We herein introduce data-specific characterizations of EDX spectral image data into a numerical optimization. We especially focus on the intrinsic smoothness of EDX spectra, which is characterized by the second-order derivative with respect to the energy of an X-ray. It is equivalent to the Whittaker smoother where we assume, for example, Gaussian noise on the data. In approximating the noise model of EDX data by Poisson distribution, we have nonnegativity and use Kullback-Leibler (KL) divergence to measure deviation from the observation. This is related to the generalized linear model , and was also considered when reducing the noise of a single X-ray diffraction data , where the original second-order smoothness was replaced with a log-scaled smoothness due to a technical reason in ensuring the nonnegativity of spectra. In contrast, we introduce the variable splitting technique to properly solve the optimization problem with the original definition of smoothness. We still found that smoothing alone is insufficient to denoise the data, even after using wPCA in the second step. This is likely because each spectrum has been smoothed independently, and so we have ignored a rich statistical assumption that all the spectra span a low-rank subspace, as assumed when applying wPCA. Therefore, we further introduce the low-rankness of the data matrix. For a feasible optimization, we relax it with the nuclear norm , which is the tightest convex surrogate of the matrix rank and has been used to solve optimization problems that seek low-rank subspaces. Although the denoised data matrix does not have an exact small rank, the shrunken singular values indicate that we have gotten closer to the subspace spanned by clean signals in this first step (Algorithm 1 in Figure ). We will demonstrate that the scree plot suggests three components, the number of components of the SiC MOSFET sample, after the preliminary noise reduction step, while the scree plot against the observed signal suggests two principal components. We then apply wPCA to project this spectrally smoothed data onto the low-dimensional subspace. The reason we use wPCA after the preliminary noise reduction, instead of the standard PCA without rescaling, is that the noise that remained after the Poisson noise reduction is also expected to have Poisson distribution. In fact, using wPCA after the preliminary noise reduction peformed better than using the standard PCA.