Sequential Projected Newton method for regularization of nonlinear least squares problems

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on discrepancy principle. formulate problem as an equality constrained optimization problem, where constraint is given by least squares data fidelity term and expresses The objective function convex that incorporates some prior knowledge, such total variation function. Using Jacobian matrix forward model, we consider sequence quadratically can all be solved using Projected Newton method. show solution sub-problem results in descent direction exact merit This then used to describe formal line-search also slightly more heuristic approach simplifies allows inexact sub-problems. illustrate behavior number numerical experiments, with Talbot-Lau X-ray phase contrast imaging main application. experiments confirm sub-problems need not high accuracy early iterations make sufficient progress towards solution. In addition, proposed method able produce reconstructions similar quality compared other state-of-the-art approaches significant reduction computational time.