Ken Sauer

Bayesian multiresolution algorithm for PET reconstruction

We introduce a spatially non-homogeneous adaptive image model and multiresolution reconstruction algorithm for Bayesian tomographic reconstruction. In contrast to existing approaches, the proposed image model is formulated in a multiresolution wavelet domain and relies on training data to incorporate the expected characteristics of typical reconstructions. The actual tomographic reconstruction is performed in the space domain to simplify enforcement of the positivity constraint. We apply the proposed algorithm to simulated data and to data acquired using the IndyPET dedicated research scanner. Our experimental results indicate that our algorithm can improve reconstruction quality over fixed resolution Bayesian methods.

Spectral Design in Markov Random Fields

Markov random fields (MRFs) have been shown to be a powerful and relatively compact stochastic model for imagery in the context of Bayesian estimation. The simplicity of their conventional embodiment implies local computation in iterative processes and relatively noncommittal statistical descriptions of image ensembles, resulting in stable estimators, particularly under models with strictly convex potential functions. This simplicity may be a liability, however, when the inherent bias of minimum mean‐squared error or maximum a posteriori probability (MAP) estimators attenuate all but the lowest spatial frequencies. In this paper we explore generalization of MRFs by considering frequency‐domain design of weighting coefficients which describe strengths of interconnections between clique members.

Quantitative comparison of FBP, EM, and Bayesian reconstruction algorithms, including the impact of accurate system modeling, for the IndyPET scanner

We quantitatively compare filtered backprojection (FBP), expectation maximization (EM), and Bayesian reconstruction algorithms as applied to the IndyPET scanner, a small to intermediate field of view dedicated research scanner. A key feature of our investigation is the use of an empirical system kernel determined from scans of line source phantoms. This kernel is incorporated into the forward operator of EM and the Bayesian reconstruction algorithms. Our results indicate that, particularly when an accurate system kernel is used, Bayesian methods can significantly improve reconstruction quality over FBP and EM.