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

Abstract

Converging collimation increases the geometric efficiency for imaging small organs, such as the heart, but also increases the difficulty of correcting for 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.

Estimation of 6-Degree-of-Freedom (6-DOF) Rigid-Body Patient Motion From Projection Data by the Principal-Axes Method in Iterative Reconstruction

“…Thus care must be applied when performing correction. As future work, we would like to investigate the influence of the more sophisticated methods like ESSE [10] and ESSI [11] on the motion detection for our approach.…”

“…Writing (3) in terms of components, we have (11) (12) (13) If for one motion state there are at least three frames (e.g., α 1 ,α 2 ,α 3 , and α 3 > α 2 > α 1 ) of projections available, the tensor T can be solved from (11)- (13). In case that we have three angular views for a motion state, we can rewrite (11), (12) as (14) Feng The matrix (14) can be solved in the least-squares sense, or analytically by using only five of six equations.…”

“…For SPECT, we estimate iteratively the motion from "scatter-and-attenuation-compensated" projection data, which are estimated iteratively as part of reconstruction. Scatter can be estimated by the ESSE [10], ESSI [11] or TEW [12] methods, and subtracted from the projection data. During reconstruction, both non-attenuated and attenuated line-integrals are calculated and their ratios are multiplied to the scatter-subtracted projection data to obtain the scatter-andattenuation-compensated projection data (Fig.…”

Modeling of pixelated detector in SPECT pinhole reconstruction

“…We could expect some scatter estimation techniques may be needed to deal with the increased inter-crystal scattering. We would prefer simple methods based on Klein-Nishina formula [9] or scattering kernels [10] than the Monte-Carlo simulations [11], because the latter are computationally much more expensive.…”

Feasibility and value of fully 3D Monte Carlo reconstruction in single-photon emission computed tomography

“…An alternative approach is to perform fully 3D reconstruction without factorizing the reconstruction problem as a set of 2D independent reconstructions. This has been proposed using approximate analytical models of a 3D projector [1][2][3][4]. The concept of using Monte Carlo simulations to estimate the 3D projector has been proposed early [5,6] but not applied in fully 3D at that time due to impractical storage and computation time.…”