A faceted prior for scalable wideband computational imaging

Hyperspectral images exhibit strong spectral correlations, which can be exploited via a low-rankness and joint-sparsity prior when reconstructed from incomplete and noisy measurements. A state-of-the-art solution consists in using a regularization term based on both the l2,1 and the nuclear norms, which however does not scale well with large numbers of spectral channels and huge image sizes. To alleviate this issue, we propose a parallelizable faceted low-rankness and joint-sparsity prior to improve the scalability of the associated imaging algorithm while preserving its reconstruction performance and better promoting local spectral correlations. We illustrate our approach on synthetic data in the context of radio-astronomy.