Domain-Informed Spline Interpolation

Research output: Contribution to journalArticle

Abstract

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain tissue. We propose an interpolation method that instead exploits prior information about domain inhomogeneity, characterized by different, potentially overlapping, subdomains. As proof of concept, the focus is put on extending conventional shift-invariant B-spline interpolation. Given a known inhomogeneous domain, B-spline interpolation of a given order is extended to a domain-informed, shift-variant interpolation. This is done by constructing a domain-informed generating basis that satisfies stability properties. We illustrate example constructions of domain-informed generating basis and show their property in increasing the coherence between the generating basis and the given inhomogeneous domain. By advantageously exploiting domain knowledge, we demonstrate the benefit of domain-informed interpolation over standard B-spline interpolation through Monte Carlo simulations across a range of B-spline orders. We also demonstrate the feasibility of domain-informed interpolation in a neuroimaging application where the domain information is available by a complementary image contrast. The results show the benefit of incorporating domain knowledge so that an interpolant consistent to the anatomy of the brain is obtained.

Details

Authors
Organisations
External organisations
  • Harvard University
  • Swiss Federal Institute of Technology
  • University of Geneva
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Other Computer and Information Science
  • Structural Biology

Keywords

  • B-splines, context-based interpolation, interpolation, multi-modal image interpolation, Sampling
Original languageEnglish
Article number8734789
Pages (from-to)3909-3921
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume67
Issue number15
Publication statusPublished - 2019 Aug 1
Publication categoryResearch
Peer-reviewedYes