Statistic-Algebraic Tuning Optimization for Regularized Iterative Reconstruction (PML and EMS) in Emission Tomography

Most of the regularized iterative reconstruction schemes employed in emission tomography (such as penalized maximum-likelihood, PML) usually require the adjustment of a scalar parameter β that determines the strength of the a priori information regarding the studied object. Empirical selection of β remains hazardous since its optimal value depends on the morphological structure of the reconstructed image and the data signal to noise ratio (SNR), which explains partly the scarce utilization of penalized reconstruction in clinical routine. In this paper, we derive a simple optimization criterion for β that relies on a statistical description of the noise propagation when iteratively updating the image estimate and on a surrogate algebraic formulation holding for both PML and expectation-maximization-smooth (EMS) iterative reconstruction. When incorporated into each iteration step, the statistic-algebraic tuning optimization (SATO) yields two new optimized regularized iterative methods: SATO-PML and SATO-EMS. These methods are compared with classical MLEM reconstruction followed by optimal Gaussian post-filtering (ML-opt) through Monte-Carlo experiments involving the Hoffman brain phantom and the Shepp-Logan phantom. It is shown that, whatever the studied object and the count rate, SATO-PML and SATO-EMS are convergent in terms of β and produce images with bias, variance and contrast properties that are at least as good as those of the ML-opt images. The two proposed algorithms are also evaluated using realistic PET data from a Hoffman phantom produced using the GATE platform in order to demonstrate the feasibility of our SATO scheme with actual data.