Using Projection Kurtosis Concentration of Natural Images for Blind Noise Covariance Matrix Estimation

Kurtosis of 1D projections provides important statistical characteristics of natural images. In this work, we first provide a theoretical underpinning to a recently observed phenomenon known as projection kurtosis concentration that the kurtosis of natural images over different band-pass channels tend to concentrate around a typical value. Based on this analysis, we further describe a new method to estimate the covariance matrix of correlated Gaussian noise from a noise corrupted image using random band-pass filters. We demonstrate the effectiveness of our blind noise covariance matrix estimation method on natural images.