Online Positron Emission Tomography By Online Portfolio Selection

The number of measurement outcomes in positron emission tomography (PET) is typically large, rendering signal reconstruction computationally expensive. We propose an online algorithm to address this computational issue. The per-iteration computational complexity of the proposed algorithm is independent of the number of measurement outcomes and linear in the signal dimension. The algorithm has a rigorous $O ( 1 / \sqrt{k} )$ convergence rate guarantee, where $k$ denotes the iteration counter. Numerical experiments on synthetic data-sets show that the algorithm can be significantly faster than expectation maximization and stochastic primal-dual hybrid gradient method. The proposed algorithm is based on an equivalent stochastic optimization formulation, the Soft-Bayes algorithm for online portfolio selection, and standard online-to-batch conversion.