Trade-off between contrast recovery, image noise and edge artifacts in PET image reconstruction using detector blurring models

Accurate system modeling is essential for improved quantitation and lesion detection. Many investigators have made efforts to accurately model detector blurring using point spread functions (PSFs) in sinogram space and to incorporate them into image reconstruction for accurate quantitation. It has been observed that incorporating detector PSF into reconstruction leads to improved contrast recovery and resolution with reduced noise but introduces edge artifacts. It is not straightforward to investigate the impact of PSF kernels on image qualities because of lack of a tool to quantitatively analyze nonlinearly object-dependent OSEM. Accordingly, there have been few methods to reduce edge artifacts in a systematically object-independent way. Our goal is to analyze edge artifacts as well as contrast recovery, resolution and image noise in image reconstruction using various PSF models including full, under-modeled and no PSF kernels, and to provide a systematic solution to reduce edge artifacts without loss of contrast recovery. We focus on penalized likelihood reconstruction with quadratic regularization. Building on previous work, we derive analytical expressions for local impulse response and covariance where a PSF model mismatch exists so that one can analytically predict image qualities, such as contrast recovery, noise and edge artifacts, as a function of regularization parameters and reconstruction PSF kernels. Using the analytical tools, we show that there exists a trade-off between contrast recovery (or resolution), image noise and edge artifacts and that one can control the trade-off by tuning regularization parameters and reconstruction PSF kernels.