The L-Curve and its Use in the Numerical Treatment of Inverse Problems

The L-curve is a log-log plot of the norm of a regularized solution versus the norm of the corresponding residual norm. It is a convenient graphical tool for displaying the trade-off between the size of a regularized solution and its fit to the given data, as the regularization parameter varies. The L-curve thus gives insight into the regularizing properties of the underlying regularization method, and it is an aid in choosing an appropriate regularization parameter for the given data. In this chapter we summarize the main properties of the L-curve, and demonstrate by examples its usefulness and its limitations both as an analysis tool and as a method for choosing the regularization parameter. 1 Introduction Practically all regularization methods for computing stable solutions to inverse problems involve a trade-off between the "size" of the regularized solution and the quality of the fit that it provides to the given data. What distinguishes the various regularization methods is how...