A Fast Fusion Method for Multi- and Hyperspectral Images via Subpixel-Shift Decomposition

Several spectral and spatial dictionary-based methods exist for fusing a high-spatial-resolution multispectral image (HR-MSI) with a low-spatial-resolution hyperspectral image (LR-HSI). However, using only one type of dictionary is insufficient to preserve spatial and spectral information simultaneously, while utilizing both dictionaries would increase the computational costs. To address this problem, we propose a fast fusion method (called FFD) for HR-MSIs and LR-HSIs via subpixel-shift decomposition. In this method, through joint optimization of low rank and sparsity within the framework of subpixel shift and sparse representation, an ultimate spectral dictionary is acquired along with its associated coefficients. Specifically, the HR-MSI is decomposed into subimage sequences of the same spatial resolution as the LR-HSI first, to replace the use of spatial dictionaries. Subsequently, a new fusion model is constructed based on this decomposition incorporating the constraints of low rank and sparsity, and especially, a low-rank term is introduced to constrain the spectral consistency along the decomposition direction. Then, the model is theoretically derived by using the alternating direction method of multipliers (ADMM) method, and a joint optimization for the spectral dictionary and its sparse coefficients is obtained. Finally, the desired HR-HSI can be reconstructed by using the above fused subimages through a simple inversed composition. Experimental results on different datasets show that compared with the other related methods, our proposed FFD can achieve an equivalent fusion effect to the best of them in a much shorter time.