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

In many fields of science one is interested in functions which are not dire ctly accessible by experiment but have to inferred from an experimentally m easurable quantity by solving an inverse problem. In general, this constitu tes an ill-posed problem. Therefore so-called regularization methods are ne cessary: Besides the constraint from the experimental data these methods im pose additional information on the solution, denoted as prior information a nd modeled by the so-called regularization term. For example, the Tikhonov regularization respectively its generalization to nonlinear inverse problem s, denoted as nonlinear regularization method and implemented in the progra m NLREG (J. Weese, Comput. Phys. Commun. 77 (1993) 429), are based on the p rior information that the solution is smooth. Thus, one is restricted to a specific linear regularization term. However, there exist some regularizati on 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 nonlinea r regularization method is implemented in the program GENEREG. (C) 2001 Els evier Science B.V. All rights reserved.