Lossless algorithm for hyperspectral imaging
I have played with SVD for 3 channel image lossy compression in the past, which prompted me to do a quick search and found the following paper which may help you out.
Randomized SVD Methods in Hyperspectral Imaging

Abstract
We present a randomized singular value decomposition (rSVD) method for the purposes of lossless compression, reconstruction, classification, and target detection with hyperspectral (HSI) data. Recent work in low-rank matrix approximations obtained from random projections suggests that these approximations are well suited for randomized dimensionality reduction. Approximation errors for the rSVD are evaluated on HSI, and comparisons are made to deterministic techniques and as well as to other randomized low-rank matrix approximation methods involving compressive principal component analysis. Numerical tests on real HSI data suggest that the method is promising and is particularly effective for HSI data interrogation.