An iterative approach for image fusion with dynamic gradient sparsity and anisotropic spectral–spatial total variation

Image with higher spectral and spatial resolution is extensively used in the field of image processing, such as satellite imaging, medical imaging, and geological exploration. However, it is challenging to obtain the high-resolution multispectral images using existing techniques due to various equipment limitations. In this paper, we develop a novel method based on a variational model for image fusion, which can restore more spatial details as well as preserve favorable spectral information. In this model, the local spectral consistency, dynamic gradient sparsity, and an anisotropic spectral–spatial total variation are combined into an energy minimization problem. Besides, an algorithm based on the framework of alternating direction method of multipliers and the fast iterative shrinkage thresholding algorithm is designed to effectively solve the proposed model and theoretically guarantee the convergence of the algorithm. Furthermore, we observe that there still exist residuals between the low-resolution image and the downsampled computed HR image, which motivates us to propose an iterative strategy to inject more details into the final results. Our method is evaluated via experiments on various datasets collected by different sensors, performing excellently compared with other representative image fusion methods both quantitatively and visually.