Monte Carlo SURE-based regularization parameter selection for penalized-likelihood image reconstruction

Penalized likelihood (PL) image reconstruction has been developed for emission tomography to improve the image quality of reconstructed images. One challenge in PL reconstruction is that the selection of a proper regularization parameter to achieve a balance between the likelihood function and penalty function can be difficult. Here we present a novel method to choose the regularization parameter by minimizing Stein´s unbiased risk estimate (SURE), which is an unbiased estimator of the true mean square error (MSE) of the PL reconstruction. A Monte-Carlo method is developed to compute SURE. Simulation studies are conducted based on a real PET scanner. Results show that the Monte Carlo SURE provides a practical and reliable way to select the optimum regularization parameter to minimize the total predicted mean squared error.