A background subtraction approach based on complex wavelet transforms in EDXRF

Subtracting the background accurately is one of the most important issues in energy‐dispersive X‐ray fluorescence (EDXRF) spectra processing. This paper presents a novel approach to perform background subtraction based on dual‐tree complex wavelet transform. Compared with real wavelet transform, the proposed method has some attractive properties, including a smooth, nonoscillating, and nearly shift‐invariant magnitude with a simple near‐linear phase encoding of signal shifts. Therefore, it outperforms real wavelet transform to decompose background into low‐frequency components. The effectiveness of the proposed approach is demonstrated via two simulated spectra with different kinds of backgrounds and one measured spectrum from an energy‐dispersive X‐ray spectrometer. Both simulated and experimental results prove that the proposed approach can subtract background in EDXRF spectra effectively. Copyright © 2014 John Wiley & Sons, Ltd.