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.

翻译：时间序列数据常受多种形式的损坏影响，如缺失值、噪声和异常值，这对预测和异常检测等任务构成重大挑战。为解决这些问题，逆问题侧重于利用关于信号底层结构的先验知识，从损坏数据中重建原始信号。尽管深度学习方法在该领域已展现出潜力，但它们通常需要大量预训练，且在分布偏移下泛化能力不足。本文提出RINS-T（面向时间序列线性逆问题的鲁棒隐式神经求解器），这是一种无需预训练数据即可实现高恢复性能的新型深度先验框架。RINS-T利用神经网络作为隐式先验，并集成鲁棒优化技术，使其对异常值具有鲁棒性，同时降低了对高斯噪声假设的依赖。为进一步提升优化稳定性和鲁棒性，我们引入了三项关键创新：引导输入初始化、输入扰动和凸输出组合技术。每项贡献都增强了框架的优化稳定性与鲁棒性。这些进展使RINS-T成为应对复杂现实世界时间序列挑战的灵活有效解决方案。我们的代码发布于 https://github.com/EPFL-IMOS/RINS-T。