A slice-by-slice blurring model and kernel evaluation using the Klein-Nishina formula for 3D scatter compensation in parallel and converging beam SPECT

Converging collimation increases the geometric efficiency for imaging small organs, such as the heart, but also increases the difficulty of correcting far the physical effects of attenuation, geometric response and scatter in SPECT. In this paper, 3D first-order Compton scatter in non-uniform scattering media is modelled by using an efficient slice-by-slice incremental blurring technique in both parallel and converging beam SPECT. The scatter projections are generated by first forming an effective scatter source image (ESSI), then forward-projecting the ESSI. The Compton scatter cross section described by the Klein-Nishina formula is used to obtain spatial scatter response functions (SSRFs) of scattering slices which are parallel to the detector surface. Two SSRFs of neighbouring scattering slices are used to compute two small orthogonal 1D blurring kernels used for the incremental blurring from the slice which is further from the detector surface to the slice which is closer to the detector surface. First-order Compton scatter point response functions (SPRFs) obtained using the proposed model agree well with those of Monte Carlo (MC) simulations for both parallel and fan beam SPECT. Image reconstruction in fan beam SPECT MC simulation studies shows increased left ventricle myocardium-to-chamber contrast (LV contrast) and slightly improved image resolution when performing scatter compensation using the proposed model. Physical torso phantom fan beam SPECT experiments show increased myocardial uniformity and image resolution as well as increased LV contrast. The proposed method efficiently models the 3D first-order Compton scatter effect in parallel and converging beam SPECT.