An approximate message passing approach for compressive hyperspectral   imaging using a simultaneous low-rank and joint-sparsity prior
  This paper considers a compressive sensing (CS) approach for hyperspectral data acquisition, which results in a practical compression ratio substantially higher than the state-of-the-art. Applying simultaneous low-rank and joint-sparse (L&S) model to the hyperspectral data, we propose a novel algorithm to joint reconstruction of hyperspectral data based on loopy belief propagation that enables the exploitation of both structured sparsity and amplitude correlations in the data. Experimental results with real hyperspectral datasets demonstrate that the proposed algorithm outperforms the state-of-the-art CS-based solutions with substantial reductions in reconstruction error. 
Yangqing Li and Saurabh Prasad and Wei Chen and Changchuan Yin and Zhu   Han
cs.IT math.IT