Liu Tingting, Liu Hai, Zhang Zhaoli, Liu Sanya
Appl Opt. 2018 Aug 1;57(22):6461-6469. doi: 10.1364/AO.57.006461.
Raman spectroscopy often suffers from the problems of band overlap and random noise. In this work, we develop a nonlocal low-rank regularization (NLR) approach toward exploiting structured sparsity and explore its applications in Raman spectral deconvolution. Motivated by the observation that the rank of a ground-truth spectrum matrix is lower than that of the observed spectrum, a Raman spectral deconvolution model is formulated in our method to regularize the rank of the observed spectrum by total variation regularization. Then, an effective optimization algorithm is described to solve this model, which alternates between the instrument broadening function and latent spectrum until convergence. In addition to conceptual simplicity, the proposed method has achieved highly competent objective performance compared to several state-of-the-art methods in Raman spectrum deconvolution tasks. The restored Raman spectra are more suitable for extracting spectral features and recognizing the unknown materials or targets.
拉曼光谱常常存在谱带重叠和随机噪声的问题。在这项工作中，我们开发了一种非局部低秩正则化（NLR）方法来利用结构稀疏性，并探索其在拉曼光谱反卷积中的应用。基于真实光谱矩阵的秩低于观测光谱的秩这一观察结果，我们的方法中制定了一个拉曼光谱反卷积模型，通过总变差正则化来正则化观测光谱的秩。然后，描述了一种有效的优化算法来求解该模型，该算法在仪器展宽函数和潜在光谱之间交替迭代直至收敛。除了概念简单之外，与拉曼光谱反卷积任务中的几种最先进方法相比，所提出的方法还取得了非常出色的目标性能。恢复后的拉曼光谱更适合于提取光谱特征以及识别未知材料或目标。
