In this paper, we investigate a low-complexity scheme for decoding compressed hyperspectral image data. We have exploited the simplicity of the subgradient method by modifying a total variation-based regularization problem to include a residual constraint, employing convex optimality conditions to provide equivalency between the original and reformed problem statements. A scheme that utilizes spectral smoothness by calculating informed starting points to improve the rate of convergence is introduced. We conduct numerical experiments, using both synthetic and real hyperspectral data, to demonstrate the effectiveness of the reconstruction algorithm and the validity of our method for exploiting spectral smoothness. Evidence from these experiments suggests that the proposed methods have the potential to improve the quality and run times of the future compressed hyperspectral image reconstructions.

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.