A constrained formulation for compressive spectral image reconstruction using linear mixture models

Recent hyperspectral imaging systems are constructed on the idea of compressive sensing for efficient acquisition. However, the traditional reconstruction model in compressive hyperspectral imaging has a high computational complexity. In this work, compressive hyperspectral imaging and unmixing are combined for hyperspectral reconstruction in a low-complexity scheme. The compressed hyperspectral measurements are acquired with a single pixel spectrometer. The reconstruction model is represented in a space of lower dimension named linear mixture model. Hyperspectral reconstruction is then formulated as a nonnegative matrix factorization problem with respect to the endmembers and abundances, bypassing high-complexity tasks involving the hyperspectral data cube itself. The nonnegative matrix factorization problem is solved by combining an alternating least-squares based estimation strategy with the alternating direction method of multipliers. The estimated performance of the proposed scheme is illustrated in experiments conducted on a simulated acquisition in real data outperforming in 3dB the state-of-the-art reconstruction algorithms.