Simultaneous confidence intervals for image reconstruction problems

We provide a methodology for specifying a set of simultaneous (1-α)% confidence intervals on the intensity of each image pixel for emission and transmission tomography. These intervals give a (1-α)% confidence region which, given a specific family of noise distributions, e.g. Gaussian or Poisson, is guaranteed to contain the actual image with probability at least 1-α. This region is a “set estimate” of the image which can be used to study confidence levels of popular image reconstructions such as filtered back projection, weighted-least-squares, and maximum likelihood. Alternatively, the set estimate can be used as a feasibility region from which particular image estimates can be selected based on additional criteria. A simulation for parallel ray projection geometries in emission tomography is given