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Domain-Informed Spline Interpolation

Behjat, Hamid LU ; Dogan, Zafer; Van De Ville, Dimitri and Sornmo, Leif LU (2019) In IEEE Transactions on Signal Processing 67(15). p.3909-3921
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... (More)

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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
B-splines, context-based interpolation, interpolation, multi-modal image interpolation, Sampling
in
IEEE Transactions on Signal Processing
volume
67
issue
15
pages
13 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85068123558
ISSN
1053-587X
DOI
10.1109/TSP.2019.2922154
language
English
LU publication?
yes
id
ce168d40-ac05-4061-a026-ddeec26c4e39
date added to LUP
2019-07-09 10:00:06
date last changed
2019-08-06 03:23:56
@article{ce168d40-ac05-4061-a026-ddeec26c4e39,
  abstract     = {<p>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.</p>},
  articleno    = {8734789},
  author       = {Behjat, Hamid and Dogan, Zafer and Van De Ville, Dimitri and Sornmo, Leif},
  issn         = {1053-587X},
  keyword      = {B-splines,context-based interpolation,interpolation,multi-modal image interpolation,Sampling},
  language     = {eng},
  month        = {08},
  number       = {15},
  pages        = {3909--3921},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Domain-Informed Spline Interpolation},
  url          = {http://dx.doi.org/10.1109/TSP.2019.2922154},
  volume       = {67},
  year         = {2019},
}