The contribution of this study is developing the spectral smoothing method regularized with low-rankness as a preliminary noise reduction, and then offering a real experimental demonstration of how the step-by-step solution improves the noise reduction performance of wPCA, against a challenging, low-count STEM-EDX data. Throughout the experiment, we compare the proposed method's performance with two standard spectral smoothing methods that retain the number of energy channels: the moving average and the 1D Gaussian smoothing. The latter is a representative of the weighted moving average that ensures nonnegative spectra. We will show the noise reduction performance of each spectral smoothing method used as the preliminary step as well as the overall performance of the step-by-step solution. In order to see the noise model's effect, we will compare the noise reduction performance when using KL divergence and Euclidean distance to measure the deviation from the observation. The effect of introducing low-rankness, in addition to the smoothness of spectra for the preliminary noise reduction, will also be discussed.