In the traditional diagnosis system of Ayurveda, wrist pulse analysis is a significant and essential tool that is extensively used for diagnosing human health. The wrist pulse signal is a pressure signal measured from the radial artery of the subject. However, wrist pulse recordings are often affected both high and low frequency such as muscle contraction, power line interference and movements, eye blink of the subject respectively. Several researchers have been reported with various denoising methods such as FIR, IIR^{ }
Baseline wander is artifacts of low frequency below 0.5 Hz occur in wrist pulse signal due to breathing, sneezing, eye blink and movement of the subject. These lowfrequency components need to be eliminated before wrist pulse analysis for proper diagnosis. Baseline wanders present in wrist pulse, can be removed by various methods like multirate empirical mode decomposition, Hilbert decomposition, adaptive mean filter and high pass filter
Wavelet transforms have great significance in denoising of wrist pulse signal. Wavelets are used for analyzing nonstationary signals both in time and frequency. In the wavelet transform, thresholding of wavelet coefficients of the filter is known as denoising
Wavelet transform processes the noise signal with lower magnitude in higher coefficients whereas, signal with higher magnitude in lower coefficients of the filter. Wavelets use short windows at higher frequencies and longer windows at lower frequencies
Wavelets methods used for denoising of wrist pulse signal are
Discrete Wavelet Transform (DWT)
Stationary Wavelet Transform (SWT)
A wavelet is a short wave that possesses energy over a certain time interval. The wavelet transform decomposes a signal into its various constituent frequency bands by dilating and translating of the mother wavelet. Expressed as
where ‘a’ and ‘b’ are the dilating and translating parameters respectively. The wavelet transform of a signal
Wavelet transform of wrist pulse series has been computed with the help of Daubechies wavelet ‘db’ to derive an additional set of features. The highest level of decomposition in the Wavelet Transform is determined based on the frequency components that are required for the specific application. Wavelet analysis of wrist pulse signal is carried with approximate and detailed coefficients of the filter at every decomposition level. At each decomposition level the length of both approximate and detail coefficients of the filter are halved, to yield a specific range of frequencies as shown in
Stationary Wavelet Transform is an undecimated wavelet transform where the wrist pulse signal is subjected to high pass and low pass filters to generated the approximate (cA_{k}) and detailed coefficients (cD_{k}) respectively. SWT is the same as DWT, except for the decimation factor 2. The number of samples of SWT at any level of decomposition is similar to that of input samples.
Wrist pulse signal data is collected from the acquisition device, sampled at 500 Hz with the resolution of 14bits/sample. Wrist pulse signal is preprocess using various wavelet methods to remove the artifacts. Denoising of wrist pulse signal using wavelets involves the following three steps as depicted in
Decomposition: Select a level N for a wavelet to be applied to the wrist pulse signal.
Threshold Function: Select a Threshold function (Thr) at each level to decompose of a noisy wrist pulse signal.
Reconstruct: Compute the Inverse Wavelet transform to obtain a noisefree Wrist pulse signal.
Wavelet thresholding is a nonlinear method, which operates on wavelet coefficients. Various thresholding functions have been developed to denoise the biomedical signal. The most commonly used methods are hard and soft thresholding methods
where
Soft thresholding method further classified as Rigrsure, Sqtwolog, Heursure and Minimaxi based on the threshold selection rules
Where
w is an approximate wavelet coefficients after decomposition.
N is the number of samples.
A variance thresholding technique is based on the variance of approximated coefficients of the filter. Variance is statically defined as the average of the squared difference from the mean of approximate coefficients.
Where
Variance based thresholding improves evaluation parameters SNR, PSNR and reduces AE, RMSE.
1. Signal to Noise Ratio (SNR): SNR is the ratio of denoised wrist signal power to noisy signal power in decibels (dB). Higher the SNR, denoised wrist pulse signal power is high could accurately diagnose the disease.
2. Peak Signal to Noise Ratio (PSNR): PSNR is the ratio of square of maximum peak denoised wrist pulse signal to mean square error.
3. Absolute Error (AE): AE is defined as an absolute difference between denoised wrist pulse signal and noisy wrist pulse signal.
where
4. Mean Square Error (MSE): MSE is defined as the mean squared error between noisy wrist pulse signal and denoised wrist pulse signal. Typically, MSE should approach zero.
Where N is the number of samples
5. Root Mean Square Error (RMSE): RMSE defines as the square root of MSE. Expressed as
A study was carried out involving 56 healthy subjects include both male and female with an average age of 25.3 years. Procedure and norm was explained to subject before acquiring the wrist pulse and analyzed using MATLAB software tool.
Wavelet/Threshold 
Universal 
Variance 

Parameters 
PSNR 
SNR 
AE 
RMSE 
STD 
PSNR 
SNR 
AE 
RMSE 
STD 

db4 
AVG 
17.32 
0.33 
0.75 
0.18 
0.11 
41.72 
26.98 
0.06 
0.02 
0.22 
SD 
5.84 
1.47 
0.69 
0.17 
0.09 
9.48 
4.48 
0.11 
0.04 
0.18 

sym4 
AVG 
14.77 
2.84 
0.80 
0.23 
0.22 
42.35 
27.27 
0.05 
0.02 
0.21 
SD 
5.29 
0.75 
0.77 
0.21 
0.18 
9.40 
4.42 
0.11 
0.04 
0.17 

bior 3.5 
AVG 
14.42 
2.59 
0.75 
0.24 
0.21 
41.99 
26.88 
0.05 
0.02 
0.21 
SD 
5.25 
0.74 
0.73 
0.21 
0.17 
9.43 
4.49 
0.09 
0.04 
0.17 

db14 
AVG 
14.77 
2.92 
0.83 
0.23 
0.22 
42.50 
27.42 
0.05 
0.02 
0.21 
SD 
5.29 
0.74 
0.78 
0.21 
0.19 
9.41 
4.44 
0.08 
0.04 
0.17 
Fig. 5a: Original noisy wrist pulse
Fig. 5b: Denoising with universal method
The pulse contour using the variance thresholding method in shown
In this study, denoising of wrist pulse with the evaluation parameters such as PSNR, SNR, AE and RMSE has been evaluated using wavelets such as Daubechies, Symlet and Biorthogonal. The performance of wavelets depends on the choice of decomposition level N and thresholding techniques. The variance thresholding technique quantified drastic improvement in PSNR, SNR and reduction in AE and RMSE compared to the Standard Universal thresholding technique. Wrist pulses signal denoised with variance method retains relevant information for future analysis. Variance thresholding method could be used for preprocessing of the biomedical signals.
We are thankful to anonymous reviewers.