2D Teager-Kaiser Analysis on Gaussian Noise

We provide here some contributions on the analysis of 2D Teager-Kaiser energy operator (TKEO) on Gaussian noise. To do so, we determine the probability density function (pdf) and the statistical distributions of its output. In addition, we show the asymmetry of the pdf and propose to fit it with a shifted log-Laplace distribution. We provide lower and higher statistical moments, and prove the dependence on the covariance matrix of the noise of both the standard deviation, coefficient of variation, skewness and kurtosis. Finally, we show the ability of 2D higher order statistics to detect object contours in highly noisy images and provide illustrations on both synthetic and real images.