Restricted total least squares solutions for hyperspectral imagery

Hyperspectral image processing is a pixel-by-pixel approach to the detection and localization of features by spectral analysis techniques. Usually, partial knowledge about the feature, noise, and clutter spectra are provided, and the problem is to 'unmix' each pixel, or to estimate the relative concentrations of the reference spectra on a per pixel basis. A popular method of linear spectral unmixing for hyperspectral imagery is linear least squares. Linear least square approaches are appropriate when observational errors predominate and are inappropriate when significant modeling errors are present. The least square approach has some disadvantages, especially in cases with few, poorly known references or significant reference variation throughout an image. In this article, the restricted total least squares (RTLS) approach is presented and evaluated on experimental data. Although the proposed RTLS require more calculations than linear least squares, its relative error performance is much better.