De-noising is a prominent step in the spectra post-processing procedure. Previous machine learning-based methods are fast but mostly based on supervised learning and require a training set that may be typically expensive in real experimental measurements. Unsupervised learning-based algorithms are slow and require many iterations to achieve convergence. Here, we bridge this gap by proposing a training-set-free two-stage deep learning method. We show that the fuzzy fixed input in previous methods can be improved by introducing an adaptive prior. Combined with more advanced optimization techniques, our approach can achieve five times acceleration compared to previous work. Theoretically, we study the landscape of a corresponding non-convex linear problem, and our results indicates that this problem has benign geometry for first-order algorithms to converge.

翻译：去噪是光谱后处理流程中的关键步骤。以往基于机器学习的方法虽速度快，但大多依赖监督学习，且需要训练集，而实际实验测量中获取训练集通常成本高昂。基于无监督学习的算法速度较慢，需要大量迭代才能收敛。为此，我们提出一种无需训练集的两阶段深度学习方法，弥补了这一不足。研究表明，通过引入自适应先验，可改进先前方法中模糊的固定输入。结合更先进的优化技术，我们的方法相比以往工作可实现五倍的加速。理论上，我们研究了相应非凸线性问题的几何结构，结果表明该问题对一阶算法具有良性几何性质，可确保其收敛。