Noise Reduction - Important Concepts in Signal Processing, Image Processing and Data Compression - page 19

Linear smoothing filters
One method to remove noise is by convolving the original image with a mask that
represents a low-pass filter or smoothing operation. For example, the Gaussian mask
comprises elements determined by a Gaussian function. This convolution brings the value
of each pixel into closer harmony with the values of its neighbors. In general, a
smoothing filter sets each pixel to the average value, or a weighted average, of itself and
its nearby neighbors; the Gaussian filter is just one possible set of weights.
Smoothing filters tend to blur an image, because pixel intensity values that are
significantly higher or lower than the surrounding neighborhood would "smear" across
the area. Because of this blurring, linear filters are seldom used in practice for noise
reduction; they are, however, often used as the basis for nonlinear noise reduction filters.
Anisotropic diffusion
Another method for removing noise is to evolve the image under a smoothing partial
differential equation similar to the heat equation which is called anisotropic diffusion.
With a spatially constant diffusion coefficient, this is equivalent to the heat equation or
linear Gaussian filtering, but with a diffusion coefficient designed to detect edges, the
noise can be removed without blurring the edges of the image.
Nonlinear filters
A median filter is an example of a non-linear filter and, if properly designed, is very good
at preserving image detail. To run a median filter:
1. consider each pixel in the image
2. sort the neighbouring pixels into order based upon their intensities
3. replace the original value of the pixel with the median value from the list
A median filter is a rank-selection (RS) filter, a particularly harsh member of the family
of rank-conditioned rank-selection (RCRS) filters; a much milder member of that family,
for example one that selects the closest of the neighboring values when a pixel's value is
external in its neighborhood, and leaves it unchanged otherwise, is sometimes preferred,
especially in photographic applications.
Median and other RCRS filters are good at removing salt and pepper noise from an
image, and also cause relatively little blurring of edges, and hence are often used in
computer vision applications.
Software programs
Most general purpose image and photo editing software will have one or more noise
reduction functions (median, blur, despeckle, etc.). Special purpose noise reduction
software programs include Neat Image, Grain Surgery, Noise Ninja, DenoiseMyImage,