Positively Constrained Multiplicative Iterative Algorithm for Maximum Penalized Likelihood Tomographic Reconstruction

This paper first develops a general multiplicative iterative (MI) algorithm for tomographic image reconstructions, where the objective function is only specified as a general function containing two components: a data mismatch component and a penalty component. This general algorithm is then applied to different objective functions deduced from different probability models for measurements in emission or transmission tomography, such as Poisson, Gaussian, or shifted Poisson models. Furthermore, an approximate line search step can be easily incorporated into the algorithm so that the objective function is guaranteed to increase during the iterations. This MI algorithm (with line search) is easy to implement, as it performs only one forward- and one or two back-projection in each iteration, and it respects the positivity constraint usually imposed on reconstructions.