A self-supervised learning approach for denoising autoregressive models with additive noise: finite and infinite variance cases
加性噪声自回归模型的自监督去噪：有限与无限方差情形AI 解读 ↓
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加性噪声自回归模型的自监督去噪：有限与无限方差情形
- 研究问题
- 自回归信号被强烈加性噪声污染，且信号或噪声可能具有无限方差时，如何恢复原始信号并进行预测？
- 方法与思路
- 作者提出受计算机视觉启发的自监督去噪方法，无需完全知道噪声分布，并在高斯与 α 稳定信号上开展实验。
- 材料陈述的贡献
- 摘要称该方法在合成与半合成数据中表现出较强去噪能力，尤其适用于强烈脉冲噪声，并展示恢复信号的预测应用。
- 阅读关注点
- 应核对自监督训练目标、对信号与噪声的依赖限制、无限方差下的评价指标，以及去噪结果如何进入预测。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收均未核实；摘要未说明训练细节和数值结果，无限方差下的理论性质也未交代。
原文摘要
The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive process and the corruptive noise may be highly impulsive, stemming from an infinite-variance distribution. The model estimation techniques that account for additional noise tend to show reduced efficacy when there is very strong noise present in the data, especially when the noise is heavy-tailed. In this paper, we propose a novel self-supervised learning method to denoise the additive noise-corrupted autoregressive model. Our approach is motivated by recent work in computer vision and does not require full knowledge of the noise distribution. We use the proposed method to recover exemplary finite- and infinite-variance autoregressive signals, namely, Gaussian and alpha-stable distributed signals, respectively, from their noise-corrupted versions. The simulation study conducted on both synthetic and semi-synthetic data demonstrates strong denoising performance of our method compared to several baseline methods, particularly when the corruption is significant and impulsive in nature. Finally, we apply the presented methodology to forecast the pure autoregressive signal from the noise-corrupted data.