On estimating measurement error in remotely-sensed images with the variogram

Previously, several methods have been developed to estimate the signal-to-noise ratio of remotely sensed imagery. Of these, the most appropriate is a method based on spatial dependence for estimating the signal-to-noise ratio of Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) imagery. The intercept on the ordinate of the modelled sample variogram, known as the nugget variance, is used to estimate noise. However, while the nugget variance is due to measurement error, it depends also on short-range spatial variation that has not been measured, underlying variation that has been measured (but which may result in a non-linear form of variogram near the ordinate), sampling effects, and the choice of model fitted to the sample variogram. For remotely-sensed imagery there is no short-range variation that has not been measured because the pixels are contiguous or overlapping. Further, there are usually many pixels and so sampling effects are negligible. However, it is impossible to account for the form of the variogram near the ordinate when selecting a mathematical model. Consequently, while the nugget variance remains as the most appropriate method of estimating measurement error in remotely sensed images, it may be less reliable than previously thought.