Reconstruction of short time PET scans using Bregman iterations

We propose a method for reconstructing data from short time positron emission tomography (PET) scans, i.e data acquired over a short time period. In this case standard reconstruction methods deliver only unsatisfactory and noisy results. We incorporate a priori information directly in the reconstruction process via nonlinear variational methods. A promising approach was the so-called EMTV algorithm, where the negative log-likelihood functional, which is minimized in the expectation maximization (ML-EM) algorithm, was modified by adding a total variation (TV) term. To improve the results and to overcome the issue of the loss of contrast we extend the algorithm by an inverse scale space method using Bregman distances, to which we refer as BREGMAN EMTV algorithm. The methods are tested on short time (5 and 30 seconds) FDG measurements of the thorax. We can show that the EMTV approach can effectively reduce the noise, but still introduces an oversmoothing, which is eliminated by the BREGMAN EMTV method, obtaining a reconstruction of comparable quality to the corresponding long time (20 and 7 minutes) scan. This correction for the loss of contrast is necessary to obtain quantitative PET images.