Nonlinear unmixing by using non-Euclidean metrics in a linear unmixing chain
Faculty of Sciences. Physics
S.l. :IEEE, 2014
IEEE-Whispers 2014 : Workshop on Hyperspectral Image and Signal Processing, Lausanne, Suisse, June 24-27, 2014
University of Antwerp
In the linear mixing model, many techniques for endmember extraction are based on the assumption that pure pixels exist in the data, and form the extremes of a simplex embedded in the data cloud. These endmembers can then be obtained by geometrical approaches, such as looking for the largest sim- plex, or by maximal orthogonal subspace projections. Also obtaining the abundances of each pixel with respect to these endmembers can be completely written in geometrical terms. While these geometrical algorithms assume Euclidean geom- etry, it has been shown that using different metrics can offer certain benefits, such as dealing with nonlinear mixing effects by using geodesic or kernel distances, or dealing with correla- tions and colored noise by using Mahalanobis metrics. In this paper, we demonstrate how a linear unmixing chain based on maximal orthogonal subspace projections and simplex pro- jection can be written in terms of distance geometry, so that other metrics can be easily employed. This yields a very flex- ible processing chain: by using other metrics, the same un- mixing methodology can be used to deal with a wide range of unmixing models and scenarios. As an example, metrics are provided for dealing with intimate mixtures, nonlinear di- mensionality reduction, and colored noise.