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

TL;DR

The implementation of an algorithm for background reduction, leading to the extraction and enhancement of the valuable information from spectra, is discussed, leading to the extraction and enhancement of the valuable information from spectra.

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.

Figures (5)

• Figure 1: a) The scaling (dashed lines) and wavelet (solid lines) functions from the Coiflet family (coif8); the number stands for a decomposition level. b) Corresponding frequency characteristics
• Figure 2: Example wavelets used in DWT selected from 3 families, i.e. Daubechies (db6), Symlet (sym6), Coiflet (coif6) of 8th level (the number followed by the name of the wavelet stands for the corresponding filter's order)
• Figure 3: The logarithm of X-ray measured spectrum intensities from (blue solid line) of $Ga_{2}O_{3}$ crystal, with well visible, high-level background; the spectrum with removed background is given as a green line. Arrows indicate artifacts remained after DWT synthesis (db5)
• Figure 4: CWT spectra of a) initial X-ray intensities and b) after slow changing components ($f<0.25$) reduction. To enhance readability, only CWT coefficients above 0 are shown; high-frequency ($f>1$) noise has been removed by means of SG filtering
• Figure 5: Comparison of wavelet families and levels of decomposition for PL spectra. To enhance the visibility, the $log_{10}(I)$ of input data (blue line) has been processed; background and outcomes are given respectively as red and green lines