Scale invariance and noise in natural images

Natural images are known to have scale invariant statistics. While some eariler studies have reported the kurtosis of marginal bandpass filter response distributions to be constant throughout scales, other studies have reported that the kurtosis values are lower for high frequency filters than for lower frequency ones. In this work we propose a resolution for this discrepancy and suggest that this change in kurtosis values is due to noise present in the image. We suggest that this effect is consistent with a clean, natural image corrupted by white noise. We propose a model for this effect, and use it to estimate noise standard deviation in corrupted natural images. In particular, our results suggest that classical benchmark images used in low-level vision are actually noisy and can be cleaned up. Our results on noise estimation on two sets of 50 and a 100 natural images are significantly better than the state-of-the-art.