Regularization of inverse problems in atmospheric remote sensing

In this chapter we present the basic concepts of numerical regularization theory. We analyze direct and iterative methods for solving nonlinear ill-posed problems in a general framework. From the category of direct methods we choose the method of Tikhonov regularization, while from the category of iterative methods we pay attention to the iteratively regularized Gauss–Newton method and the regularizing Levenberg–Marquardt method. For the Tikhonov regularization, we discuss the practical aspects of the regularization parameter choice methods, which are decisive for obtaining a reliable solution of the inverse problem. The efficiency of the regularization methods is analyzed from the numerical point of view by considering several test problems of atmospheric remote sensing