The difference between linear filtering algorithm and nonlinear filtering algorithm in image processing, the difference between Gaussian noise and salt and pepper noise and their respective characteristics

The original data and filter result of linear filter is an arithmetic operation, which is realized by subtraction, such as mean filter (average of pixel gray value in template), Gaussian filter (Gaussian weighted average) and so on. Since linear filters are arithmetic operations, there are fixed templates, Therefore, the transfer function of the filter can be determined and unique (the transfer function is the Fourier transform of the template).
The original data of the nonlinear filter and the filter result is a kind of logical relation, that is realized by the logic operation, such as the maximum filter, the minimum value filter, the median filter, etc., by comparing the gray value size in a certain neighborhood, there is no fixed template, Thus there is no specific transfer function (because there is no template for the Fourier transform), and the expansion and corrosion are also achieved by the maximum and minimum filters.
Gaussian noise refers to the Gaussian distribution of noise, that is, the maximum number of noise points of a certain intensity, the lower the number of noise points from this intensity, and this rule obeys the Gaussian distribution. Gaussian noise is an additive noise that is directly added to the original image, so it can be filtered with a linear filter.
Salt and pepper noise similar to the salt and pepper in the image, so named, is a lot of white or black spots on the image of the noise, such as the snow noise on the TV. Salt and pepper noise can be considered as a logical noise, the result of filtering with a linear filter is not good, generally using median filter filter can get better results.