  Fusing hyperspectral images (HSIs) with multispectral images (MSIs) has
become a mainstream approach to enhance the spatial resolution of HSIs. Many
HSI-MSI fusion methods have achieved impressive results. Nevertheless, certain
challenges persist, including: (a) A majority of current methods rely on
accurate registration of HSI and MSI, which can be challenging in real-world
applications.(b) The obtained HSI-MSI pairs may not be fully utilized. In this
paper, we propose a hybrid registration and fusion constrained optimization
model named RAF-NLRGS. With respect to challenge (a), the RAF model integrates
batch image alignment within the fusion process, facilitating simultaneous
execution of image registration and fusion. To address issue (b), the NLRGS
model incorporates a nonconvex low-rank and group-sparse structure, leveraging
group sparsity to effectively harness valuable information embedded in the
residual data. Moreover, the NLRGS model can further enhance fusion performance
based on the RAF model. Subsequently, the RAF-NLRGS model is solved within the
framework of Generalized Gauss-Newton (GGN) algorithm and Proximal Alternating
Optimization (PAO) algorithm. Theoretically, we establish the error bounds for
the NLRGS model and the convergence analysis of corresponding algorithms is
also presented. Finally, extensive numerical experiments on HSI datasets are
conducted to verify the effectiveness of our method.
