On the errors of two estimators of sub-pixel fractional cover when mixing is linear

The authors consider the problem of estimating ground cover at sub-pixel scales from remotely sensed imagery. In particular, they examine two strategies that make use of a set of reference pixels, or training pixels, for which fractional ground cover is already known. These strategies are the so-called classical and inverse methods. The former proceeds by assuming that signals received at a sensor are area-weighted averages of characteristic signals for each ground cover component, estimates those characteristic signals from the training pixels, and predicts fractions for a general pixel to be those that give the best match of the modeled and observed image signals. The latter approach proceeds by direct multivariate regression of ground cover proportions on pixel spectral values. The authors show that when ground cover types are spectrally well separated, and mixing is indeed linear, the difference between the two estimators is much smaller than the prediction error associated with either. This means that it is perfectly acceptable to use standard methods of multivariate regression to perform spectral unmixing. They also show that the inverse estimator can be regarded as a regularized form of the classical estimator and that the supposed optimality of the inverse method may be compromised if the training dataset is not a random subset of the complete set of image pixels.