Bayesian inversion of imaging spectrometer data using a fuzzy geological outcrop model

Abstract

In geological remote sensing, in particular when studying the Earth with use of high spectral resolution sensors (so-called imaging spectrometers), ‘mineral maps' are the outcome of the image processing. Such mineral maps portray the spatial arrangement of classes of surface mineralogy derived from a comparison between known mineral signatures from spectral libraries and unknown (imaged in the hyperspectral domain) pixel spectra. With this information, geologists can build up a geological model of an area. Here, the reverse approach is advocated by introducing the geological model (where geology is converted to physical measurements by introducing spectra) at the start of the hyperspectral processing chain. This model is refined in an iterative way by comparing its mismatch with the observed reflectance measurements. Hence, a (geophysical) inversion of the hyperspectral dataset to a geological model is done. In a previous article explaining the physics and mathematics of the Bayesian inversion techniques, a ‘rigid geological model’ was used. Although the model takes on the advantage of including spatial arrangement and contextual information, hard field evidence is not included. Here an extension to this model is presented in the form of a ‘fuzzy outcrop geological model’. It is shown that the fuzzy outcrop model, which uses known outcrops and inferred outcrop patterns, outperforms the rigid geological model.

Acknowledgment

The article by Davis et al. (1995) inspired the work presented here. I thank Dr Yang Hong for allowing the use of the artificial neural network. Discussions with Steven de Jong and comments by Dr Alex Goetz led to the idea of an outcrop geological model for data inversion. The referees are thanked for their constructive criticism that led to improvement of an earlier version of the manuscript.