Purpose: In hybrid medical imaging devices combining positron emission tomography (PET) with magnetic resonance imaging, PET attenuation correction remains challenging. Known approaches to estimating attenuation (μ-)maps from PET emission data, especially maximum-likelihood reconstruction of activity and attenuation (MLAA), take into account true coincidences only and exhibit two kinds of ambiguities: First, the attenuation sinogram can only be determined up to a constant offset (sinogram ambiguity). Second, the attenuation sinogram is unknown outside of the support of the activity sinogram and does not completely define a μ-map (image-space ambiguity). In this work, the authors aim at using additional information from scattered coincidences to resolve these ambiguities--information that is unavailable using true coincidences.
Methods: The authors propose a two-level scheme for combining measurements of true and scattered coincidences. On the top level, scatter-to-attenuation (S2A) reconstruction recovers the μ-map from a measurement of scattered coincidences and results available from trues-based algorithms. On the lower level, S2A reconstruction is implemented by iterative scatter simulation and a proposed (simplified) S2A back-projection. The S2A back-projection is based on determining possible scattering locations in image space from energy measurements (via Compton-scattering angles) and summing contributions from scattered coincidences in image space. S2A back-projection is validated with GATE simulations of activity-attenuation configurations with both sinogram and image-space ambiguities. The authors further evaluate the impact of asymmetric source and activity distributions, extended source distributions, and energy uncertainty to demonstrate the limitations of the simplified noniterative S2A back-projection approach. Feasibility of the iterative S2A reconstruction is evaluated in a low-resolution, analytical 2D problem.
Results: S2A back-projection of scattered coincidences with scattered-photon energies in the range of 248-478 keV provides image-space information about the attenuation distribution, even in challenging cases of perfect spherical symmetry of attenuation and activity distributions as well as attenuation outside of the activity support. Realistic energy uncertainties (5% and 10% full width at half maximum at 511 keV) deteriorate spatial image resolution in the proposed noniterative method. The iterative S2A reconstruction is able to recover the full μ-map (errors less than 3.7 × 10(-5)/cm) as well as the unknown scaling factor (error smaller than 0.0005%) from scattered coincidences and an activity distribution with unknown scaling.
Conclusions: Scattered coincidences provide information to complement existing PET attenuation-correction approaches such as MLAA. The proposed scatter-to-attenuation back-projection and reconstruction may constitute a missing piece for resolving ambiguities in the simultaneous reconstruction of activity and attenuation, and improving the quality of μ-maps reconstructed from PET emission data.