Fast Polynomial Spline Approximation for Large Scattered Data Sets via L1 Minimization

摘要

In this article, we adress the problem of approximating scattered data points by C~1-smooth polynomial spline curves using L_1-norm optimization. The use of this norm helps us to preserve the shape of the data even near to abrupt changes. We introduced a five-point sliding window process for L_1 spline approximation but this method can be still time consuming despite its linear complexity. Consequently, based on new algebraic results obtained for L_1 approximation on any three points, we define in this article a more efficient method.