Regularization parameter selection for Bayesian reconstruction of attenuation map

Previously the authors developed algorithms to obtain transmission reconstructions from truncated projections and from emission data without transmission measurements. The optimal basis set of "knowledge set" was used to create an approximate attenuation map, and the expansion coefficients were estimated using optimization algorithms. Since a truncated expansion does not represent an image precisely and the projections of the basis vectors are not orthogonal, the estimated coefficients can be unstable in the presence of systematic errors. A constraint, based on distribution of the expansion coefficient, is considered here to regularize the estimation problem. The parameter selection methods based on different assumptions are applied to find the optimal regularization parameter. The selected regularization parameter obtained from a projection data set has been shown to provide satisfactory reconstruction results.