Weighted least squares estimation of background in EELS imaging

In quantitative Electron Energy Loss Spectrometry, a weighted least squares estimation should theoretically be used to estimate the background law below core edge energy, since the variances of the data vary. However, it is found that proper weighting makes the above edge signal-to-noise ratio decrease rather than increase. This result is discussed, and the influence of the bias introduced by the logarithmic transformation of the data is quantified.