In calculating projections for iterative SPECT, a particularly time consuming part of the calculation is convolution of the activity at each depth by the point-spread function, using FFTs. We find that space-based convolutions with a short-range kernel are equivalent and faster, if one uses the central limit theorem to generate a gaussian, depth-dependent point- spread function. This technique is applied to forward and backward projections.
Direct inverse Fourier transform reconstruction methods once had a reputation for generating reconstructions with intolerable artifacts, but since 1980 the methods have been shown to be robust, with artifacts no worse than those in filtered backprojection. This paper shows how such a method was appied to nuclear medicine and tested. The emphasis is on speed of execution, signal-to-noise vs. resolution, and reduction of artifacts below the level of the noise.
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