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arXiv · 1608.04571

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

Alessandro Cultrera·Luca Callegaro
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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.

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Alessandro Cultrera, Luca Callegaro. 2016-08-16. A simple algorithm to find the L-curve corner in the regularisation of ill-posed inverse problems. https://doi.org/10.1088/2633-1357%2Fabad0d

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