Understanding Fourier space and filter selection

I. George Zubal, Gary Wisniewski
Review Articles
Volume 4, Issue 3 / May , 1997

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Conclusion

By appreciating the technical basis of Fourier representations and filtering, a better interpretation of SPECT images can be gained. The ramp filter has no selectable parameters and is the required filter used in tomography. The resulting noisy reconstructed image is smoothed by using a filter where the cut-off and order can be selected. By relating frequencies to sizes of structures in the image, reasonable values for the cut-off frequency for the smoothing filter can be selected. Most important, the realization that the ramp-filtered image (without the smoothing filter applied) is the most correct image means that subsequent smoothing can slightly degrade the numeric correctness of the reconstructed image. Smoothing filters make the image easier for clinical interpretation because noisy structures are difficult for the human eye to perceive. Selection of the smoothing filter to maximize noise reduction and image structure preservation is accomplished by matching the cut-off frequency to the image noise or camera resolution. This understanding should reduce the amount of time spent searching for a smoothing filter, which is used routinely in clinical imaging studies.

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