A New Wavelet Denoising Method for Selecting Decomposition Levels and Noise Thresholds

Abstract

A new method is presented to denoise 1-D experimental signals using wavelet transforms. Although the state-of- the-art wavelet denoising methods perform better than other denoising methods, they are not very effective for experimental signals. Unlike images and other signals, experimental signals in chemical and biophysical applications for example, are less tolerant to signal distortion and under-denoising caused by the standard wavelet denoising methods. The new method 1) provides a method to select the number of decomposition levels to denoise, 2) uses a new formula to calculate noise thresholds that does not require noise estimation, 3) uses separate noise thresholds for positive and negative wavelet coefficients, 4) applies denoising to the Approximation component, and 5) allows the flexibility to adjust the noise thresholds. The new method is applied to continuous wave electron spin resonance (cw-ESR) spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion. Also, its computation time is more than 6 times faster.

A New Wavelet Denoising Method for Noise Threshold

“…This study is used wavelet transform because of simple and naive for denoise represented of single level discrete 1-D wavelet transform that is the state-of-the-art wavelet denoising [9]. This method has become common signal processing technique in different area and the result indicate that wavelet functions Daubechies 44 (db44) provides a better fit to tested biosignals [22] but experiment of this study is found that the Coiflets1 wavelet is better suited in this study.…”

“…The solutions of it are a detail wavelet coefficient is either a signal or a noise coefficient that the hard thresholding is better suited, whereas it is both signal and noise that the soft thresholding is better suited and the wavelet shrinkage method better signal denoising with minimum computation complexity [9] and wavelet shrinkage denoising algorithm (see Table 1 and Fig. 1) where S(x) is a noisy speech of input signal, Di is a Detail wavelet coefficient of noisy speech where i = 1, 2, …, n, Ai approximate coefficient is where i = 1, 2, …, n, and the S(x') is noisy speech of output signal.…”

“…Table 1. Wavelet shrinkage denoising Algorithm [9]. A limitation of shrinkage methods is fixed threshold of method was not adjusted.…”

“…In addition, other problem with current wavelet denoising is the number of decomposition levels for denoise, and alternative wavelet because they have the flexibility to adjust the thresholds [9]. Many researches have evaluated result of denoising with signal-to-noise ratio [2,10], segmental signal-to-noise ratio [2,11,12], Mean Squared Error (MSE) [7,13], and used realistic noisy environment [2,8,[11][12][13].…”

“…This new method is presented to denoise 1-D using wavelet transforms because of it is the state-of-theart wavelet denoising method [9] and improved the hard and soft wavelet threshold denoising with idea of the parameter is used to change the size of the deviation between reconstruction signal and the original signal. These measurement performances are SNR and MSE.…”