Consistency Set Estimation for PET Image Reconstruction

We give a method for determining a set of images which are consistent with measured projections data and error bounds on the projections noise The error bounds can account for both statistical noise uncertainty and model uncertainty e g due to a mismodeled or un calibrated system matrix If one knows the statistical distribution of the projections errors then one can se lect the error bounds to give a consistency set which is a con dence region on the true image given the measured data This region is a set estimate of the image which can be used to study con dence levels of popular image reconstructions such as ltered back projection weighted least squares and maximum likeli hood Alternatively the set estimate can be used as a feasibility region from which particular image estimates can be selected based on additional criteria We pro vide some numerical results for parallel ray projection geometries with Poisson projection statistics