The denoised spectra using KL-smooth-LR were smooth and the peaks of C, O, and Si were more enhanced compared to the results using the other smoothing techniques. Although the low-rank regularization alone was insufficient for noise reduction (KL-LR) no matter how its parameter µ was tuned, it improved the shape of spectra using KL-smooth-LR compared to those using only the smoothness (KL-smooth): the single Si-peak for SiO 2 was more split without the low-rank regularization (KL-smooth), and the shift of Si-peak for the Si phase was reduced by regularizing the smoothing term by the low-rankness. Using the comparative smoothing level, we had broader spectra when using Euclidean distance compared to KL divergence due to their different metrics. As a result of using Euclidean distance, false peaks (blue line) appeared at the C-peak region (EUC-smooth-LR/EUC-LR). This is because the deviation from the observation is equal when using Euclidean distance, even though we are dealing with count data. KL divergence, in contrast, allows larger deviation from the observation at larger counts, and thus the small peaks tend to be less affected. In addition, the Si-peaks for the Si and SiC phases are distorted when using Euclidean distance (EUC-smooth) compared to those obtained using KL divergence (KL-smooth). The 1D Gaussian smoothing resulted in similar spectra as those obtained using EUC-smooth. As a result of using the moving average, the shapes of the reference spectra and the spectral resolution were clearly degraded the most. Note that both the 1D Gaussian smoothing and the moving average do not consider the statistics of noise, in contrast to the proposed method.