Simultaneous reconstruction of activity and attenuation in PET: crosstalk measurements

摘要

Quantitative tomographic reconstruction based on positron emission (PET) requires attenuation correction on projections. The objective of this work is to analyze an algorithm for attenuation estimation which is used simultaneously with activity reconstruction (PET-AA) based only on emission data. The focus is on measurement of crosstalk effects on activity due to non-uniform attenuation. The derived algorithms are based on maximization of likelihood, but using minorization function approach. The activity estimator turned out to be the same as EM-ML for attenuated projections. On the other hand, the proposed algorithm for attenuation is simple and, basically, corrects the previous estimation of attenuation in a voxel by the ratio between the backprojection of estimated projections and backprojection of measured projections. Preliminary assessments were carried out via tridimensional phantoms with non-uniform attenuation emulating 3D PET with and without noise. Individually, the algorithms for attenuation and activity presented very good results with negligible crosstalk and global reconstruction error less than 2% for noiseless projections. For the case of simultaneous estimation, even without noise, the crosstalks in estimating activity and attenuation are significant (-0.223 ± 0.051) yielding global errors for activity between 10% and 20%. With noise, the error increased to 36% and the crosstalk to (-0.688 ± 0.139). The proposed algorithm for attenuation estimation presents encouraging behavior and the results confirm the necessity of methodologies to deal with crosstalk effects in PET-AA.