Mean estimation empirical mode decomposition method for terahertz time-domain spectroscopy de-noising

Abstract

The wavelet-domain de-noising technique has many applications in terahertz time-domain spectroscopy (THz-TDS). However, it requires a complex procedure for the selection of the optimal wavelet basis and threshold, which varies for different materials. Inappropriate selections can lead to de-noising failure. Here, we propose the Mean Estimation Empirical Mode Decomposition (ME-EMD) de-noising method for THz-TDS. First, the THz-TDS signal and the collected reference noise are decomposed into the intrinsic mode functions (IMFs); second, the maximum and mean absolute values of the noise IMF amplitudes are calculated and defined as the adaptive threshold and adaptive estimated noise value, respectively; finally, these thresholds and estimated noise values are utilized to filter the noise from the signal IMFs and reconstruct the THz-TDS signal. We also calculate the signal-to-noise ratio (SNR) and mean square error (MSE) for the ME-EMD method, the "db7" wavelet basis, and the "sym8" wavelet basis after de-noising in both the simulation and the real sample experiments. Both theoretical analysis and experimental results demonstrated that the new ME-EMD method is a simple, effective, and high-stability de-noising tool for THz-TDS pulses. The measured refractive index curves are compared before and after de-noising and demonstrated that the de-noising process is necessary and useful for measuring the optical constants of a sample.

Terahertz spectroscopy in biomedical field: a review on signal-to-noise ratio improvement

“…9. The de-noising results are shown in Table 1, which is better than that from "Db7" and "Sym8" [56]. Zou et al reported using principle component analysis (PCA) to reconstruct the time-domain THz signal, which can be used for the diagnosis of myelin deficit brain [57].…”

“…In particular, algorithms normally have various parameters that should be properly set according to Fig. 9 The algorithm flowchart [56] the data. Therefore, wrong setting of the parameters may lead to the information loss of the sample and cause errors in the final spectral recognition.…”

Statistical Models for Averaging of the Pump–Probe Traces: Example of Denoising in Terahertz Time-Domain Spectroscopy

“…where ܰ ௧ is the number of THz pulses used in the fitting, and ܰ ఠ is the number of frequency components in the Fourier spectrum of the measured pulses. In order to find the minimum of the weighting functions (13,14) we have to solve a system of ܰ ఠ + 2ܰ ௧ generally non-linear equations: Additionally, we note that for each model, a system of equations (15)(16)(17) is ill-posed and does not lead to a unique solution. This is related to the fact that the analytical fitting functions (7)(8)(9) are degenerate with respect to certain transformations of the groups of the fitting variables as explained further in the text.…”

“…. In matrix form (14) can be written as: (11.15) where diagonal matrix ‫ܦ‬ has the following elements…”

Defect Identification Method of CMC Bonding Structure based on Dynamic Time Warping and Simulation Analysis

“…There has been much research in recent years on nondestructive testing of CMC bonding structures using THz TDS. For the quality detection of glue layer of CMC bonding structure, the maximum value of the time-domain signal, flight time, variance, and other parameters are used for nondestructive testing signal analysis 10,11 , whereas Fourier transforms, wavelet transform, EMD, and other methods are used to enhance weak signal 2,12 , for improving the efficiency of defect identification. Simultaneously, in recent years, there have been some researches on the nondestructive detection of debonding defects of CMC materials using neural network intelligent recognition algorithm 1 .…”