Evaluation of a New Regularization Prior for 3-D PET Reconstruction Including PSF Modeling

The response of a PET system can be described by its characteristic Point Spread Function (PSF) representing the spatial degradation of a point source due to physical effects and system design. If the PSF is accounted for in the reconstruction algorithm, better image quality and spatial resolution may be achieved. Un- fortunately, a common behaviour of unregularized iterative reconstruction techniques is represented by the increase of noise as the iterations proceed, while-on the other hand-a high number of iterations is usually needed to recover a significant percentage of the signal and to reach convergence, especially when resolution modelling is used in the reconstruction to recover the degraded signal. Moreover, a recognized effect of PSF-based reconstructions is the overenhancement of sharp transitions (edges) in the reconstructed images. In an attempt to solve both these problems, regularization strategies can be employed: a) to control the noise amplification as the iterations proceed and b) to reduce the edge overenhancement effect. In this work, a new prior for variational Maximum a posteriori regularization is proposed to be used in a 3-D One-Step-Late (OSL) reconstruction algorithm which also accounts for the PSF of the PET system. The new regularization prior is characterized by a strong smoothing component for regions in the image with a magnitude of the gradient below a given threshold (set to discriminate between background and signal), while preserving transitions above this threshold. The new algorithm has been validated on phantom and clinical data. The results showed that the use of the proposed regularization prior allows: a) a better control of the noise compared to un- regularized reconstructions, while maintaining high enough signal recovery thanks to the PSF action, and b) the control and reduction of the edge overenhancement, with a contemporary good preservation of spatial resolution.