Active constrained truncated Newton method for simple-bound optical tomography
In the past, nonlinear unconstrained optimization of the optical imaging problem has focused on Newton-Raphson techniques. Besides requiring expensive computation of the Jacobian, the unconstrained minimization with Tikhonov regularization can pose significant storage problems for large-scale reconstructions, involving a large number of unknowns necessary for realization of optical imaging. We formulate the inverse optical imaging problem as both simple-bound constrained and unconstrained minimization problems in order to illustrate the reduction in computational time and storage associated with constrained image reconstructions. The forward simulator of excitation and generated fluorescence, consisting of the Galerkin finite-element formulation, is used in an inverse algorithm to find the spatial distribution of absorption and lifetime that minimizes the difference between predicted and synthetic frequency-domain measurements. The inverse approach employs the truncated Newton method with trust region and a modification of automatic reverse differentiation to speed the computation of the optimization problem. The reconstruction results confirm that the physically based, constrained minimization with efficient optimization schemes may offer a more logical approach to the large-scale optical imaging problem than unconstrained minimization with regularization.