  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.
