Signal-to-noise ratios for attenuation correction in PET imaging

Attenuation correction is an important part of accurate image reconstruction in positron tomography. The usual correction method involves direct measurement of attenuation correction factors (ACFs). A reconstruct-reproject method, which has been suggested as providing superior noise properties, is sometimes employed; an attenuation image is first reconstructed from the measurement and then ACFs are obtained by reprojection through this image. Here the authors present a model which follows the signal-to-noise ratio (SNR) through the attenuation correction by both the direct and reconstruct-reproject methods. This model is applicable to both 2D and 3D imaging geometry, but applies to the central elements of emission and transmission objects with circular symmetry and constant amplitude. For this simplified geometry, the model predicts that the SNR of the emission image following attenuation correction is the same for both direct and reconstruct-reproject methods, although the SNRs of the ACFs are themselves substantially different. The authors also present the measured SNR at the various steps of attenuation correction for both the direct and reconstruct-reproject methods using simulated transmission and emission data. The measured SNRs agree with the model; no significant difference between the direct and reconstruct-reproject SNRs was observed.