Methods for compressing hyperspectral image data include receiving sets of coefficients associated with each pixel of the hyperspectral image data, a set of basis vectors utilized to generate the dimensionally reduced data from the hyperspectral image, and either a maximum error value or maximum data size. The methods include associating the coefficients with a subset of the basis vectors, and storing the association. Methods of decompressing the compressed hyperspectral image data are also disclosed, utilizing the association.