1. A method for compressing hyperspectral image data having a number of spatial pixels associated with a hyperspectral image, and a number of spectral dimensions associated with each spatial pixel, the method comprising: 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 a maximum error value; verifying whether the set of basis vectors is a set of orthonormal basis vectors if unknown, and if not, converting the set of basis vectors to the set of orthonormal basis vectors, and modifying the coefficients in response to said converting; ranking, using the processor, a magnitude of each of the set of coefficients on a per pixel basis; computing, using the processor, a minimal set of coefficients from the set of coefficients by computing an error associated with one or more subsets of the set of coefficients and selecting coefficients wherein the magnitude is larger over coefficients where the magnitude is smaller, and comparing the error of the one or more subsets with the received maximum error; storing an association between the minimal set of coefficients and a subset of the set of orthonormal basis vectors; and outputting, using the processor, compressed data comprising the minimal set of coefficients for each pixel, the set of orthonormal basis vectors, and the association.