Implementation of Sawtooth Wavelet Thresholding for Noise Cancellation in One Dimensional Signal

Abstract

Wavelet families have different statistical characteristics and specifications which give them a different response against the same signal or image when they are used for a certain task such as signal denoising. Therefore, a comparison evaluation study using new proposed procedure is required to obtain the optimal results when wavelet analysis tool is used to remove the noise from a synthetic signal. In this work, a sawtooth wavelet thresholding method is proposed and evaluated as compared to the other wavelet thresholding methods such as (soft and hard). The main goal of this work is to design and implement a new wavelet thresholding method and evaluate it against other classical wavelet thresholding methods and hence search for the optimal wavelet mother function among the above mentioned families with a suitable level of decomposition followed by a novel thresholding method among the existing methods. This optimal method will be used to shrink the wavelet coefficients and yield an adequate denoised pressure signal prior the transmission. There are different performance indices to establish the comparison and evaluation process for signal denoising; but the most well-known measuring scores are: NMSE (normalized mean square error), ESNR (enhancement of signal to noise ratio), and PDR (percentage root mean squared difference). The obtained results shown the outperformance of the sawtooth wavelet thresholding method against other methods using different measuring scores and hence the conclusion is to suggest the adopting of this proposed wavelet thresholding for 1D signal denoising in future researches.