Optimal Regularization Method Based on the L-Curve for Solving Rational Function Model Parameters

Rational polynomial coefficients in a rational function model (RFM) have high correlation and redundancy, especially in high-order RFMs, which results in ill-posed problems of the normal equation. For this reason, this article presents an optimal regularization method with the L-curve for solving rational polynomial coefficients. This method estimates the rational polynomial coefficients of an RFM using the L-curve and finds the optimal regularization parameter with the minimum mean square error, then solves the parameters of the RFM by the Tikhonov method based on the optimal regularization parameter. The proposed method is validated in both terrain-dependent and terrain-independent cases using Gaofen-1 and aerial images, respectively, and compared with the least-squares method, L-curve method, and generalized cross-validation method. The experimental results demonstrate that the proposed method can solve the RFM parameters effectively, and their accuracy is increased by more than 85% on average relative to the other methods.