Unmixing Mineral Spectra Using a Neural Net with Maximum Entropy Regularization

Abstract

Neural nets are widely used in pattern recognition and classification problems. We consider the problem of unmixing mineral spectra as linear combinations of a set of reference spectra. To do this, we train a neural net, the distributed associative memory [DAM], to remember the reference spectra. If the reference spectra are linearly independent, and in particular, if the number of features characterizing the spectra is greater than the number of reference spectra, the DAM technique produces good results. In the case of linear dependency between reference spectra, we reformulate the DAM methodology as a linear inverse problem of estimating a spectral abundance vector from a matrix of reference spectra and an unclassified input spectral mixture. Two techniques are discussed for estimating a response from this implicit DAM: singular value decomposition and a maximum entropy method. In mineral exploration, the number of spectral values measured [the pattern features] is substantially less than the number of possible constituent minerals and the unmixing problem is under determined. These two techniques were used to unmix Geoscan 24-channel imaging spectrometer data and a Thematic Mapper [TM] 6-channel satellite image of Cuprite, Nevada, with promising results.