A Generalized Model for 3D Compton Scatter in Single Photon Emission Computed Tomography Using Slice-by-Slice Blurring and Scatter Projection Rebinning

The modeling of 3D Compton scatter in SPECT is complicated by the use of a variety of collimator geometry. To date, effective and efficient modeling of 3D Compton scatter in parallel-beam SPECT has been made possible by Frey and Tsui [1], Zeng et al [2], and Bai et al [3]. For fan-beam and cone-beam SPECT, the model in [3] can effectively model first order 3D Compton scatter. But for varying-focal-length fan-beam and cone-beam SPECT, no effective scatter models have been developed so far. We propose in this work a generalized model for 3D first order Compton scatter in SPECT for different collimator geometry. The slice-by-slice blurring technique in [3] is used to generate a complete set of first order Compton scatter projections; the scatter projections are then properly rebinned according to the specific collimator geometry to obtain the scatter estimation. When generating the complete set of scatter projections, a set of virtual planar detectors with parallel-beam collimation are used to orbit around the object for scatter detection. Detailed discussion of this generalized model is provided in the METHODS section.