De-noising plays a crucial role in the post-processing of spectra. Machine learning-based methods show good performance in extracting intrinsic information from noisy data, but often require a high-quality training set that is typically inaccessible in real experimental measurements. Here, using spectra in angle-resolved photoemission spectroscopy (ARPES) as an example, we develop a de-noising method for extracting intrinsic spectral information without the need for a training set. This is possible as our method leverages the self-correlation information of the spectra themselves. It preserves the intrinsic energy band features and thus facilitates further analysis and processing. Moreover, since our method is not limited by specific properties of the training set compared to previous ones, it may well be extended to other fields and application scenarios where obtaining high-quality multidimensional training data is challenging.

翻译：去噪在光谱后处理中起着关键作用。基于机器学习的方法在从含噪数据中提取本征信息方面表现出良好的性能，但通常需要高质量的训练集，而这在实际实验测量中往往难以获得。本文以角分辨光电子能谱（ARPES）中的光谱为例，开发了一种无需训练集即可提取本征光谱信息的去噪方法。该方法之所以可行，是因为其利用了光谱自身的自相关特性。该方法能够保留本征能带特征，从而便于后续分析与处理。此外，与以往方法相比，本方法不受训练集特定性质的限制，因此可以很好地推广到难以获取高质量多维训练数据的其他领域及应用场景。