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

TL;DR

This paper introduces a straightforward algorithm combining Menger curvature and golden section search to efficiently identify the L-curve corner, aiding in optimal regularisation parameter selection for ill-posed inverse problems.

Contribution

The proposed method offers a simple, effective approach to locate the L-curve corner without relying on analytical curvature, improving regularisation parameter selection.

Findings

Algorithm successfully identifies the L-curve corner in test problems.

Compared favorably to traditional curvature-based methods.

Applied effectively to electrical resistance tomography data.

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.