Effect of reconstruction kernel width on optimal regularization for focal lesion detection in PET

Abstract

Iterative statistical algorithms offer desirable properties; however, the maximum likelihood solution provides sub-maximal performance for detecting focal lesions unless noise effects are regularized. Typical approaches include stopping the algorithm prior to convergence, penalizing objective functions, or post-reconstruction filtering. The width of the reconstruction kernel-i.e. the geometric component of the system matrix describing the projection operation and associated detector effects-dramatically affects noise correlations. This work explores the relationship between reconstruction kernel width and optimal regularization parameters that maximize focal lesion detection in PET. Experiments from the Utah PET Lesion Detection Database were used to model fully-3D oncologic whole-body FDG imaging, including multiple scans with- and without numerous lesions distributed throughout the phantom. Three reconstruction kernels were studied: a ray-driven projector with delta-function kernel; an area-driven projector with kernel width matched to the coincidence line spacing; and a volumetric projector with approximate point spread function model. Images were reconstructed to 250 iterations MLEM, storing intermediate iterations, and localization receiver operating characteristics analysis was applied using the channelized non-prewhitened observer. Maximal performance was obtained at 40, 70, and 100 iterations for the ray-driven, area-driven, and volumetric projectors, respectively. Conversely, optimal filter strength varied inversely with reconstruction kernel width. Overall, detection improved with broader kernels that more accurately modeled the tomograph's actual response. These results clarify the complex relationship between reconstruction kernel width and the regularization needed to maximize focal lesion detection-important considerations when selecting regularization parameters and interpreting published results from different scanners or reconstruction methods.