To actually compute performance of a model observer on a specific task, it is necessary to have a complete and accurate characterization of the statistical properties of the reconstructed images. Noise in the images arises from Poisson noise in the data as well as from random variabilty in the object being imaged.
For linear reconstruction algorithms, it is not too difficult to compute at least the mean and covariance of a reconstructed image, but until recently it has not been possible to analyze the image statistics with nonlinear algorithms such as EM. We have recently solved this for EM-reconstructed images as a function of the number of iterations [9,10]. Monte-Carlo studies have verified the accuracy of the density, and current studies are extending the approach to a wide variety of other algorithms, including Bayesian algorithms that incorporate prior knowledge about the object.
A related problem aries when it is necessary to estimate certain object parameters from a tomographic image. For example, it might be desirable to estimate the diameter of a tumor to see how well a patient is responding to chemotherapy. We have investigated a number of different nonlinear estimation methods for such problems, and Craig Abbey has devised a method to compute the statistical properties of the resulting estimates. Again, theory and Monte Carlo experiments are in excellent agreement.