Global mean values in linear spectral unmixing: double fallacy!

Almost all conventional linear spectral unmixing techniques are based on the principle of least squares. The global mean digital number (DN) of an end-member is taken as the representative (i.e. contributory) DN for the end-member. This paper sets out to prove that the notion is a fallacy, and will always lead to negative percentages, super-positive percentages and non-100% sum of percentages if the unmixed pixel is not composed of, to within some tolerance, the global mean DNs only. Three sets of spectral end-members (two, three and four spectral end-members) are generated from Landsat ETM+ data. Practical percentages (between 0% and 100% and totalling 100%) of the end-members are returned by pixels in which the local mean DNs of the spectral end-members do not differ from the global mean DNs by, on average, 4.