Filter banks and the EM algorithm

In this paper, we present a wavelet based modification of the ML-EM algorithm for reconstructing positron emission tomography images. By using the filter bank implementation of the wavelet transform, this algorithm has the flexibility to incorporate a priori information, while maintaining the same computational complexity as the standard ML-EM algorithm. Thus, it has a significant computational advantage over usual Bayesian methods. It differs from recent wavelet-based Bayesian methods as it achieves open-quotes regularizationclose quotes by an adaptive, wavelet-based method of thresholding which minimizes Stein's Unbiased Estimate of Risk. The basic method consists of applying Donoho and Johnstone's SureShrink wavelet denoising of the Poisson data, and then applying the standard ML-EM algorithm to the denoised data. A more elaborate method is discussed in which a wavelet denoising step is inserted after each EM iteration. This technique differs from previous smoothing techniques applied to the ML-EM algorithm since it is able to recover edges in discontinuous images