Untrained Compact Neural Network Prior for High-Dimension Multispectral and Hyperspectral Data Fusion with Spectrally Varying Blurs

The information in a spectrally degraded dataset (multispectral data) and a spatially degraded one (hyperspectral data) can be processed jointly to reconstruct data with enhanced spatial and spectral resolutions. The problem of multispectral and hyperspectral (MS/HS) data fusion with spatial blurs is an ill-posed inverse problem, commonly solved by minimizing a mixed criterion containing data adequacy terms and a Tikhonov regularization term. However, such regularizations suffer from poor discriminative ability. Instead, the recently proposed Untrained Neural Network Priors (UNNP) have surpassed classical handcrafted priors in most imaging inverse problems without requiring prior learning with a labeled database. Few works have been proposed to solve the MS/HS fusion problem with UNNP, but none have explored the fusion with spectrally-varying spatial blurs. This paper aims to solve the MS/HS fusion problem with high dimension data degraded with spectrally-varying spatial blurs by relying on a simple and compact neural network architecture as prior, made possible by using a dimension reduction model. It demonstrates the superior performances of such a prior against handcrafted priors for the fusion of simulated realistic MS and HS data from the Mid-Infrared Instrument (MIRI) of the James Webb Space Telescope (JWST) in a high noise regime.