A method for reducing dimensionality of hyperspectral images may include receiving a hyperspectral image having a plurality of pixels. A basis vector set including a number of members may then be established, wherein each of the members comprises a basis vector. For each of the plurality of pixels, a spectral vector for the pixel may be read and decomposed with the members of the basis vector set to derive a residual vector for the pixel. A basis vector for the pixel may then be added to the members of the basis vector set if the residual vector for the pixel has a magnitude exceeding a predetermined threshold, and the basis vector set may then be optimized to eliminate one of the members of the basis vector set, whereby the optimized basis vector set includes the number of members. A system configured to perform the method may also be provided.