## Abstract

Pulse oximeter is widely used in the monitoring of blood oxygen in clinic for its convenience and efficiency. However, synchronizing light source flashing with data collecting is required, otherwise the separation of the data from different LEDs will fail. More importantly, synchronous acquisition makes the pulse oximetry system vulnerable. Meanwhile, the pulse waveform extraction is a crucial procedure in the measurement. Hence, in this paper, an asynchronous acquisition pulse oximetry system based on wavelet transform has been built. PhotoPlethysmoGraph (PPG) and photoelectric detection technology are applied in our homemade system. The adaptive soft-threshold de-noising is realized by Stein's Unbiased Risk Estimate (SURE). The principle and system configuration are described. The preliminary experiment results from wavelet transforms and Fourier transforms are compared. The results show that our homemade system is adaptive, accurate, robust and simple.

© 2013 Optical Society of America

## 1. Introduction

Since 1974 Aoyagi developed an oximeter-like device to measure the arterial hemoglobin saturation [1], non-invasive oximetry had been taken into practical stage. The theory can be traced back to the 19th century known as the Lambert-Beer law. What should be remarked is that in 1983 Wilber applied 2 solid state LEDs as the light sources which reduced the complexity of oximeter and made it practical for clinic [2]. Nowadays, pulse oximeter has been widely used in clinic for patients monitoring, especially during anesthesia, for its non-invasive, real-time and continuous blood oxygen measurement.

Due to dual-wavelength is used in the pulse oximetry device, synchronous clock controlling in light sources flashing and data collecting is required in conventional pulse oximeter in order to separate each of the wavelength of light, otherwise the detector may collect data at the moment when the state of light source is between on and off which makes the data separation fail. However, the synchronous relationship between light sources and detectors makes the pulse oximetry system vulnerable. On the other hand, motion artifact, baseline drift and background noises are the main interferences which prevent the pulse signals extracted correctly. Hence, signal processing is an important procedure during the measurement. Various signal processing algorithms in pulse oximetry system had been reported [3–7]. Among these, Fourier transform (FT) method and Wavelet transform (WT) method are more capable and commonly used. However, FT method can only filter out specified frequency of signals, meanwhile the pulse waves are non-stationary signals which means the frequency of pulse signals are not stable. Therefore, the results of FT method obtained are just a rough waveform. Furthermore, FT method is short of time resolution which means some details of the pulse waveform maybe lost. For dynamic measurement and non-stationary signals like pulse wave, wavelet transform is a better choice with its superior time-frequency characteristic. Hence, in this paper, an asynchronous acquisition pulse oximeter was built based on wavelet transform. In addition, to reduce the noises, Stein's Unbiased Risk Estimate (SURE) was applied to estimate the thresholds adaptively. Finally, Fourier transform (FT) was also performed as a comparison in signal processing procedure. The preliminary experiment and analysis show that our homemade pulse oximetry system is adaptive, robust, simple and accurate.

## 2. Description of pulse oximeter

#### 2.1 The theoretical basis of blood oxygen measurements

In clinic, functional hemoglobin saturation which ignores the carboxyhemoglobin (COHb) and methemoglobin (MetHb) is defined as

where*HbO*and

_{2}*Hb*represent their concentration respectively. In pulse oximetry, PhotoPlethysmoGraph (PPG) and photoelectric detection technology are applied. Meanwhile, according to the Lambert-Beer law, the measured tissue, normally the fingertip, is regarded as a cuvette containing the blood sample which is assumed to be a dual-solute (HbO

_{2}and Hb) solution. In order to simplify the measurement, the two quasi-monochromatic light sources used to measure Hb and HbO

_{2}should have several characteristics. First, Hb and HbO

_{2}should have the same absorbance on the wavelength of one light source. Second, Hb and HbO

_{2}should have large difference absorption coefficients on the other wavelength. Therefore, Eq. (1) can be expressed as following [8]where

*ΔA*and

_{1}*ΔA*are the modulation degree of each incident light respectively which are modulated by pulse fluctuation,

_{2}*R*is the ratio of the modulation degree,

*a*and

*b*are system constants, which are related to detector and measurement condition and both of them can be obtained by system calibration. In our experiment, two LEDs are selected: one of them is 660 nm (Hb and HbO

_{2}have large differences absorption coefficients on this wavelength) and the other is 940 nm (Hb and HbO

_{2}have almost the same absorbance on this wavelength).

In oximetry measurement, the signal is weak and coupled with various interferences, hence signal processing is crucial. FT and WT are performed respectively to get *ΔA _{1}* and

*ΔA*from the original data.

