Abstract
A new approach is developed for denoising signals using the Empirical Mode Decomposition (EMD) technique and the Information-theoretic method. The EMD technique is applied to decompose a noisy sensor signal into the so-called intrinsic mode functions (IMFs). These functions are of the same length and in the same time domain as the original signal. Therefore, the EMD technique preserves varying frequency in time. Assuming the given signal is corrupted by high-frequency Gaussian noise implies that most of the noise should be captured by the first few modes. Therefore, our proposition is to separate the modes into high-frequency and low-frequency groups. We applied an information-theoretic method, namely mutual information, to determine the cut-off for separating the modes. A denoising procedure is applied only to the high-frequency group using a shrinkage approach. Upon denoising, this group is combined with the original low-frequency group to obtain the overall denoised signal. We illustrate our approach with simulated and real-world data sets. The results are compared to two popular denoising techniques in the literature, namely discrete Fourier transform (DFT) and discrete wavelet transform (DWT). We found that our approach performs better than DWT and DFT in most cases, and comparatively to DWT in some cases in terms of: (i) mean square error, (ii) recomputed signal-to-noise ratio, and (iii) visual quality of the denoised signals.
