Compressed hyperspectral image recovery via total variation regularization assuming linear mixing

We present an algorithm that exploits the assumption that materials mix linearly in a scene to reconstruct hyperspectral images from compressed hyperspectral imaging data. With endmember spectra known a priori, we propose a simple first-order variant of the projected subgradient method that promotes low spatial variation of each material´s abundance map. Combining the large decrease in computational complexity offered by assuming linear mixing with making search directions conjugate with all previous steps, and taking advantage of the characteristics of large and small steps sizes, we improve run-times by between 3 and 34 times when compared to a similar algorithm that does not assume material mixing. Additionally, the extra information provided by the material spectra typically grants improved reconstruction fidelities, particularly when the original measurements are corrupted by noise.