Characterization of the modulation transfer function of discrete filtered backprojection

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Abstract
A mathematical expression for the modulation transfer function (MTF) of image reconstruction by discrete filtered backprojection (DFBP) is derived. A simulation study is used to investigate the dependence of the MTF of DFBP on: (1) the number of projection views; (2) the type of ramp filter used; (3) the interpolation method used during backprojection; and (4) the position of the object. These results were compared to MTFs calculated from point-source single-photon-emission computed tomographic (SPECT) acquisitions in air. The experimentally obtained MTFs contained much of the same structure as the MTFs of DFBP obtained through simulation. It is shown that the discretization of the filtered backprojection process can cause the tomographic transfer function to be anisotropic and nonstationary. However, through proper selection of the methods used in reconstruction, a nearly isotropic and stationary MTF can be obtained.