An EELS signal-from-background separation algorithm for spectral line-scan/image quantification

Background removal is an important step in the quantitative analysis of electron energy-loss structure. Existing methods usually require an energy-loss region outside the fine structure in order to estimate the background. This paper describes a method for signal-from-background separation that is based on subspace division. The linear space is divided into two subspaces. The signal is recovered from a linear subspace containing no background information, and the other subspace containing the background is discarded. This method does not rely on any signal outside the energy-loss range of interest and should be very helpful for multiple linear least-squares (MLLS) regression analysis on experimental signals with little or no available smooth pre-edge region or with overlapping pre-edge features. Use of the algorithm is demonstrated with several practical applications, including closely overlapping core-loss spectra and zero-loss peak removal. Tests based on experimental data indicate that the algorithm has similar or better performance relative to conventional pre-edge power-law fitting methods in applications such as MLLS regression for electron energy-loss near-edge structure.