Partial volume correction for penalized-likelihood image reconstruction in oncological PET applications

Partial volume errors, caused by finite image resolution, that is, blurring in reconstructed images, prevent accurate quantitation of lesion uptake in oncological applications of PET. However, partial volume correction (PVC) is a challenging problem because image resolution is affected in a nontrivial way by a number of factors including patient, imaging protocol, background activity, and reconstruction parameters such as iteration numbers in OSEM and smoothing parameters in penalized-likelihood (PL). One of the advantages of PL over OSEM is that one can systematically identify key factors affecting image resolution and exploit them for PVC. Indeed, image resolution can be efficiently and accurately predicted for PL particularly with quadratic penalties. However, quadratic penalties do not necessarily offer clinically acceptable visual image quality comparable to OSEM. Here we focus on nonquadratic relative difference penalties, which we have previously found provide clinically acceptable visual image quality while achieving better quantitation accuracy than OSEM. It is straightforward to apply the methods presented here to conventional nonquadratic edge-preserving penalties. Our approach to PVC is to correct for partial volume errors through correcting for contrast recovery errors. First, we analytically identify key factors affecting contrast recovery and tabulate the functional dependence of contrast recovery coefficients (CRCs) on those factors empirically from a simulation study. Then we use the precomputed CRC table for PVC given an individual clinical data set. A main contrast between our approach and existing PVC methods using CRC or recovery coefficients is that thanks to PL we can analytically identify crucial factors affecting partial volume errors and correct for their effects.