Signal denoising using a low computational translationin-variant- like strategy involving multiple wavelet bases: application to synthetic and ECG signals

In this paper, an efficient method for the denoising of electrocardiogram (ECG) signals is presented. As it is well-known, the efficient translation-invariant (TI) denoising technique, first introduced by Coifman and Donoho, uses K pre-processing shift-rotation operations, K denoising operations similar to the standard Donoho’s thresholding algorithm, K post-processing inverse shift-rotation operations, and finally, the K new less noisy copies generated by the preceding steps are averaged to produce a final denoised signal. Thus and conversely to the previously mentioned TI algorithm, the suggested technique consists of the design of a low computational translation-invariant-like strategy that eliminates the K pre-processing shift-rotation and the K post-processing inverse shift-rotation operations and only keeps the K wavelet-based denoising operations where for each one we use a different mother wave among a set of K mother waves ψ1; ψ2;...; ψK. Consequently, each mother wave generates a new less noisy copy from the original noisy signal. Finally, the produced less noisy multiple copies are averaged to reach the final denoised signal. Through this strategy, we can avoid the use of multiple hardware sensors to generate multiple noisy copies to be averaged to restore the clean version of the signal. Consequently, the proposed approach can considerably reduce the cost of the acquisition system. Additionally, the several results produced from extensive simulations show that the proposed algorithm outperforms many translation-invariant-like methods and can be considered as one of the top-ranking recent algorithms to tackle the denoising problem.