Geostatistically estimated image noise is a function of variance in the underlying signal

Estimation of noise contained within a remote sensing image is often a prerequisite to dealing with the deleterious effects of noise on the signal. Image based methods to estimate noise are attractive to researchers for a range of applications because they are in many cases automatic and do not depend on external data or laboratory measurement. In this paper, the geostatistical method for estimating image noise was applied to Compact Airborne Spectrographic Imager (CASI) imagery. Three CASI wavebands (0.46–0.49 μm (blue), 0.63–0.64 μm (red), 0.70–0.71 μm (near-infrared)) and four land covers (coniferous woodland, grassland, heathland and deciduous woodland) were selected for analysis. Five sub-images were identified per land cover resulting in 20 example cases per waveband. As in previous studies, the analysis showed that noise was related to land cover type. However, the noise estimates were not related to the mean of the signal in any waveband. Rather, the noise estimates were related to the square root of the semivariogram sill, which represents the variability in the underlying signal. These results suggest that the noise estimates produced using the geostatistical method may be inflated where the variance in the image is large. Regression of the noise estimates on the square root of the sill may lead to a stable noise estimate (i.e. the regression intercept), which is not affected by the variability in the image. This provides a refined geostatistical (GS) method that avoids the problems outlined above.