Joint estimation of activity image and attenuation sinogram using time-of-flight positron emission tomography data consistency condition filtering.

Attenuation correction is essential for quantitative reliability of positron emission tomography (PET) imaging. In time-of-flight (TOF) PET, attenuation sinogram can be determined up to a global constant from noiseless emission data due to the TOF PET data consistency condition. This provides the theoretical basis for jointly estimating both activity image and attenuation sinogram/image directly from TOF PET emission data. Multiple joint estimation methods, such as maximum likelihood activity and attenuation (MLAA) and maximum likelihood attenuation correction factor (MLACF), have already been shown that can produce improved reconstruction results in TOF cases. However, due to the nonconcavity of the joint log-likelihood function and Poisson noise presented in PET data, the iterative method still requires proper initialization and well-designed regularization to prevent convergence to local maxima. To address this issue, we propose a joint estimation of activity image and attenuation sinogram using the TOF PET data consistency condition as an attenuation sinogram filter, and then evaluate the performance of the proposed method using computer simulations.