RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems

TL;DR

RINS-T tackles time-series linear inverse problems under realistic degradations including non-Gaussian noise and outliers by uniting neural priors with a robust huber-based data-fit. The method operates unsupervised, using an untrained CNN as an implicit prior and three core techniques—guided input initialization, input perturbation, and convex output combination—to stabilize optimization and improve recovery. The framework is validated across denoising, imputation, and audio compressed sensing, with extensions to multivariate signals, consistently outperforming strong baselines and showing robustness to noise, missing data, and corruption. The work offers a practical, data-efficient approach for robust time-series reconstruction with potential extensions to multi-scale architectures and nonlinear forward models.

Abstract

Time series data are often affected by various forms of corruption, such as missing values, noise, and outliers, which pose significant challenges for tasks such as forecasting and anomaly detection. To address these issues, inverse problems focus on reconstructing the original signal from corrupted data by leveraging prior knowledge about its underlying structure. While deep learning methods have demonstrated potential in this domain, they often require extensive pretraining and struggle to generalize under distribution shifts. In this work, we propose RINS-T (Robust Implicit Neural Solvers for Time Series Linear Inverse Problems), a novel deep prior framework that achieves high recovery performance without requiring pretraining data. RINS-T leverages neural networks as implicit priors and integrates robust optimization techniques, making it resilient to outliers while relaxing the reliance on Gaussian noise assumptions. To further improve optimization stability and robustness, we introduce three key innovations: guided input initialization, input perturbation, and convex output combination techniques. Each of these contributions strengthens the framework's optimization stability and robustness. These advancements make RINS-T a flexible and effective solution for addressing complex real-world time series challenges. Our code is available at https://github.com/EPFL-IMOS/RINS-T.

Figures (9)

• Figure 1: Illustration of the measurement forward and inverse problems. In the forward problem, a clean signal passes through a measurement system (e.g., sensor and acquisition chain) and is degraded by noise, producing the observed signal. The inverse problem seeks to reconstruct the clean signal from these corrupted measurements.
• Figure 2: Illustration of the Huber loss transition as the threshold parameter $\lambda$ varies. Curves are shown for several representative $\lambda$ values.
• Figure 3: Overview of the architecture used for Deep Prior, including encoder and decoder blocks connected through skip connections.
• Figure 4: Ability of the Network to Fit Gaussian Noise and a Clean Audio Signal
• Figure 5: Comparison of average SNR values across three denoising scenarios using different methods. The proposed RINS-T method consistently achieves the best SNR across all scenarios.