Exploring the geostatistical method for estimating the signal-to-noise ratio of images

The signal-to-noise ratio (SNR) has been estimated for remotely sensed imagery using several image-based methods such as the homogeneous area (HA) and geostatistical (GS) methods, For certain procedures such as regression, an alternative SNR (SNRvar), the ratio of the variance in the signal to the variance in the noise, is potentially more informative and useful. In this paper, the GS method was modified to estimate the sNR(var), referred to as the SNRvar(GS). Specifically, the sill variance c of the fitted variogram model was used to estimate the variance of the signal component and the nugget variance c(0) of the fitted model was used to estimate the variance of the noise, The assumptions required in this estimation are presented. The SNRvar(GS) was estimated using the modified GS method for six different land-covers and a range of wavelengths to explore its properties. The SNR* (var(GS)) was found to vary as a function of both wavelength and land-cover. The SNR* (var(Gs)) represents a useful statistic that should be estimated and presented for different land-cover types and even per-pixel using a local moving window kernel.