Nonlinear noise smoothing

Nonlinear (spatial) filters also operate on neighborhoods and are implemented by sliding a kernel (mask) over an image like a linear filter. However, the filtering operation is based conditionally on the values of the pixels in the neighborhood, and they do not explicitly use coefficients in the sum-of-products manner in general. For example, noise reduction can be effectively done with a non-linear filter whose basic function is to compute the median gray-level value in the neighborhood where the filter is located. This filter is a nonlinear filter, since the median computation is a non-linear operation. Median filters are quite popular since, for certain types of random noise (for example, impulse noise), they provide excellent noise-reduction capabilities, with considerably less blurring than linear smoothing filters of similar size. Non-linear filters are more powerful than linear filters; for example, in terms of suppression of non-Gaussian noise such as spikes...