A two-steps inexact newton method for atmospheric remote sensing

In this paper we deal with regularization procedures for the nonlinear inverse problem of atmospheric profile retrievals from measurements of electromagnetic radiations. Since the inverse problem is severely ill-posed, Newton's linearization gives unsatisfactory results. In that case the linearized system is ill-conditioned, and its resolutions is very sensitive to the noise of input data. Here we propose an outer-inner two-steps iterative algorithm which belongs to the general class of inexact Newton method. The outer iteration is the Newton method and the inner iteration is the truncated Landweber one. In particular, truncated Landweber method regularizes the resolution of any outer Newton linearized step. The mathematical formulation of the 1-d problem is analyzed and the algorithm is described. Numerical experiments are performed, and the results are compared with the classical (i.e., one-step) Landweber method for nonlinear inverse problems.