Figure shows the results of applying wPCA to the preliminary denoised data using the proposed method or existing smoothing techniques. The first to third columns show the denoised images at the peak energy of C, O, and Si. The C-peak image obtained by using KL-smooth-LR has distributions mainly at the area of SiC (first column, top row of Figure ). We also had zero intensities at points where the ROI images also had zero intensities. Although we cannot go in-depth on the phenomenological interpretation of the observed intensities, this result is consistent with the observation. The C-peak images obtained by using the other smoothing techniques, in contrast, have C distributions at the area of pure Si (first column, second to the last rows of Figure ), and is not consistent with the observation. Two columns at the right end show the denoised spectra after the projection step. Compared to the results of directly applying wPCA (the bottom row of Figure ), the denoised spectra using the proposed method are smooth and the peaks correspond to those of C, O, and Si. False C-peaks appeared in the reconstructed signals (blue lines), except for KL-smooth-LR. These false peaks are inconsistent with the observation, as we had zero intensities at this energy region, as shown in the left of Figure . A result using Euclidean distance is shown at the 4th row of Figure . Not only was there a false O-peak at the energy of C-peak, another false O-peak (yellow) appeared at the O-peak region, and the Si-peak for the SiO 2 phase shifted. EUC-smooth and EUC-LR had similar or even more unreasonable results and thus are not displayed. The results of using the 1D Gaussian and the moving average both had false C-peaks, and notably, the small Ga-peak was too enhanced. This is considerable because any tradeoff between the data fidelity and smoothness is not considered in these smoothing methods as it has been considered for the proposed method.