Block-based spectral image reconstruction for compressive spectral imaging using smoothness on graphs

A novel reconstruction method for compressive spectral imaging is designed by assuming that the spectral image of interest is sufficiently smooth on a collection of graphs. Since the graphs are not known in advance, we propose to infer them from a panchromatic image using a state-of-the-art graph learning method. Our approach leads to solutions with closed-form that can be found efficiently by solving multiple sparse systems of linear equations in parallel. Extensive simulations and an experimental demonstration show the merits of our method in comparison with traditional methods based on sparsity and total variation and more recent methods based on low-rank minimization and deep-based plug-and-play priors. Our approach may be instrumental in designing efficient methods based on deep neural networks and covariance estimation.