_{2}#### 2.2 System configuration

The powers of the two LEDs are the same (1 W). Each LED lights up for 10 ms, while one LED distinguishes, the other lights up. The two LEDs are as juxtaposed against each other closely, and covered with the fingertip. To collect the intensity of transmitted light, a Si-biased detector DET36A (U.S. THORLABS Company) is adopted at a sampling frequency of 20000 Hz. The sampling time is 50 s. The detector is placed at the opposite side of the fingertip as shown in Fig. 1.

Unlike conventional pulse oximeter, in which synchronous clock is applied to control LEDs’ flashing and data collection, in our system, asynchronous acquisition is realized by use of the algorithm we developed, which means LEDs flash timing is independent of the data collection.

#### 2.3 Original signal explanation

In this section a brief explanation on the original signal will be illustrated. A part of the original signals collected by the detector are shown in Fig. 2. Due to the asynchronous acquisition applied in our homemade system, the intensities of light from both LEDs are collected indiscriminately. According to our experiments, it is found that the upper envelop of the original signal contains the data of red LED and the lower contains the data of infrared LED. Meanwhile, these signals are coupled with several types of noise. The data points between upper and lower envelops are collected by the detector at the moment when the LEDs are between on and off. We call this kind of data ‘half-lighted’. Baseline drift which has a low frequency of change and high-frequency noise are also the main influencing factors to each LED’s pulse signal which can be seen in Fig. 2. The above noises are what should be removed to obtain the proper pulse signals.

## 3. Principles of signal processing

#### 3.1 WT method

Based on the priori knowledge described in section 2.3, the wavelet transform is first used in pulse signal extraction. Assuming *s(t)* is the signal of a single LED, the discrete wavelet transform (DWT) can be express as

*j*is scale factor,

*k*is time shifting,

*φ*is the mother wavelet,

*WT*is the wavelet coefficient sequence of each resolution level (stratified according to scale factor

_{s}(j,k)*j*).

Due to the time-frequency localization and multi-scale features of wavelet transform, the signal energy of pulse fluctuation is centralized in minority wavelet coefficients with larger value than the wavelet coefficients of noises. Therefore, threshold method is applied to screen out the wavelet coefficients of pulse fluctuation and the reconstruction is conducted to obtain the pulse waveform. It is clear that the quality of the threshold setting has a significant impact on the noise reduction. Hence, after careful study, Stein's Unbiased Risk Estimate (SURE) [9] was found as the suitable and adaptive method to estimate the threshold in our homemade system. The SURE of a single level of the wavelet coefficients can be express as

*WT*is the original wavelet coefficients,

*σ*is the variance of

^{2}*WT*,

*p(WT)*is an estimator of pulse’s wavelet coefficients from

*WT*,

*g*is the estimator of the wavelet coefficients of noise which is denote as the difference between

*p(WT)*and

*WT*, $\Vert \xb7\Vert $is the Euclidean norm. According to the definition of SURE, the SURE is an unbiased estimate of the mean-squared error (MSE) of

*p(WT)*which meanswhere

*pulse*stands for the wavelet coefficients of actual pulse signal which cannot be obtained directly. However, based on Eq. (6), the MSE of

*p(WT)*can be computed by

*p(WT)*independently. Therefore, minimizing the risks in

*p(WT)*to obtain the adaptive threshold value [10]. Hence, WT method becomes an adaptive algorithm as a result of the threshold selection by Stein's Unbiased Risk Estimate. The procedure of selecting the adaptive threshold is shown in Fig. 3.

To conduct the noise reduction, soft-threshold method is applied to the original wavelet coefficients (*WT*). Assuming *ST* is the threshold of a single resolution level, the soft-threshold method can be denoted as

*η(WT)*is the wavelet coefficients after thresholding,

*sgn(x)*is the sign function. After this, the reconstruction of the wavelet coefficients is conducted as followingwhere

*f(t)*is the ideal signal. Figure 4 shows the signal processing procedure by DWT.

#### 3.2 FT method

It is well known that the frequency of normal human pulse fluctuation ranges from 0.5 Hz to 2 Hz approximately. Depending on this priori knowledge, a frequency domain filter was designed to filter out the pulse waveform. According to section 2.3, baseline drift, ‘half-lighted’ data and high-frequency noise are the main noises in pulse signal. Among these noises, baseline drift is a low-frequency noise meanwhile data caused by ‘half-lighted’ is a high-frequency noise. Therefore, a band-pass filter is applied in signal processing procedure with the lower-cut-off frequency 0.5 Hz and higher-cut-off frequency 2 Hz.

As assumed in section 3.1, let *s(t)* denote the signal of a single LED, the discrete Fourier transform (DFT) can be expressed as

^{th}root of unity. Pulse wave and noises are converted into frequency spectrum. Therefore, it is convenient to conduct the band-pass filtering. The frequency ranges from 0.5 Hz to 2 Hz is selected to rebuild the signal. Assuming

*F*is the frequency spectrum which contains the target frequency, and then the reconstruction can be expressed aswhere

*f*is the pulse waveform. Figure 5 shows the signal processing procedure by FT.

