Efficient determination of multiple regularization parameters in a generalized L-curve framework 论文

摘要

. The selection of multiple regularization parameters is considered in a generalized Lcurve framework. Multiple dimensional extensions of the L-curve for selecting multiple regularization parameters are introduced, and a minimum distance function (MDF) is developed for approximating the regularization parameters corresponding to the generalized corner of the L-curve. It is shown through an L-curve model that the regularization parameters minimizing the MDF essentially maximize the curvature of the L-curve. Furthermore, the MDF approach leads to a simple fixed point iterative algorithm for computing regularization parameters. Examples indicate that the algorithm quickly converges, thereby reducing the cost associated with the implementation of generalized Lcurve method significantly. Key words. inverse problems, regularization parameter, L-curve AMS subject classifications. 65R30, 65F99 1. Introduction. In many inverse problems occurring in the physical sciences the observed data, g(...