1. A method for analyzing a spectral image of a sample, comprising: a) measuring a spectral image of the sample with a spectroscopic imaging system, whereby the spectral image is represented by a matrix of spectral image data D; b) factoring the matrix of spectral image data D into the product of a matrix of orthogonal scores vectors T and a matrix of orthonormal loading vectors P using Principal Component Analysis; c) determining a rotation matrix R; d) rotating the matrix of orthonormal loading vectors P to provide a simplified loading matrix {tilde over (P)}, according to {tilde over (P)}=PR; and e) inverse rotating the matrix of orthogonal scores vectors T to provide estimated pure-component spectra {tilde over (T)}, according to {tilde over (T)}=TR −1 , and a spatially rotated data matrix D, according to D={tilde over (P)}{tilde over (T)} T .