Feb 12, 2001

Frequency Space Filtering

First step is to center everything; the image data must be multiplied by (-1)^x+y, while the x and y frequencies, n and m, must be offset by N/2:

f(x,y) => f(x,y)(-1)^x+y,

while for an NxN array

Sometimes an image is blurred or degraded by an optical system, motion, defects, etc. If the transfer function of the degradation is known (this is a big if) then a process of inverse filtering can restore the original image.

Assuming little or no noise,

G = HF so F = G/H

This works if there is little noise and the transfer function H(n,m) is known. If there is noise, the process falls apart. Even then, a more sophisticated method using the so-called Weiner filter can sometimes give back a fairly well restored image. However, the real limitation of such methods is the need to know H.

Instead of using the spatial mask in a convolution process, sometimes the mask is used simply to obtain the neighboring values of a pixel, and various ordering systems are used to determine the proper substitution to obtain a good new pixel value. This may include using the median value (as in the median filter discussed earlier), the maximum or the minimum value, a weighted value (throw away some of the values from both ends). This is called using rank or order statistics.

Last modified on February 12, 2001