Computer implemented methods for compressing 3D hyperspectral image data having a plurality of spatial pixels associated with a hyperspectral image, and a number of spectral dimensions associated with each spatial pixel, include receiving, using a processor, the 3D hyperspectral image data, a set of basis vectors associated therewith, and either a maximum error amount or a maximum data size. The methods also include partitioning the 3D hyperspectral image data into a plurality of 2D images, each associated with one of the number of spectral dimensions, and an associated one of the set of basis vectors. The methods additionally include ranking the set of basis vectors if not already ranked. The methods may further include iteratively applying lossy compression to the 2D images, in an order determined by the ranking. Other embodiments and features are also disclosed.