If we filter an ensemble of natural images with a high-pass filter, the output is a random variable. The probability density for this variable will, under fairly general assumptions, be a Gaussian scale mixture. The kurtosis for this type of distribution is always positive.
© 2001 Optical Society of America
Eric Clarkson and Harrison H. Barrett, "High-pass filters give histograms with positive kurtosis," Opt. Lett. 26, 1253-1255 (2001)