THE USE OF THE L-CURVE IN THE REGULARIZATION OF DISCRETE III-POSED PROBLEMS

Regularization algorithms are often used to produce reasonable solutio ns to ill-posed problems. The L-curve is a plot-for all valid regulari zation parameters-of the size of the regularized solution versus the s ize of the corresponding residual. Two main results are established. F irst a unifying characterization of various regularization methods is given and it is shown that the measurement of ''size'' is dependent on the particular regularization method chosen. For example, the 2-norm is appropriate for Tikhonov regularization, but a 1-norm in the coordi nate system of the singular value decomposition (SVD) is relevant to t runcated SVD regularization. Second, a new method is proposed for choo sing the regularization parameter based on the L-curve, and it is show n how this method can be implemented efficiently. The method is compar ed to generalized cross validation and this new method is shown to be more robust in the presence of correlated errors.