Abstract
Effective signal denoising methods are essential for science and engineering. In general, denoising algorithms may be either linear or non-linear. Most of the linear ones are unable to remove the noise from the real-world measurements. More suitable methods are usually based on non-linear approaches. One of the possible algorithms to signal denoising is based on empirical mode decomposition. The typical approach to the empirical mode decomposition-based signal denoising is the partial reconstruction. More recently, a new concept inspired by the wavelet thresholding principle was proposed. The method is named the interval thresholding. In this article, we further extend the concept by the application of the sparse reconstruction to the empirical mode decomposition-based signal denoising algorithm. To this end, we state and then solve the problem of signal denoising as a regularization problem. In the article, we consider three cases, that is, three types of penalty functions. The first algorithm is combining total variation denoising with empirical mode decomposition approach. In the second one, we applied the fused LASSO Signal Approximator to design the empirical mode decomposition-based signal denoising algorithm. The third approach solves the denoising problem by applying a non-convex sparse regularization. The proposed algorithms were validated on synthetic and real-world signals. We found that the proposed methods have the ability to improve the accuracy of the signal denoising in comparison to the reference methods. Significant improvements from both the synthetic and the real-world signals were obtained for the algorithm based on non-convex sparse regularization. The presented results show that the proposed approach to signal denoising based on empirical mode decomposition algorithm and sparse regularization gives a great improvement of accuracy, and it is the promising direction of future research.
Highlights
The signal denoising is one of the fundamental and the most challenging tasks in science and engineering
We proposed new algorithms for signal denoising which are improving the performance of the existing ensemble empirical mode decomposition (EEMD)-based approach
The proposed approach exhibits an enhanced performance compared with the wavelet inspired algorithm EEMD-CIIT in almost all cases
Summary
The signal denoising is one of the fundamental and the most challenging tasks in science and engineering. Because of the imperfections present in the measurement system, the obtained signals can be deteriorated during the processes of acquisition and transmission. The main challenge of signal denoising is to preserve and enhance the desirable features of the collected signals. Filters may be either linear or nonlinear. Removing noises from the acquired signals by applying linear filters usually leads to unsatisfactory results. This is due to the fact that these filters are suitable when the unknown signal is
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