A slice-by-slice blurring model and kernel evaluation using theKlein-Nishina formula for 3D scatter compensation in parallel and convergingbeam SPECT

Abstract

Converging collimation increases the geometric efficiency for imaging smallorgans, such as the heart, but also increases the difficulty of correcting forthe physical effects of attenuation, geometric response and scatter in SPECT. Inthis paper, 3D first-order Compton scatter in non-uniform scattering media ismodelled by using an efficient slice-by-slice incremental blurring technique inboth parallel and converging beam SPECT. The scatter projections are generatedby first forming an effective scatter source image (ESSI), thenforward-projecting the ESSI. The Compton scatter cross section described by theKlein-Nishina formula is used to obtain spatial scatter response functions(SSRFs) of scattering slices which are parallel to the detector surface. TwoSSRFs of neighbouring scattering slices are used to compute two small orthogonal1D blurring kernels used for the incremental blurring from the slice which isfurther from the detector surface to the slice which is closer to the detectorsurface. First-order Compton scatter point response functions (SPRFs) obtainedusing the proposed model agree well with those of Monte Carlo (MC) simulationsfor both parallel and fan beam SPECT. Image reconstruction in fan beam SPECT MCsimulation studies shows increased left ventricle myocardium-to-chamber contrast(LV contrast) and slightly improved image resolution when performing scattercompensation using the proposed model. Physical torso phantom fan beam SPECTexperiments show increased myocardial uniformity and image resolution as well asincreased LV contrast. The proposed method efficiently models the 3D first-orderCompton scatter effect in parallel and converging beam SPECT.