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

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.