Iterative algorithms for nonlinear problems in remote sensing

Abstract

First a brief review of the Backus and Gilbert method for the linear problems is given. Then a comprehensive presentation of iterative algorithms for constructing approximate solutions of nonlinear problems from erroneous inadequate data is given. Proofs of convergence and error estimates of these iterative algorithms are obtained. It is found that locally the limit of the iterates does not satisfy the original nonlinear operator equation, but a somewhat different nonlinear equation which depends on the initial iterate. A nonlinear radiative transfer equation in remote sensing of the atmospheric temperature profiles is used as an example to demonstrate the applicability of the iterative algorithms. Finally, a discussion of the present status of research in this domain and some personal views on what should be the useful lines for future research is given.