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 dictionaries 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 as FFD) for HR-MSI and LR-HSI via subpixel-shift decomposition. In this method, through a 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 firstly, to replace the use of spatial dictionaries. Subsequently, a new fusion model is constructed based on this decomposition incorporating with the constraints of low-rank and sparsity, and especially, a low-rank term is introduced to constraint 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 sub-images 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.