Univariate subdivision schemes for noisy data

TL;DR

This paper introduces univariate subdivision schemes that refine noisy data by fitting local least squares polynomials, analyzing their convergence, smoothness, and comparing their performance with local linear regression methods.

Contribution

The paper presents new linear, stationary subdivision schemes for noisy data, including their analysis and comparison with existing local regression techniques.

Findings

Schemes effectively refine noisy data and produce smooth limit functions.

Numerical experiments demonstrate the schemes' convergence and performance.

Comparison shows advantages over traditional local linear regression methods.

Abstract

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.