PET image reconstruction by vector norm optimization

Ultimately, positron emission tomography (PET) image reconstruction boils down to solving an overdetermined system of linear equations with nonnegative variables. The latter requirement gets a natural treatment if the problem is reformulated as an optimization problem. The deviation ||Ax-b|| can be measured by different vector norms leading to different optimization problems. In the paper we give some preliminary results of our investigations about the usefulness of advanced optimization techniques for the solution of different formulations of the problem