An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems

This paper considers an efficient iterative approach to solve separable nonlinear least squares problems that arise in large scale inverse problems. A variable projection GaussNewton method is used to solve the nonlinear least squares problem, and Tikhonov regularization is incorporated using an iterative Lanczos hybrid scheme. Regularization parameters are chosen automatically using a weighted generalized cross validation method, thus providing a nonlinear solver that requires very little input from the user. An application from image deblurring illustrates the effectiveness of the resulting numerical scheme.