Fully three-dimensional OSEM-based image reconstruction for Compton imaging using optimized ordering schemes

Abstract

Although the ordered subset expectation maximization (OSEM) algorithm does not converge to a true maximum likelihood solution, it is known to provide a good solution if the projections that constitute each subset are reasonably balanced. The Compton scattered data can be allocated to subsets using scattering angles (SA) or detected positions (DP) or a combination of the two (AP (angles and positions)). To construct balanced subsets, the data were first arranged using three ordering schemes: the random ordering scheme (ROS), the multilevel ordering scheme (MLS) and the weighted-distance ordering scheme (WDS). The arranged data were then split into J subsets. To compare the three ordering schemes, we calculated the coefficients of variation (CVs) of angular and positional differences between the arranged data and the percentage errors between mathematical phantoms and reconstructed images. All ordering schemes showed an order-of-magnitude acceleration over the standard EM, and their computation times were similar. The SA-based MLS and the DP-based WDS led to the best-balanced subsets (they provided the largest angular and positional differences for SA- and DP-based arrangements, respectively). The WDS exhibited minimum CVs for both the SA- and DP-based arrangements (the deviation in mean angular and positional differences between the ordered subsets was smallest). The combination of AP and WDS yielded the best results with the lowest percentage errors by providing larger and more uniform angular and positional differences for the SA and DP arrangements, and thus, is probably optimal Compton camera reconstruction using OSEM.

Use of a LYSO‐based Compton camera for prompt gamma range verification in proton therapy

“… represents the probability that a PG is emitted from voxel j and is detected by the pair of CC detectors. To calculate the sensitivity image for each subset, scattering angle‐based subsets were used, which quantize the scattering angles of the incident PGs into 64 discrete angles between 0° and 90°. Each subset contains multiple scattering angles and each scattering angle contains all possible combinations of PG interaction positions in the two detectors.…”

“…Compton cameras (CCs) that consist of multistage (either two‐ or three‐stage) detectors were designed to construct the three‐dimensional (3D) distribution of gamma rays. CCs have been used in such varied fields as astrophysics, homeland security, and nuclear medicine. More recently, new proton range verification techniques, including PG timing measurements, PG spectroscopy, and the PG peak integrals, have been proposed.…”

Numerical Algorithms for Scatter-to-Attenuation Reconstruction in PET: Empirical Comparison of Convergence, Acceleration, and the Effect of Subsets

“…In this work, the random subsets partitioning scheme was chosen since other, geometrically established subsetization rules do not immediately apply to the extended measurement space of SORs, due to the different shapes of different SORs. While the subset sensitivities were reasonably balanced in the cases we verified, optimized ordering schemes might help eliminate the uncertainty associated with our random selection [25]. …”

Improved iterative reconstruction method for Compton imaging using median filter

“…The ML-EM algorithm is widely used for image reconstruction. Although OS-EM works in a similar way to ML-EM, the algorithm is optimized by performing an update after each subset of the total amount of data has been PLOS ONE processed [25,26]. For L subsets, these steps are calculated as follows: is the updated value of the kth image using l subsets, S j is the detection efficiency vector, and t ij is the transition probability of the ith event at the reference point.…”