Abstract Rayleigh scattering signals, not conforming bilinear and trilinear structure of spectral excitation–emission matrices (EEMs), significantly increases the difficulty of spectral resolution. To eliminate or reduce the interference of Rayleigh scattering, we propose missing data recovery (MDR) coupled with principal component analysis (PCA) or parallel factor analysis (PARAFAC) as a novel strategy for Rayleigh scattering correction and corresponding EEM decomposition. MDR treats the scattering data as missing by weighting them as zeros to remove Rayleigh scattering signals thoroughly. Then, sample signals are dramatically recovery in the scattering missing region during rapid iterative process of PCA or PARAFAC to repair bilinearity and trilinearity of EEMs. For significant Rayleigh scattering leading to severe signal loss, profile constraint on both of excitation and emission spectra following fluorescence spectral laws is further proposed for MDR-PCA and MDR-PARAFAC. It is so as to avoid mathematical reasonable but chemical meaningless solutions. The results reveal MDR-PCA and MDR-PARAFAC enable robust Rayleigh scattering correction and EEM decomposition both for simulated and practical data sets. Without the need of any specific priori knowledge and pretreatment such as wavelength selection, it therefore suggests great potential of the proposed method to be a generalized strategy for robust Rayleigh scattering correction and spectral resolution of EEMs.

中文翻译：

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用于荧光光谱分析的瑞利散射校正

摘要 瑞利散射信号不符合光谱激发-发射矩阵（EEMs）的双线性和三线性结构，显着增加了光谱分辨率的难度。为了消除或减少瑞利散射的干扰，我们提出缺失数据恢复 (MDR) 与主成分分析 (PCA) 或并行因子分析 (PARAFAC) 相结合，作为瑞利散射校正和相应 EEM 分解的新策略。MDR 通过将散射数据加权为零以彻底去除瑞利散射信号来将散射数据视为缺失。然后，在 PCA 或 PARAFAC 的快速迭代过程中，样本信号在散射缺失区域显着恢复，以修复 EEM 的双线性和三线性。对于导致严重信号丢失的显着瑞利散射，进一步提出了对 MDR-PCA 和 MDR-PARAFAC 遵循荧光光谱定律对激发光谱和发射光谱的轮廓约束。这是为了避免数学上合理但化学上无意义的解决方案。结果表明，MDR-PCA 和 MDR-PARAFAC 能够为模拟和实际数据集实现稳健的瑞利散射校正和 EEM 分解。不需要任何特定的先验知识和预处理（例如波长选择），因此表明所提出的方法具有巨大的潜力，可以成为强大的瑞利散射校正和 EEM 光谱分辨率的通用策略。结果表明，MDR-PCA 和 MDR-PARAFAC 能够为模拟和实际数据集实现稳健的瑞利散射校正和 EEM 分解。不需要任何特定的先验知识和预处理（例如波长选择），因此表明所提出的方法具有巨大的潜力，可以成为强大的瑞利散射校正和 EEM 光谱分辨率的通用策略。结果表明，MDR-PCA 和 MDR-PARAFAC 能够为模拟和实际数据集实现稳健的瑞利散射校正和 EEM 分解。不需要任何特定的先验知识和预处理（例如波长选择），因此表明所提出的方法具有巨大的潜力，可以成为强大的瑞利散射校正和 EEM 光谱分辨率的通用策略。