Physics and Radiobiology of Nuclear Medicine

of a series of sinusoidal waves of different amplitudes, spatial frequencies,
and phase shifts running across the image (Fig. 12.7B). This is equivalent to
sound waves that are composed of many sound frequencies. Thus, the data
for each row and column of the acquisition matrix can be considered as
composed of sinusoidal waves of varying amplitudes and frequencies in the
frequency domain. The process of determining the amplitudes of sinusoidal
waves is called the Fourier transformation (Fig. 12.7C) and the method of
changing from the frequency domain to the spatial domain is called the
inverse Fourier transformation.

Single Photon Emission Computed Tomography 161

Fig. 12.6. A filter in the spatial domain. The negative side-lobes in the spatial
domain cancel out the unwanted contributions that lead to blurring in the recon-
structed image.

Fig. 12.7. Representation of an object in the spatial and frequency domains. A
profile in the spatial domain can be expressed as an infinite sum of sinusoidal func-
tions (the Fourier series). For example, the activity distribution as a function of dis-
tance in an organ (A) can be composed by the sum of the four sine functions (B).
The Fourier transform of this activity distribution is represented in (C), in which
the amplitude of each sine wave is plotted at the corresponding frequency of the
sine wave.