Optimization of Gibbs priors based on object size and contrast for maximum a posteriori reconstruction in SPECT

An attempt is made to determine how Gibbs priors can be designed to optimize the reconstruction of objects of specific sizes and contrasts using a MAP-EM (maximum a posteriori, expectation maximization) algorithm. Two-dimensional parallel projection datasets were realistically simulated for phantoms with various object sizes and contrasts. The resulting datasets were reconstructed using a MAP-EM algorithm with a Gibbs prior whose potential function is determined by a set of parameters. Analysis of the contrast and root-mean-squared-errors (RMSEs) of reconstructed objects revealed a tradeoff between noise reduction and contrast for the MAP-EM approach. It is found that the Gibbs priors can be designed to reduce noise and maintain edge sharpness, as compared to ML-EM (maximum-likelihood, EM), only for certain high-contrast objects, but that such priors may smooth over low-contrast objects. Methods for designing priors to optimize the reconstruction of high- or low-contrast objects are demonstrated. It is concluded that MAP-EM significantly reduces noise at the price of some object contrast and that Gibbs priors should be chosen carefully to avoid smoothing out important small and/or low-contrast objects