Variational EM approach for high resolution hyper-spectral imaging based on probabilistic matrix factorization

High resolution hyper-spectral imaging works as a scheme to obtain images with high spatial and spectral resolutions by merging a low spatial resolution hyper-spectral image (HSI) with a high spatial resolution multi-spectral image (MSI). In this paper, we propose a novel method based on probabilistic matrix factorization under Bayesian framework: First, Gaussian priors, as observations' distributions, are given upon two HSI-MSI-pair-based images, in which two variances share the same hyper-parameter to ensure fair and effective constraints on two observations. Second, to avoid the manual tuning process and learn a better setting automatically, hyper-priors are adopted for all hyper-parameters. To that end, a variational expectation-maximization (EM) approach is devised to figure out the result expectation for its simplicity and effectiveness. Exhaustive experiments of two different cases prove that our algorithm outperforms many state-of-the-art methods.