Evaluating coherence of natural images by smoothness membership in Besov spaces

Smoothness membership in Besov spaces B_q^α (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 ε(M) when the image is approximated by its M-largest quantized wavelet coefficient. The technique was applied to a set of nine normalized difference vegetation index (NDVI) time series data as a quantitative quality measure of spatial coherence. The NDVI data set comprises different compositing and atmospheric correction techniques. The estimates of the complexity index give a quantitative measure of the performance of these techniques that agrees well with visual evaluation and with the physics of the image collection process. The authors demonstrate the maximum value NDVI composites with Rayleigh, ozone, and water vapor correction consistently provide the highest spatial coherence among the compositing and atmospheric correction techniques evaluated. They also show the complexity index is regionally dependent and is higher in dry periods than in wet periods where residual cloud interference is more likely to appear