ABSTRACT
The theory of nonlinear filtering is still in its infancy and authors know the exact statistical characterizations only for very few filters and even then only for the simplest cases. The simplest but an important case is to find the output distribution of the filter when the input is white noise, i.e., a sequence of independent and identically distributed random variables. The variance of the signal is directly linked to the power of the signal. Thus, a filter whose output variance is small for white noise input reduces the energy of noise. In images this means that after filtering the image looks less rough. However, it is important to remember that the visual appearance of the filtered images depends much on factors other than the noise attenuation capability of the filter.
