# Why does increasing sampling density in the frequency domain separate overlapping artifacts in the spatial domain?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I take the FFT of this image and get a 3D volume in the frequency domain. I then take a 2d slice from this 3D volume at an arbitrary angle making sure that the centre of the slice and the centre of the 3D FFT image volume pass through the same point. I then inverse FFT this 2d extracted plane to get a projection of my 3d volume.

I have noticed that I get an overlapping of artifacts but they are shifted by bit, also their intensity is reduced. If I sample at a higher rate the shift becomes greater to a point where it doesn't overlap anymore. Why does sampling at a higher rate increase the shift of the overlapped image? What can I do to stop the artifacts from being produced?

• I suspect that this question will be more likely to get an answer in Mathematics or possibly Signal Processing. – Dave Tweed Sep 17 '12 at 4:06
• Can you describe more about these 'overlapping artifacts?'. Perhaps post the code. – geometrikal Sep 30 '12 at 12:28

edited for more depth & clarity to avoid artifacts, pun intended

You can control your artifacts with an improved "anti-alias" filter to eliminate all content of signals above the Nyquist rate. This is often more critical if the image has been digitized already by another system at some unknown pixel rate.

For example a high resolution scan of magazine photo without the appropriate anti-alias filter setting will result in herringbone artifacts that are much worse than the original. This is a similar effect to the stripes of a shirt on TV with harmonic pixel interference herringbone patterns or the fringing patterns of lenses on a digital camera or camcorder in the presence of infrared light and similar resolution subject matter above the pixel resolution of the camera.

How you implement the anti-alias filter depends on the original signal.

• In the more general sense, if the original signal is natural light to be captured for 2D imaging, you might use an AA optical "blur filter".
• If the original signal is light reflected from a digital printed object in a scanner, you might tune the alias digital blur filter to match the resolution of the original print and synchronously if possible. e.g. 100 dpi for fax content
• If the original signal is a 3D scan using magneto-resonant imaging then you need to determine is it from stop-band remnant signals or pass-band group delay distortion.

The quality factors of low artifacts depend on the relative levels of interference from each to avoid alias artifacts.

Over-sampling makes the job of ideal bandstop filtering easier but ends up with huge file sizes so this can be followed by undersampling to achieve easier brick wall filters with desired blur filter in pass band.

Wiki has a more examples of various anti-alias filters and also spacial filtering applications.