L- and V-curves for Optimal Smoothing

The L-curve is a tool for the selection of the regularization parameter in ill-posed inverse
problems. It is a parametric plot of the size of the residuals vs that of the penalty. The
corner of the L indicates the right amount of regularization. In the context of smoothing
the L-curve is easy to compute and works surprisingly well, even for data with correlated
noise. We present the theoretical background and applications to real data together with an
alternative criterion for finding the corner automatically. We introduce as simplification, the
V-curve, which replaces finding the corner of the L-curve by locating a minimum.