On estimation of noise variance in two-dimensional signal processing

Estimation of noise variance is an important component of digital signal processing, in particular of image processing. In this paper the authors develop methods for estimating the variance of white noise in a two-dimensional degraded signal. They discuss optimal configurations of pixels for difference-based estimation, and describe asymptotically optimal selection of weights for the component pixels. After extensive analysis of possible configurations the authors recommend averaging linear configurations over a variety of different orientations (usually two or four). This approach produces estimators with properties of both statistical and numerical efficiency.