restoration in the presence of noise only-spatial filtering
- Mean filter: all kinds of mean filters. overall the geometric mean filters are better suited for random noise like Gaussian or uniform noise. contra harmonic filter is well suited for impulse noise (but with carefully selected Q).
- 1) arithmetic mean filter; define a m x n rectangular subimage window, and centered at (x,y); for each (x,y) the restored value is from the average of all the pixels in the m x n window (i.e. sliding the window to get all the restored value). the noise is reduced as a result of blurring.
- 2) geometric mean filter: a geometric mean filter achieves smoothing comparable to the arithmetic mean filter but it tends to lose less image details in the process
- 3) harmonic mean filter: working well for salt noise, but fails for pepper noise. it also does well with other types of noise like Gaussian noise.
- 4) contraharmonic mean filter: the filer is well suited for reducing or virtually eliminating the effects of salt-and-pepper noise. for positive order of filter Q, it removes pepper noise, and for negative order of filter Q, it eliminates salt noise. it cannot do both simultaneously. when the order Q=0, it reduces to arithmetic mean filter; when Q=-1, it reduces to harmonic mean filter.
- Order-statistics filter: an order statistics filter is a spatial filter whose response is based on ordering (ranking) the pixels contained in the image area encompassed by the filter, and response of the filter at any point is determined by the ranking result.
- 1) median filter: recover the pixel value by the median of the gray levels in the neighborhood of that pixel, this is very popular since for certain types of random noise, the filter provides excellent noise-reduction capabilities, with considerably less blurring than linear smoothing filter of the similar size. (particularly useful for bipolar and unipolar impulse noise)
- 2) max and min filters: these filters are useful for finding the brightest or darkest points in the image
- 3) mid-point filter: it's the mid-point of max and min value for a restored pixel, so this combines order statistics and averaging. this filter works best for randomly distributed noise, like Gaussian or uniform noise.
- 4）alpha-trimmed mean filter：exclude the d/2 min and d/2 max gray-level values of the subimage; and use the rest for filtering.
- Adaptive filter: the behavior changes based on statistical characteristics of the image inside the filter region defined by the m x n rectangular window.