Frequency Domain Filter

Take the removal of periodic noise as an example to visualize what a filter is. There are many reasons for the periodic noise, such as the acquisition of electronic components in the system, we are artificially added to the image of the 1/4 area of the periodic noise. First, intuitively feel the effect of noise down

　　

(1) original (2) periodic noise figure (3) filter (4) Filter processing image

The figure (3) is a band-stop filter, the black part is not through the frequency portion, the middle white and the periphery is allowed to pass the frequency portion, so that the noise portion can be removed, of course, sometimes it is to experiment to find out the frequency range of the noise. Figure (4) As a result, it can be seen that the periodic noise of the image is largely removed, but because I am setting the band-stop filter Center frequency is 50, the width is 5, so the image is also a bit blurred, we can only for the image of the noise part of the filter, or the use of other parameters to experiment.

Now we introduce three kinds of common band-stop filters, we can set other filters as needed.

(1) Ideal band resistance filter

(5) Frequency domain characteristics of ideal Band-stop filter

D0 is the distance from the center frequency of the band to the frequency origin, W is the blocking band width (this experiment is 5), D (u,v) is the distance from the point to the origin of the frequency (u,v), and when D (U,V) is located in the part of the SAG, between D0-W/2 and D0+W/2, Figure (5) the part that is concave is the corresponding black part of the figure (3), which is the frequency part that cannot be passed. Can achieve the purpose of noise removal. However, because it is suddenly 0 at the boundary, which is hard to implement with hardware, the band-stop filter can cause ringing effect.

(2) Butterworth Band Resistance Filter

(6) Frequency domain characteristics of Butterworth Band-stop Filter

D0 is the distance between the center frequency of the blocking band and the frequency origin, W is the bandwidth of the blocking band, D (U,v) is (u,v) the distance from the point to the frequency origin, can see its edge to a certain extent does not mutate, Butterworth is the transition between the other two kinds of filters, when the extremum is relatively close.

(3) Gaussian band resistance filter

(7) Frequency domain characteristics of Gaussian band-stop filter

D0 is the distance between the center frequency of the blocking band and the frequency origin, W is the width of the blocking band, and D (U,V) is the distance from the (u,v) point to the frequency Origin point.

Results analysis, this experiment is a Gaussian band-stop filter, the figure (4) can see the noise is very well removed, but with the band-stop filter is not good to save the details of the image, because the part of the information in the frequency domain in the blocked band. The image is blurred to a certain extent and is not a good choice between noise and image details.

Frequency Domain Filter