Patent ID: 7451173

Claim:
A fast combinatorial algorithm for estimating the pure component spectra and concentrations in multivariate spectral images by solving a multiple right-hand-side least squares problem AX=B, subject to a set of equality constraints E j X j =F j, j=1, 2, . . . , n, wherein A is an m×p matrix containing an m-channel pure component spectrum for each of p chemical components. B is an m×n matrix containing an m-channel spectrum observed at each of n pixels, and X is an p×n matrix containing the p pure component concentrations to be estimated at each of the n pixels in a sample image, comprising: a) computing constant parts of the pseudoinverse of A; b) partitioning column indices C of B into q column subsets C k corresponding to q unique constraint matrices E k , k=1, 2, . . . , q; c) choosing a column subset to be a particular subset C k corresponding to a k th unique constraint that has not yet been solved; d) forming a general set of linear equations using the constant parts of the pseudoinverse and the constraint matrices E k and F k for the column subset ; e) factoring the coefficient matrix of the general set of linear equations to provide an equivalent triangular set of linear equations; f) solving the triangular set of linear equations for the j th column vector of X for a j in the column subset g) repeating step f) until all column vectors of X corresponding to the column subset have been solved for; and h) repeating steps c) through g) for a next column subset until all q column subsets have been solved for, thereby providing a solution matrix {circumflex over (X)} of estimated component concentrations at the n pixels in the image.