Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the development of several algorithms. However, we have observed that the efficacy of these algorithms tends to diminish when the time series exhibit non-stationary oscillatory behavior. In this paper, we introduce a novel algorithm, coined Harmonic Level Interpolation (HaLI), which enhances the performance of existing imputation algorithms for oscillatory time series. After running any chosen imputation algorithm, HaLI leverages the harmonic decomposition based on the adaptive nonharmonic model of the initial imputation to improve the imputation accuracy for oscillatory time series. Experimental assessments conducted on synthetic and real signals consistently highlight that HaLI enhances the performance of existing imputation algorithms. The algorithm is made publicly available as a readily employable Matlab code for other researchers to use.

翻译：处理含缺失值的时间序列，包括受低质量或过饱和影响的数据，是一项重大的信号处理挑战。恢复这些缺失值的任务（即插补）已催生多种算法。然而，我们观察到当时间序列呈现非平稳振荡行为时，这些算法的效能往往下降。本文提出一种新型算法——谐波水平插值法（Harmonic Level Interpolation, HaLI），该算法可增强现有插补算法对振荡时间序列的性能。在运行任意选定的插补算法后，HaLI 利用基于初始插补的自适应非谐波模型的谐波分解，提升振荡时间序列的插补精度。在合成信号与真实信号上进行的实验评估一致表明，HaLI 能增强现有插补算法的性能。该算法以可直接使用的 Matlab 代码形式公开发布，供其他研究人员使用。