Ultra efficientand robust estimation of the attenuation map in PET imaging

Time-of-Flight (TOF) PET data determines the attenuation map up to a constant. MLAA (Maximum Likelihood Activity and Attenuation Estimation) was proposed for this purpose. However, in real systems the estimated attenuation map usually results in bias and artifacts, due to various factors such as non-uniform timing resolution, detector timing drift, and biased scatter estimation. Moreover, MLAA has much higher computational cost than conventional PET reconstruction. Improving the practical performance of MLAA is important. We proposed an efficient and robust emission-attenuation joint estimation framework, based on the condition that regions with almost uniform attenuation coefficients are segmented. Following the derivation, the update of attenuation map only requires a few weighted additions in sinogram space, which reduces overall computational cost significantly compared with conventional MLAA, as the latter demands at least two backward projections in each iteration. Furthermore, as the parameter space for the attenuation map is reduced and that the math model encourages an averaging effect in reach region, the bias and artifacts due to various factors above can be reduced. We used clinical TOF PET data to evaluate the performance of our proposed method. In each iteration, the computation time for updating the attenuation map was less than 20% of that for conventional MLAA, leading to significant improvement in overall computation efficiency (twice as fast as conventional MLAA). More importantly, the method resulted in high quantitative accuracy. In population study, SUV computed with the estimated attenuation map and the CT based attenuation map had maximum relative error less than 5.7% in multiple VOIs including the spine, liver, kidney, and heart. Our method can be used as a robust and efficient solution to estimate the attenuation map for quantitative PET image reconstruction, based on a single assumption that the attenuation coefficients are similar in each segmented regions. The numerical error caused by treating attenuation coefficients as uniform within each segmented region is acceptable.