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We consider the numerical solution of noisy ill-posed nonlinear least squares problems with small residual. They arise when a mathematical model approximating a true distribution is fit to given data, in parameter estimation, experimental design and imaging problems. We propose an elliptical trust-region reformulation of a Levenberg-Marquardt procedure that, thanks to an appropriate choice of the trust-region radius, guarantees an automatic choice of the regularization parameters. Constrained problems are considered, too. Numerical results are provided.
This presentation is part of Minisymposium “MS71 - Nonlinear and adaptive regularization for image restoration”
organized by: Claudio Estatico (University of Genoa) , Giuseppe Rodriguez (University of Cagliari) .