# Interpolation in the Presence of Domain Inhomogeneity

## TL;DR

This paper introduces a domain-informed interpolation method that leverages prior knowledge of domain inhomogeneity to improve signal reconstruction, especially near sharp boundaries, demonstrated on 1D signals and 2D fMRI images.

## Contribution

It presents a novel interpolation approach that incorporates domain inhomogeneity information through a domain-similarity metric, enhancing boundary recovery.

## Key findings

- Improved interpolation near domain boundaries.
- Effective in 1D and 2D applications.
- Demonstrated on real fMRI data.

## Abstract

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity, characterized by different, potentially overlapping, subdomains. By introducing a domain-similarity metric for each sample, the interpolation process is then based on a domain-informed consistency principle. We illustrate and demonstrate the feasibility of domain-informed linear interpolation in 1D, and also, on a real fMRI image in 2D. The results show the benefit of incorporating domain knowledge so that, for example, sharp domain boundaries can be recovered by the interpolation, if such information is available.