Univariate subdivision schemes for noisy data

We introduce and analyse univariate, linear, and stationary subdivision schemes for refining noisy data, by fitting local least squares polynomials. We first present primal schemes, based on fitting linear polynomials to the data, and study their convergence, smoothness, and basic limit functions. We provide several numerical experiments that illustrate the limit functions generated by these schemes from initial noisy data, and compare the results with approximations obtained from noisy data by an advanced local linear regression method. We conclude by discussing several extension and variants.