A simple algorithm to find the L-curve corner in the regularisation of ill-posed inverse problems

Abstract

We propose a simple algorithm to locate the "corner" of an L-curve, a function often used to select the regularisation parameter for the solution of ill-posed inverse problems. The algorithm involves the Menger curvature of a circumcircle and the golden section search method. It efficiently finds the regularisation parameter value corresponding to the maximum positive curvature region of the L-curve. The algorithm is applied to some commonly available test problems and compared to the typical way of locating the l-curve corner by means of its analytical curvature. The application of the algorithm to the data processing of an electrical resistance tomography experiment on thin conductive films is also reported.

11 pages, 6 figures. Keywords: inverse problem, ill-posed problem, regularization parameter, L-curve, golden section search, Menger curvature, electrical resistance tomography