A robust reconstruction method based on local Bayesian estimation combined with CURE clustering

Due to their good approximation accuracy and local fitting characteristics, the moving least squares (MLS) and moving total least squares (MTLS) methods are widely used in various engineering fields. However, neither of these two methods is robust and they cannot effectively deal with outliers in measurement data. To eliminate the negative influence of outliers and achieve robust reconstruction, a novel MTLS method is proposed in this paper, which introduces local Bayesian estimation combined with clustering using representatives (CURE) algorithm. In the support domain, this method adopts a two-step process to remove the abnormal points and adjust the weights of discrete points through compound weighting. Bayesian estimation is first performed on discrete points to derive the reference model, and the residuals are calculated as the input of CURE clustering. The points with large residuals are classified into one cluster and removed. The remaining points undergo repeated processing until the iteration concludes. A gradient weight function based on the residuals and a compact support weight function are combined to determine the final estimated value using weighted Bayesian estimation. The simulations and experiments demonstrate that the proposed reconstruction method achieves excellent accuracy and robustness, surpassing several existing methods when handling highly contaminated datasets.