Application of dual-tree complex wavelet transform for spectra background reduction

Abstract: This paper presents a method for background removal in experimental data processing using the Dual-Tree Complex Wavelet Transform (DTCWT). The technique is based on discrete wavelet theory (DWT) and addresses limitations of commonly used numerical approaches, such as fitting or filtering methods. Compared with Fourier-transform-based techniques, DTCWT provides improved performance for signal extraction. The proposed method is universal and enables analysis of arbitrary data ranges without restrictions on their position in time. It satisfies key requirements of signal analysis, including signal preservation and reduction of processing bias. An algorithm for background reduction is implemented to extract and enhance meaningful spectral information. The approach is demonstrated on two different types of spectra: X-ray powder diffraction and photoluminescence measured for the $Ga_{2}O_{3}$ crystal. Practical aspects of DWT-based processing are also discussed, including the selection of wavelet families and decomposition levels. The method is available as a software package for spectral background reduction.