Investigation of the stationarity of the modulation transfer function and the scatter fraction in conjugate view SPECT restoration filtering

The application of restoration filters assumes that the two-dimensional modulation transfer function (2DMTF) is unchanging throughout the image. It was hypothesized that an approximately stationary camera response could be obtained by combing opposing views using either the arithmetic or geometric mean before filtering SPECT (single-photon-emission computed tomography) images. Images of Tc-99m point sources at various positions in circular and elliptical phantoms were used to investigate this hypothesis. The arithmetic and geometric means of opposing SPECT views were used to calculate 2DMTFs and scatter fractions as a function of camera angle and source location for each phantom. Results show that the geometric mean provides an approximately stationary 2DMTF and scatter fraction except near the edge of the phantoms. The arithmetic mean does provide 2DMTFs and scatter fractions which are more nonstationary than the geometric mean, but they are significantly less nonstationary than planar imaging. However, the arithmetic mean may be preferred for use with restoration filtering, because calculating the geometric mean is a nonlinear operation. Application of restoration filters to the geometric or arithmetic mean of projections is proposed as the method of choice for prereconstruction filtering of SPECT studies