Spatial-spectral unmixing using the sensor PSF

Multispectral image data can be processed to ''unmix'' component fractions for each pixel. Traditionally, however, these techniques do not account for the spatial spread of the signal due to the sensor point spread function (PSF). Optical PSFs typically have a width of about 0.5 to 1 pixels, which mixes spectral signatures from outside the, ground-instantaneous-field-of-view (GIFOV) of the pixel of interest. We have devised a mathematical and algorithmic framework for incorporating the sensor PSF into the unmixing problem. The approach requires solution of additional simultaneous equations from the neighboring pixels around the pixel of interest. These equations include weighting factors derived from the PSF, which is assumed to be adequately known for the specific sensor. The spatial-spectral algorithm has yielded a 28% error reduction for a simulated terrestrial scene when compared to a traditional unmixing method. In addition, the spatial-spectral algorithm significantly reduces the spatial width of unmixing error at class boundaries. In conclusion, the modified unmixing algorithm achieves notably improved unmixing results by including the previously ignored PSF effect on spatial-spectral mixing.