wsdenoise

The wavelet shrinkage is a signal denoising technique based on the idea of thresholding the wavelet coefficients. Wavelet coefficients having small absolute value are considered to encode mostly noise and very fine details of the signal. In contrast, the important information is encoded by the coefficients having large absolute value. Removing the small absolute value coefficients and then reconstructing the signal should produce signal with lesser amount of noise. The wavelet shrinkage approach can be summarized as follows:

• Apply the wavelet transform to the signal.

• Estimate a threshold value.

• The so-called hard thresholding method zeros the coefficients that are smaller than the threshold and leaves the other ones unchanged. In contrast, the soft thresholding scales the remaining coefficients in order to form a continuous distribution of the coefficients centered on zero.

• Reconstruct the signal (apply the inverse wavelet transform).

The biggest challenge in the wavelet shrinkage approach is finding an appropriate threshold value. In this method, we use the universal threshold T = σ sqrt(2*log(N)), where N is the length of time series and σ is the estimate of standard deviation of the noise by the so-called scaled median absolute deviation (MAD) computed from the high-pass wavelet coefficients of the first level of the transform.

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