Approximation of noisy data using multivariate splines and finite element methods. (April 2021)

• Record Type: Journal Article
• Authors: Lamichhane, Bishnu P; Harris, Elizabeth; Le Gia, Quoc Thong
• Is Part Of: Journal of algorithms & computational technology. Volume 15(2021)
• Publication Date: 2021-04
• Subjects: Sobolev space -- scattered data interpolation -- Gaussian noise -- impulsive noise; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/17483026211008405
• Languages: English
• ISSNs: 1748-3018

Abstract

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.