SUGAR: Structured Unsupervised Geometry-Aware CT Attenuation Alignment and PET Activity Reconstruction

A misaligned computed tomography (CT)-derived attenuation map can bias time-of-flight positron emission tomography (TOF-PET) activity reconstruction. This bias can persist after subsequent image registration, motivating joint estimation of activity and CT geometry from emission data. We present SUGAR, a Structured Unsupervised Geometry-aware framework for CT attenuation Alignment and TOF-PET activity Reconstruction. SUGAR fits a differentiable acquisition model to the measured data. A coordinate network is fitted to the CT attenuation map and frozen; a global transformation and neural residual warp control its sampling coordinates. A separate positive neural field represents the PET activity. To reduce redundancy between the two geometry components, SUGAR suppresses sampled infinitesimal rigid modes in the residual deformation. It further factorizes the positive activity coefficients into a scalar magnitude and a simplex-valued composition. The activity field initially uses coarse hash-grid features, with finer features introduced on a preset schedule. In evaluations on digital brain and torso phantoms, SUGAR improves activity reconstruction over the evaluated comparison methods, while controlled tests assess attenuation-prior alignment. The results support structured geometry, activity coefficients, and resolution scheduling for coupled activity–attenuation inverse problems.