ℓ1-Regression based subdivision schemes for noisy data

Fitting curve and surface by least-regression is quite common in many scientific fields. It, however cannot properly handle noisy data with impulsive noises and outliers. In this article, we study ℓ1-regression and its associated reweighted least squares for data restoration. Unlike most existing work, we propose the ℓ1-regression based subdivision schemes to handle this problem. In addition, we propose fast numerical optimization method: dynamic iterative reweighted least squares to solve this problem, which has closed form solution for each iteration. The most advantage of the proposed method is that it removes noises and outliers without any prior information about the input data. It also extends the least square regression based subdivision schemes from the fitting of a curve to the set of observations in 2-dimensional space to a p-dimensional hyperplane to a set of point observations in (p+1)-dimensional space. Wide-ranging experiments have been carried out to check the usability and practicality of this new framework.