Uncertainty Estimation for Bayesian Reconstructions from Low-Count SPECT Data

Bayesian analysis is especially useful to apply to lowcount medical imaging data, such as gated cardiac SPECT, because it allows one to solve the nonlinear, ill-posed, inverse problems associated with such data. One advantage of the Bayesian approach is that it quantifies the uncertainty in estimated parameters through the posterior probability. We compare various approaches to exploring the uncertainty in Bayesian reconstructions from SPECT data including: 1) the standard estimation of the covariance of an estimator using a frequentist approach, 2) a new technique called the "hard truth" in which one applies "forces" to the parameters and observes their displacements, and 3) Markov-chain Monte Carlo sampling of the posterior probability distribution, which in principle provides a complete uncertainty characterization.