Hyperspectral images (HSIs) usually have high spectral and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolution. The fusion of HSI and MSI aims to create spectral images with high spectral and spatial resolution. In this paper, we propose a fusion algorithm by combining linear spectral unmixing with the local low-rank property. By taking advantage of the local low-rank property, we first partition the corresponding spectral image into patches. For each patch pair, we cast the fusion problem as a coupled spectral unmixing problem that extracts the abundance and the endmembers of MSI and HSI, respectively. It then updates the abundance and the endmember through an alternating update algorithm. In fact, the convergence of the alternative update algorithm can be mathematically and empirically supported. We also propose a multiscale postprocessing procedure to combine fusion results obtained under different patch sizes. In experiments on three data sets, the proposed fusion algorithms outperformed state-of-the-art fusion algorithms in both spatial and spectral domains.