Reconstruction of Hyperspectral Imagery From Random Projections Using Multihypothesis Prediction

Abstract—Reconstruction of hyperspectral imagery from spec-tral random projections is considered. Specifically, multiple predictions drawn for a pixel vector of interest are made from spa-tially neighboring pixel vectors within an initial non-predicted re-construction. A two-phase hypothesis-generation procedure based on partitioning and merging of spectral bands according to the correlation coefficients between bands is proposed to fine-tune the hypotheses. The resulting prediction is used to generate a residual in the projection domain. This residual being typically more compressible than the original pixel vector leads to improved reconstruction quality. To appropriately weight the hypothesis predictions, a distance-weighted Tikhonov regularization to an ill-posed least-squares optimization is proposed. Experimental re-sults demonstrate that the proposed reconstruction significantly outperforms alternative strategies not employing multihypothesis prediction. Index Terms—Compressed sensing, hyperspectral data, mul-tihypothesis prediction, principal component analysis, Tikhonov regularization. I