Evaluating coherence of natural images by smoothness membership in Besov spaces

Smoothness membership in Besov spaces B-q(alpha) (I) is used to compare the spatial coherence of satellite images. Smoothness is given by a complexity index computed as the rate of decay of the approximation error epsilon (M) when the image is approximated by its M-largest quantized wavelet coeffici ent. The technique was applied to a set of nine normalized difference veget ation index (NDVI) time series data as a quantitative quality measure of sp atial coherence. The NDVI data set comprises different compositing and atmo spheric correction techniques. The estimates of the complexity index give a quantitative measure of the performance of these techniques that agrees we ll with visual evaluation and with the physics of the image collection proc ess. We demonstrate the maximum value NDVI composites with Rayleigh, ozone, and water vapor correction consistently provide the highest spatial cohere nce among the compositing and atmospheric correction techniques evaluated. We also show the complexity index is regionally dependent and is higher in dry periods than in wet periods where residual cloud interference is more l ikely to appear.