Gaussian Processes for Estimating Wavelength Position

Many economically important minerals have absorption features in the short-wave infrared (SWIR; 2000-2500 nm). Sensors which measure this part of the spectrum cannot detect the wavelength minimum of a feature at ‘900 nm (F900), indicative of ferric iron mineralogy. A method based on Gaussian processes (GPs) was developed and compared with multiple linear regression (MLR) to estimate the wavelength position of F900 from SWIR data (1002-1355 nm). SWIR data with different signal-to-noise ratios were acquired from crushed rock samples by a nonimaging spectrometer and an imaging spectrometer. GP estimates of wavelength position were converted to the proportion of goethite using coefficients from a regression of the proportion of goethite determined from X-ray diffraction (XRD) on wavelength position measured directly from spectra.

GP-estimated wavelength positions were within the 2-nm and ‘4-nm root-mean-square error of measurements made directly from spectra for nonimaging and imaging spectrometer data, respectively. Proportions of goethite derived from these estimates were respectively within 4% and 6% of the values measured by XRD. MLR performed poorly compared to GPs when applied to data with no added noise and failed when applied to data with added noise or to imaging spectrometer data. These findings indicate that the wavelength position of F900-an indicator of ferric iron mineralogy-can be estimated from data acquired at SWIR wavelengths (1002- 1355 nm). This opens up possibilities for using a single (SWIR) sensor to acquire information on ferric iron mineralogy (using F900) and other minerals with diagnostic absorptions between 1000 and 2500 nm