Multiclass spectral decomposition of remotely sensed scenes by selective pixel unmixing

Linear pixel unmixing is a straightforward and efficient approach to the spectral decomposition of multichannel remotely sensed scenes. A main drawback to its utilization in operational cases, however, is that the number of spectral components that can be correctly treated must be less or equal to the scene dimensionality (the so-called "condition of identifiability"). To overcome the limitations deriving from this condition, a two-step strategy is currently proposed for application to each scene pixel. Provided that many spectral end-members are available, a subset with a prefixed number of end-members that optimally decompose the candidate pixel is first selected by a procedure based on the Gramm-Schmidt orthogonalization process. This restricted subset is then employed for conventional linear pixel unmixing. The final result is the decomposition of the multispectral scene into all the end-members considered while reducing the residual errors deriving from interclass spectral variability. The new procedure has been tested in three case studies representative of different environmental situations and data sets. The results of these experiments, compared to those of a conventional procedure, show that the new method identifies more clearly the spectral signal associated to all scene components and significantly reduces (20-30%) the residual error of the decomposition process. This is confirmed by further tests using synthetic scenes that are linear combinations of known end-members. In these cases, the reduction of the residual error by the new method is much higher (up to 70-80%) and the abundance images produced are more accurate estimates of the real components.