Super-Resolution Hyperspectral Reconstruction With Majorization-Minimization Algorithm and Low-Rank Approximation

Hyperspectral imaging (HSI) has become an invaluable imaging tool for many applications in astrophysics or Earth observation. Unfortunately, direct observation of hyperspectral images is impossible since the actual measurements are 2-D and suffer from strong spatial and spectral degradations, especially in the infrared. We present in this work an original method for high-resolution hyperspectral image reconstruction from heterogeneous 2-D measurements degraded by integral field spectroscopy (IFS) instrument. A fundamental part of this work is developing a forward model that accounts for the limitations of the IFS instrument, such as wavelength-dependent spatial and spectral blur, subsampling, and inhomogeneous sampling steps. The reconstruction method inverts the forward model using a deterministic regularization framework for edge-preserving. It fuses information from different observations and spectral bands for resolution enhancements. We rely on the Majorize-Minimize memory gradient (3MG) optimization algorithm to solve the inverse problem while considering a low-rank approximation for the unknown to handle the high-dimensionality of the problem.