Basically, wPCA relies on the low-rank assumption of the data matrix, which reflects the fact that a material is usually composed of a small number of components. However, the aforementioned difficulties inhibit the estimation of the low-rank subspace directly from a heavily noisy data, even if given the correct number of components. To mitigate this issue, we consider a step-by-step solution with a preliminary noise reduction step and a projection step (Figure ). The first step gets the data closer to the subspace, not rigorously with a small number of components, but moderately, based on a model that characterizes EDX spectral image data. We then, in the second step, apply wPCA to rigorously extract the principal components.