A generalized regularization method for nonlinear ill-posed problems enhanced for nonlinear regularization terms

Abstract

In many fields of science one is interested in functions which are not directly accessible by experiment but have to inferred from an experimentally measurable quantity by solving an inverse problem. In general, this constitutes an ill-posed problem. Therefore so-called regularization methods are necessary: Besides the constraint from the experimental data these methods impose additional information on the solution, denoted as prior information and modeled by the so-called regularization term. For example, the Tikhonov regularization respectively its generalization to nonlinear inverse problems, denoted as nonlinear regularization method and implemented in the program NLREG (J. Weese, Comput. Phys. Commun. 77 (1993) 429), are based on the prior information that the solution is smooth. Thus, one is restricted to a specific linear regularization term. However, there exist some regularization methods which make use of more elaborate prior information. Accordingly, there is a need for a program that can handle more general, in particular nonlinear regularization terms. Hence, the nonlinear regularization method is generalized in order to comply with this need. This generalized nonlinear regularization method is implemented in the program GENEREG.