cut-off value should be chosen so that primarily noise is removed, and
image detail is preserved. Note that the Nyquist frequency is the highest
cut-off frequency for a reconstruction filter and typical cut-off frequencies
vary from 0.2 to 1.0 times the Nyquist frequency. Filters are selected based
on the amplitude and frequency of noise in the data. Normally, a filter with
a lower cut-off value is chosen for noisier data as in the case of obese
patients and in^201 Tl myocardial perfusion studies or other studies with poor
count density.
Hann, Hamming, Parzen, and Shepp–Logan filters are all low-passfilters
because they preserve low-frequency structures, while eliminating high-
frequency noise. All of them are defined by a fixed formula with a
user-selected cut-off frequency. It is clear from Figure 12.10 that most
smoothing is provided by the Parzen filter and the Shepp–Logan filter pro-
duces the least smoothing.
An important low-pass filter that is most commonly used in nuclear med-
icine is the Butterworth filter (Fig. 12.11). This filter has two parameters:
the critical frequency (fc) and the order or power (n). The critical frequency
is the frequency at which the filter attenuates the amplitude by 0.707, but
not the frequency at which it is reduced to zero as with other filters. The
parameter, order or power n, determines how rapidly the attenuation of
amplitudes occurs with increasing frequencies. The higher the order, the
sharper the fall. Lowering the critical frequency, while maintaining the
order, results in more smoothing of the image.
Another class of filters, the Weiner and Metz filters, enhances a specific
frequency response.
Single Photon Emission Computed Tomography 165Fig. 12.11. Butterworth filter with different orders and cutoff frequencies.