Definition of Spatially Variable Spectral Endmembers by Locally Calibrated Multivariate Regression Analyses

Linear regression procedures can be applied to derive spectral endmembers using satellite images and superimposed abundance estimates of known components. A common problem, however, is represented by the spatial variability of the spectral endmembers to estimate, which may be caused by variations in several environmental factors (topography, water availability, soil type, etc.). This problem is currently addressed by a modified multivariate regression procedure that can define spatially variable spectral endmembers. The procedure is based on a local calibration of the regression statistics (mean vectors and variance/covariance matrices), which is obtained by weighting the values of the training pixels according to their distance from each pixel examined. The locally found regression statistics are then used to extrapolate pure class spectral endmembers, which are therefore different for each image pixel. An experiment was carried out using multitemporal NOAA-AVHRR NDVI profiles and class abundance estimates of Tuscany region in central Italy. The results show that the spatially variable spectral endmembers are far more accurate than conventional fixed endmembers to recompose the original NDVI imagery. Finally, it is discussed how these spatially variable pure class NDVI values can serve for data integration and as input for agro-meteorological applications and ecosystem simulation modeling.