Primal-dual approach to optical tomography with discretized path integral with efficient formulations

We propose an efficient optical tomography with discretized path integral. We first introduce the primal-dual approach to solve the inverse problem formulated as a constraint optimization problem. Next, we develop efficient formulations for computing Jacobian and Hessian of the cost function of the constraint nonlinear optimization problem. Numerical experiments show that the proposed formulation is faster ([Formula: see text]) than the previous work with the log-barrier interior point method ([Formula: see text]) for the Shepp-Logan phantom with a grid size of [Formula: see text], while keeping the quality of the estimation results (root-mean-square error increasing by up to 12%).