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.

A simple algorithm to find the L-curve corner in the regularisation of ill-posed inverse problems / Cultrera, Alessandro; Callegaro, Luca. - In: IOP SCINOTES. - ISSN 2633-1357. - 1:2(2020), p. 025004. [10.1088/2633-1357/abad0d]

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

Cultrera, Alessandro
;
Callegaro, Luca
2020

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11696/64814
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