05/29/2026
Imputing missing values in non-uniformly sampled time series often comes with a distinct trade-off. Standard methods like linear or spline interpolations typically introduce sharp derivative discontinuities, which can degrade velocity or acceleration calculations, while systematically damping cross-channel covariance.
To address these limitations, we have released Non-Uniform Fourier Infilling (NUFI), a new open-source spectral reconstruction framework.
Licensed under the MIT License, NUFI is designed to reconstruct continuous-time representations of multi-dimensional irregular time series while preserving underlying physical and statistical properties.
Here is a breakdown of how the framework operates:
🔹 Infinite Differentiability (C∞): By projecting irregular, incomplete signals onto a smooth trigonometric basis, the reconstructed signal's derivatives of all orders remain analytically continuous.
🔹 Covariance Preservation: Rather than treating channels independently, NUFI employs a pivoted LDL^T-based spectral covariance compensation scheme to maintain the original joint correlation structure of the observed variables.
🔹 Accelerated & Scalable Solvers: Supports both direct SVD-based solvers and an iterative, PyTorch-accelerated Conjugate Gradient (CG) solver O(NlogN) compatible with CUDA and Apple Silicon (MPS) for high-dimensional scaling.
🔹 Automated Hyperparameter Tuning: Optimizes frequency bins (M) and Tikhonov regularization (α) automatically using SVD-based Generalized Cross-Validation (GCV) to minimize predictive error without explicit test partitions.
🔹 Stochastic Multiple Imputation: Supports posterior process sampling to capture and represent reconstruction uncertainty, rather than relying solely on deterministic means.
We have also designed the library with an agent-native architecture, featuring zero-config entrypoints, append-only transaction logging, and Git/DVC-style lightweight snapshot versioning for data lineage tracking.
If you work with irregular physical signals, IoT sensor networks, or high-frequency financial time series, we hope this framework helps improve your data preparation pipelines.
Explore the codebase, read the technical whitepaper, or support the project with a star on GitHub:
👉 https://github.com/dataopsnick/nonuniform-fourier-infill
We welcome your feedback, issues, and contributions.
https://www.linkedin.com/feed/update/urn:li:activity:7466005849799553026/
