L-surface and V-valley for multi-dimensional smoothing parameter selection

Multi-dimensional smoothing applications require the selection of a vector of smoothing parameters. Standard procedures can be computational demanding and tend to under smooth the observed measurements when noise correlation is present. The L-surface is an attractive two-dimensional generalization of the L-curve procedure for optimal smoothing. It preserves all the desirable feature of its uni-dimensional counterpart. However, one has to locate the point of maximal curvature of the surface, which is not easy. We introduce the V-valley as a simplified
procedure that replaces maximum curvature by a distance to be minimized.