Maximum entropy algorithms for image reconstruction from projections

Abstract

Image reconstruction from projections can be viewed as a linear inverse problem with discrete data if the number of projections is small. The input data corresponds to integral equations in the mathematical model for numerical reconstruction. As this problem does not have unique solution, these equations may be viewed as the equality constraints for maximization of a functional such as entropy. Applying the dual formulations in optimization of entropy, one finds that they correspond to the well known algorithms MART and MENT respectively. This equivalence applies only if the natural basis is adopted in MART. For MENT, in this case, the non-discrete formulation is identical to the discrete dual one.