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

Abstract

Rational polynomial coefficients in a rational function model (<small>RFM</small>) have high correlation and redundancy, especially in high-order <small>RFMs</small>, 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 <small>RFM</small> using the L-curve and finds the optimal regularization parameter with the minimum mean square error, then solves the parameters of the <small>RFM</small> 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 <small> RFM</small> parameters effectively, and their accuracy is increased by more than 85% on average relative to the other methods.