## 4. Experiment

The system was configured as described in section 2.2. Due to asynchronous acquisition applied in our homemade system, the intensities of light from both LEDs were collected indiscriminately. In order to separate the two LEDs’ signals, the original data shown in Fig. 2 was divided into two parts through the mean value of the amplitude, and the separated signals are shown in Fig. 6 and Fig. 7 respectively.

The red LED signal (see Fig. 6) is taken for instance to illustrate the comparison of WT and FT method. In WT method, sym8 was selected as the mother wavelet and the wavelet decomposition was conducted into 11 levels to filter out the high-frequency noise and ‘half-lighted’ data. The result is shown in Fig. 8(a). As a comparison, 2 Hz was set in FT method as the higher-cut-off frequency and the result is shown in Fig. 8(b).

To obtain the baseline drift (low-frequency noise), the wavelet decomposition was conducted into 15 levels and 0 – 0.5 Hz was selected in FT method. The performance is shown in Fig. 9(a) and Fig. 9(b).

Then the baseline drift was removed from the signal to obtain the pulse waveform. The final result is illustrated in Fig. 10(a) and Fig. 10(b).

From Fig. 10, it can be seen that the pulse wave extracted by WT method has a little larger amplitude than the one extracted by FT method. What does it imply will be discussed in next section.

For the purpose of blood oxygen measurement and according to Eq. (2), the modulation degree of each incident light (*ΔA _{1}* and

*ΔA*) is desired.

_{2}*ΔA*and

_{1}*ΔA*are normalized to eliminate the detector’s different response between each wavelength and the changes of the arterial perfusion caused by pressure variation. The normalization can be expressed as

_{2}*AC*is the difference between the wave peaks and troughs in the same pulse wave cycle,

*DC*is the baseline of the same cycle. Then Eq. (2) can be re-written as

A comparison was conducted between our homemade system with 2 signal processing methods. Meanwhile an industry-accepted oximeter Prince-100H (Shenzhen Creative Industry Co., Ltd) was used to compare the measuring accuracy of the above two methods. A subject was selected to be measured. Before the measurement, the subject was required to calm down for several minutes in order to reach the resting-state, and then held his breath for a different while before the beginning of each measurement in order to show different *SaO _{2}* values [11]. The measurement conducted by our homemade system and Prince-100H at the same time. The results are shown in Table 1 (The decimal parts of measuring results of our homemade system are kept intentionally).

## 5. Discussion

It can be seen in Fig. 10 that the FT method removes noises with a slight reduction of the pulse wave amplitude while the WT method retains the reasonable details at the peak and the valley of the pulse wave. Meanwhile, in Table 1, at each stage of *SaO _{2}*, FT obtains smaller

*SaO*value than WT. This is because the reduction of the amplitude shown in Fig. 10. To figure out the relationship between

_{2}*SaO*value and amplitude, the total differential of Eq. (13) is performed as

_{2}*d(SaO*is the variation of

_{2})*SaO*,

_{2}*d(AC*and

_{1})*d(AC*are the amount of the amplitude reduction of red and infrared respectively. Because the same band-pass filter is applied in both red and infrared signals, the amount of the amplitude reduction of each signal can be regarded as the same which means

_{2})*d(AC*) =

_{1}*d(AC*). Therefore, Eq. (14) can be simplified as

_{2}*AC*is found less than 1,

_{2}*b*and

*d(AC*are both negative values while

_{1})*DC*,

_{2}*AC*and

_{2}*DC*are all positive values. Hence, the variation of

_{1}*SaO*(

_{2}*d(SaO*) is negative which means the

_{2})*SaO*is reduced as a result of the slight reduction of the pulse wave amplitude caused by FT. Therefore, a slight reduction of the pulse wave amplitude will lead to a lower level of SaO

_{2}_{2}value which reduces the accuracy of the pulse oximetry system.

## 6. Conclusion

A new pulse oximetry system based on wavelet transform has been built. The system is simple and robust due to omitting the synchronizing data acquiring system of detector and two wave-length LEDs. Moreover, the measurement process is adaptive as a result of the adaptive algorithm is applied in the signal processing procedure which is based on Stein's Unbiased Risk Estimate. The average error is 0.378% at the present time. In addition, SaO_{2} values computed from WT and FT, respectively, are compared. The preliminary experimental results show that the measuring result with WT is more accurate than that with FT.

## Acknowledgments

The authors acknowledge the finical support from Chinese National Natural Science Foundation 51275033.

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