Multispectral and Hyperspectral Image Fusion With Spectrally Varying Blurs and MM Algorithm

The fusion of multispectral and hyperspectral data allows for restoring data with enhanced spatial and spectral resolutions. In cases of varying spatial blur, the current approach is to solve an ill-posed inverse problem by minimizing a mixed criterion. This minimization commonly involves an iterative gradient-based method. This paper proposes a new algorithm based on the Majorize-Minimize approach to compute the minimizer of a semi-quadratic convex edge-preserving criterion. The proposition relies on a reachable explicit solution of the quadratic majorant without the need to solve a Sylvester equation and for which we developed the proof of existence that was missing in a previous work. We conduct experiments on realistic synthetic measurements for the James Webb Space Telescope and show that our proposed solutions outperform the state-of-the-art in both computation time, achieving a 7000-fold speedup with the closed-form solution, and reconstruction quality, with a 2 dB PSNR improvement for the MM-based solution.