Study On Regularization Parameter Choice—Based On The L-curve

The choice of regularization parameter is one of the key issues of the various regularization strategies. In this paper, we use the L-curve method to estimate the optimal regularization parameter in truncated singular value decomposition(TSVD). Since the optimal regularization parameter corresponds to the point with the maximum curvature of the L-curve, and the point is called the L-corner, so the use of L-curve method to choose the optimal regularization parameter is actually to find the L-corner. To choose the optimal regularization parameter in TSVD, we provide a new method which based on triangle method to find the L-corner. Firstly, we use the triangle method which is used to determine the iterative number in conjugate gradient least square(GCLS) to determine the optimal regularization parameter in TSVD, and then we propose to use quadratic spline interpolation to improve it so that we can determine the L-corner by comparing the curvature of the different quadratic spline interpolation curves.Numerical results of several test problems are given to illustrate the effectiveness of the new method and it is better than triangle method.