Recent developments in iterative image reconstruction for PET and SPECT [Editorial]

T HREE articles that begin this issue of TMI describe distinct regularized approaches to iterative image reconstruction from emission tomography data [24], [27], [39]. Their publication in this issue provides us with the opportunity to explain the background to this work and speculate on the future of such methods. Model-based iterative approaches to image reconstruction in PET and SPECT allow optimal noise handling [37] and accurate system response modeling [38], [34]. Research in model-based image reconstruction methods addresses two key issues: how to select a cost function that produces images with the desired properties and how to find these images quickly. In the first category we include work addressing statistical and physical models for the data, selection of image smoothing terms or priors that regularize the solution and the choice of cost function to be optimized over the image space [30]. The second area addresses the issue of rapidly finding a solution once a cost function has been selected. In principle, the solutions to the concave maximization problems typically encountered in image reconstruction are independent of the numerical algorithm selected to find them. In practice however, fast algorithms are often terminated before convergence so that the solution becomes a function of the algorithm. Nevertheless, it is useful to maintain the distinction between classes of algorithms that compute, ostensibly, the same solution and those that optimize different cost criteria and, hence, result in different solutions. Here we are primarily concerned with the choice of iterative algorithm rather than issues relating to cost function selection. The early iterative algorithms for image reconstruction, which form the broad class of algebraic reconstruction techniques (ART’s), solve sets of simultaneous, possibly under-determined, linear equations [4], [17], [21]. While the ART methods have much in common with more recently developed statistically-based iterative methods, they do not themselves directly model noise in the data. Shepp and Vardi’s maximum likelihood (ML) algorithm, based on the EM (expectation maximization) methods of Dempster, Laird, and Rubin, was among the first to explicitly model the Poisson distribution of noise in photon limited imaging systems such as PET and SPECT [37]. The EM formalism for this problem gives rise to an elegant update equation reminiscent of the earlier multiplicative ART algorithms. The improvements in image quality the EMML produced inspired a tremendous amount of subsequent research. Much of this work has addressed the problem of speeding up EMML’s