Intelligent background correction using an adaptive lifting wavelet

• An algorithm based on lifting wavelets is developed for background correction.
• The algorithm adaptively constructs lifting wavelets for different signals.
• A feed-back operation is proposed to insure a correct removal of the background.

Wavelet transform has been a powerful tool for signal processing. Various wavelet filters make the technique flexible for processing diverse signals. However, finding a suitable filter is a task for different signals and different purposes. In this work, an adaptive wavelet transform based on lifting scheme and least mean square (LMS) algorithm is proposed for background correction of analytical signals. Lifting scheme is used to calculate the detail and approximation coefficients for decomposing the signal into different components, and adaptive lifting wavelet filter is generated with an LMS algorithm. Due to the difference in frequency of the components, the background in the signal can be identified and removed. The benefit of using the proposed method is the adaptation that makes the wavelet transform suitable to process any signal for various purposes without the trouble of selecting the filters. The signals of gas chromatography, nuclear magnetic resonance (NMR) and Raman spectroscopy for analyzing pesticide mixture, blood sample, and pharmaceutical tablets are used to test the proposed method. The results indicate that the background in all the three signals is clearly eliminated.