INR Aliasing Limits
Identifiability and anti-aliasing sample design for fixed-Fourier-feature implicit representations.
Research question
A model can fit every sample on a grid while an out-of-band Fourier component is exactly indistinguishable from an in-band atom. This project asks when that silent reconstruction failure is unavoidable and how sampling design can expose it.
Approach
The work develops a visibility and aliasability analysis for fixed Fourier dictionaries, quantifies how off-grid jitter and randomized sampling break exact aliases, and constructs a sample design with a continuum certificate over a frequency band. CPU experiments cover synthetic signals, real signals, and two-dimensional folding.
Evidence and boundaries
The repository links theoretical checks to synthetic and real-signal experiments. The claims concern a fixed-feature, linear-coefficient model; they do not cover every implicit neural representation. Learned frequency sets are outside scope, and the repository reports that its nonlinear extension does not hold for SIRENs. This is active research and the manuscript is not presented here as a publication.
Artifacts and provenance
- Source code
- Repository manuscript — research manuscript; no publication claim
- Two-dimensional figure source
- Real-signal figure source
- Code and repository figures are distributed under the repository’s MIT license; external signal provenance remains recorded in the source repository.