Information operator approach and iterative regularization methods for atmospheric remote sensing

In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss–Newton and Levenberg–Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO2 retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen.