Noise in imaging systems is usually either additive or multiplicative. This thesis deals only with additive noise which is zero-mean and white. White noise is spatially uncorrelated: the noise for each pixel is independent and identically distributed (iid). Common noise models are:
The Gaussian distribution has an important property: to estimate the mean of a stationary Gaussian random variable, one can't do any better than the linear average. This makes Gaussian noise a worst-case scenario for nonlinear image restoration filters, in the sense that the improvement over linear filters is least for Gaussian noise. To improve on linear filtering results, nonlinear filters can exploit only the non-Gaussianity of the signal distribution.
Nonlinear estimators can provide a much more accurate estimate of the mean of a stationary Laplacian random variable than the linear average .
Figure 1.2 illustrates these PDFs for zero-mean, unit variance noise.
Figure 1.2: Probability density functions of the Gaussian, Laplacian and Uniform distributions