Hyperspectral measurements from long range sensors can give a detailed
picture of the items, materials, and chemicals in a scene but analysis can be
difficult, slow, and expensive due to high spatial and spectral resolutions of
state-of-the-art sensors. As such, sparsity is important to enable the future
of spectral compression and analytics. It has been observed that environmental
and atmospheric effects, including scattering, can produce nonlinear effects
posing challenges for existing source separation and compression methods. We
present a novel transformation into Hilbert spaces for pruning and constructing
sparse representations via non-negative least squares minimization. Then we
introduce max likelihood compression vectors to decrease information loss. Our
approach is benchmarked against standard pruning and least squares as well as
deep learning methods. Our methods are evaluated in terms of overall spectral
reconstruction error and compression rate using real and synthetic data. We
find that pruning least squares methods converge quickly unlike matching
pursuit methods. We find that Hilbert space pruning can reduce error by as much
as 40% of the error of standard pruning and also outperform neural network
autoencoders