1. A computer implemented method 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, the method comprising: receiving, using a processor, the 3D hyperspectral image data, a set of basis vectors associated therewith, and a maximum error amount; partitioning, using the processor, 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; ranking, using the processor, the set of basis vectors if not already ranked; iteratively applying a lossy compression to the plurality of 2D images using the processor, starting with 2D images associated with a lowest ranked basis vector, as compressed 2D images; comparing, using the processor, an error associated with the compressed 2D images with the maximum error amount, to maximize an amount of volume compression within the maximum error amount; and, setting aside, using the processor, pixels of the 2D images with errors exceeding the maximum error amount.