Simulation of the Impact of a Sensor's PSF on Mixed Pixel Decomposition: 1. Nonuniformity Effect

The nonuniformity of the spatial response to surface radiation is a fundamental characteristic of all airborne and spaceborne sensors that inevitably introduces uncertainty into the estimation of object proportions by the spectral unmixing of mixed pixels. Simulated data of the surface radiation distribution and a TM (thematic mapper) response matrix were developed and utilized to imitate the generation of mixed pixels and the extraction of the object proportion via a Monte Carlo simulation, and then, the nonuniformity effect of a sensor’s PSF (point spread function) was explored. The following conclusions were drawn: (1) given a nonuniform spatial response of a sensor to a surface scene with a constant object proportion and various object distribution patterns, the mixed pixel DN (digital number) of a remotely-sensed image becomes a random variable, which causes a PSF nonuniform effect on the object proportion extraction; (2) for the estimated object proportion, the corresponding true object proportion appears with a random variation; its upper and lower bounds take on an asymmetrical spindle shape; and models of these bound curves at any probability level were established; (3) there exists a negative linear relationship between the bias of the spectral unmixing and the estimated proportion; the bias is zero at an estimated proportion of 50%, and when the estimated proportions are approximately 100% and 0%, the object proportion is overestimated by 0.78% and underestimated by 0.78%, respectively; (4) the relationship between the standard deviation of the spectral unmixing and the estimated proportion follows a symmetrical polynomial function opening downward; the standard deviation reaches a maximum of 4.4% at the estimated proportion of 50%, and when the estimated proportion is approximately 100% or 0%, the standard deviation is a minimum, 1.05%. The above findings contribute to a comprehensive understanding of the PSF nonuniformity effect, have the potential to compensate for the bias of proportion estimation and present its confidence interval at any probability level.