Cross-reference weighted least square estimates for positron emission tomography.

An efficient new method, termed as the cross-reference weighted least square estimate (WLSE) [CRWLSE], is proposed to integrate the incomplete local smoothness information to improve the reconstruction of positron emission tomography (PET) images in the presence of accidental coincidence events and attenuation. The algebraic reconstruction technique (ART) is applied to this new estimate and the convergence is proved. This numerical technique is based on row operations. The computational complexity is only linear in the sizes of pixels and detector tubes. Hence, it is efficient in storage and computation for a large and sparse system. Moreover, the easy incorporation of range limits and spatially variant penalty will not deprive the efficiency. All this makes the new method practically applicable. An automatically data-driven selection method for this new estimate based on the generalized cross validation is also studied. The Monte Carlo studies demonstrate the advantages of this new method.