HyDeFuse: provably convergent denoiser-driven hyperspectral fusion

Abstract Hyperspectral (HS) images provide fine spectral resolution but have limited spatial resolution, whereas multispectral (MS) images capture finer spatial details but have fewer bands. HS–MS fusion aims to integrate HS and MS images to generate a single image with improved spatial and spectral resolution. This is commonly formulated as an inverse problem with a linear forward model. However, reconstructing high-quality images using the forward model alone is challenging, necessitating the use of regularization techniques. In this work, we investigate the paradigm of denoiser-driven regularization, where a powerful off-the-shelf denoiser is used for implicit regularization within an iterative algorithm. This has shown much promise but remains relatively underexplored in HS imaging. The technical challenge lies in designing HS denoisers that can guarantee convergence—while strong denoisers can produce high-quality reconstructions, they may also cause instability or divergence. Specifically, we consider a denoiser-driven fusion algorithm, HyDeFuse, which leverages a class of pseudo-linear denoisers for implicit regularization. We demonstrate how the contraction mapping theorem can be applied to establish global linear convergence of HyDeFuse. Finally, we validate our theoretical findings and present fusion results on publicly available datasets to demonstrate the performance of HyDeFuse.