A Bayesian MAP-EM algorithm for PET image reconstruction using wavelet transform

In this paper, we present a PET reconstruction method using the wavelet-based maximum a posteriori (MAP) expectation-maximization (EM) algorithm. The proposed method, namely WV-MAP-EM, shows several advantages over conventional methods. It provides an adaptive way for hyperparameter determination. Since the wavelet transform allows the use of fast algorithms, WV-MAP-EM also does not increase the order of computational complexity. The spatial noise behavior (bias/variance and resolution) of the proposed MAP estimator is analyzed. Quantitative comparisons to MAP methods with Markov random field (MRF) prior models point out that our alternative method, wavelet-base method, offers competitive performance in PET image reconstruction. Index Terms--Expectation-maximization (EM), image reconstruction, maximum a posteriori (MAP), positron emission tomography (PET), wavelet transform.