A piecewise mirror extension local mean decomposition method for denoising of near-infrared spectra with uneven noise

As a new signal analysis tool, local mean decomposition (LMD) can decompose a spectrum into a set of single-component signals with different frequencies. However, LMD may produce endpoint effect. At the same time, due to instrumental instability and experimental errors, uneven noise may occur in the measurement process of near-infrared (NIR) spectra. A piecewise mirror extension local mean decomposition (PME-LMD) method is proposed for denoising of NIR spectrum with uneven noise. Firstly, the NIR spectrum with uneven noise is segmented to obtain several intervals. Then, each interval is mirrored extension to the left and right for overcoming the endpoint effect. Subsequently, a series of product functions (PFs) are obtained by LMD for each piecewise mirror extended NIR spectrum. Finally, the denoised NIR spectrum is obtained by intercepting and reconstructing the components without noise. One artificial noised signal and NIR spectra of traditional Chinese medicine (TCM) and beer samples are used to validate the performance of this method. As comparison to PME-LMD method, Savitzky-Golay (SG) smoothing, discrete wavelet transform (DWT), empirical mode decomposition (EMD) and LMD have also been investigated. Visualization spectra, signal-to-noise ratio (SNR) and modeling results of partial least squares (PLS) are used as evaluation indicators. The results demonstrate that the proposed method performed best in terms of SNR, root mean squared error of prediction (RMSEP) and correlation coefficient (R) of PLS. Furthermore, the piecewise step is critical to perform LMD denoising for NIR spectrum with uneven noise. At the same time, the endpoint effect of LMD is effectively overcome by mirror extension.