Sparse Reconstruction for Enhancement of the Empirical Mode Decomposition-Based Signal Denoising

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.