Fast maximum entropy approximation in SPECT using the RBI-MAP algorithm

In this work, we present a method for approximating constrained maximum ent ropy (ME) reconstructions of SPECT data with modifications to a block-itera tive maximum a posteriori (MAP) algorithm, Maximum likelihood (ML)-based re construction algorithms require some form of noise smoothing. Constrained M E provides a more formal method of noise smoothing without requiring the us er to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a give n distance from the noisy measured data, with that distance determined by t he magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images, We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reco nstruction is critical because feasibility is not meaningful unless the pro jection model is as accurate as possible. Because the constrained ME soluti on is the same as a MAP solution for a particular value of the MAP weightin g parameter, beta, the constrained ME solution can be found with a MAP algo rithm if the correct value of beta is found. We show that the RBI-MAP algor ithm, if used with a dynamic scheme for estimating beta, can approximate co nstrained ME solutions in 20 or fewer iterations, We compare results for va rious methods of achieving feasible images on a simulation of Tl-201 cardia c SPECT data. Results show that the RBI-MAP ME approximation provides image s and quantitative estimates close to those from a slower algorithm that gi ves the true ME solution, Also, we find that the ME results have higher spa tial resolution and greater high-frequency noise content than a feasibility -based stopping rule, feasibility-based tow-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with t he dynamic procedure or a feasibility-based stopping rule, and that such re constructions may be particularly useful in applications where resolution i s critical.