|Year : 2009 | Volume
| Issue : 1 | Page : 10-15
A Comparative Analysis of De-Noising Algorithms for Fetal Phonocardiographic Signals
Vijay S Chourasia1, AK Mittra2
1 Electronics Engineering Department, MIET, Kudwa, Gondia (M.S.), India
2 Assistant Professor, Electronics Engineering Department, MIET, Gondia (M.S.), India
Vijay S Chourasia
Electronics Engineering Department, MIET, Kudwa, Gondia (M.S.)
This paper is aimed at the selection of de-noising algorithm for de-noising of the fetal phonocardiographic (fPCG) signals. Fourier-based analyzing tools have some limitations concerning frequency and time resolutions. Although wavelet transform (WT) overcomes these limitations, it requires selection of appropriate de-noising algorithm. The universal threshold, minimax threshold and rigorous SURE (Stein's Unbiased Risk Estimate) threshold algorithms along with soft or hard thresholding rule have been compared for de-noising of these signals. The mean-squared error (MSE) is used to evaluate the performance of these algorithms. The results show that, the rigorous SURE threshold algorithm with soft thresholding rule has a better performance for the analysis of fPCG signals when using the fourth-order Coiflets wavelet. The proposed approach is simple and proves to be effective when applied for the selection of de-noising algorithm for the fPCG signals. These de-noised signals can be used for the accurate determination of fetal heart rate (FHR) and further diagnostic applications pertaining to the fetus.
Keywords: De-noising algorithms, Fetal phonocardiography, Wavelets.
|How to cite this article:|
Chourasia VS, Mittra A K. A Comparative Analysis of De-Noising Algorithms for Fetal Phonocardiographic Signals. IETE J Res 2009;55:10-5
| 1. Introduction|| |
Phonocardiography is a continuous noninvasive, low- cost and accurate monitoring method that takes care of fetal well-being  . Using this method, long-term measurement of the FHR and collection of heart sound artifacts becomes possible. The widely accepted ultrasound Doppler process is not suitable for taking measurements over extended periods of time  . The main advantages of the fPCG technique are its passivity (noninvasiveness) and simplicity  .
Despite all these advantages of fPCG, this technique is not popular with the obstetricians because of its poor signal-to-noise ratio (SNR) at the time of recording  . The fPCG signals recorded from maternal abdominal surface are contaminated by various unwanted signals, like maternal organ sounds, fetal movement effects and the ambient noise; hence this technique requires robust signal-processing to extract the fetal heart sound signals  . To overcome this limitation of poor SNR and to exploit the advantages of fPCG technique for fetal home-care applications, it is required to adopt an effective de-noising method for the extraction of accurate FHR from the fPCG signals. There have been significant efforts to develop long-term monitoring methods based on fPCG technique. All these methods have projected different types of sensors and filtering schemes, as well as different numbers of channels, for this purpose.
The main difficulty in dealing with the fPCG signals is their extreme variability and necessity to operate on a case-to-case basis  . Another important aspect of these signals is that the information of interest is often a combination of features that are well localized temporally or spatially. This requires the use of analytical methods sufficiently versatile to handle events that can be at opposite extremes in terms of their time-frequency localization. Wavelet analysis has proved to be one of the most successful techniques for the analysis of signals at multiple scales and has rendered many successful applications in the area of biomedical signal processing  .
The choice of wavelet family, mother wavelet and de-noising algorithm greatly affects the accuracy of the wavelet analysis of the signal. The presented work deals with this problem in two steps - first, by choosing the appropriate de-noising algorithm from universal threshold, minimax threshold and rigorous SURE (Stein's Unbiased Risk Estimate) threshold along with soft or hard thresholding rule for de-noising of the fPCG signals; and second, by selecting the best wavelet family and mother wavelet on the basis of the nature of the signal to be analyzed and properties of the wavelet families.
The rest of the paper is organized as follows. In section 2 theory of wavelet transform is discussed. A brief description of the various wavelet families and de-noising algorithms are presented in section 3. Section 4 elaborates the comparison and results. Finally, section 5 summarizes the conclusions drawn from the previous sections.
| 2. Theory of Wavelet Transforms|| |
In WT the time domain waveforms are mapped into a frequency-time domain while preserving both frequency and time information. The main idea of wavelet analysis is to measure the degree of similarity between the original waveform s(t) and the basic function of the WT, also called the mother wavelet, through wavelet coefficients computation. The calculation process is performed on shifted version of the mother wavelet, thus moving along the time; and on stretched or compressed version of the mother wavelet, thus varying the frequency. The continuous wavelet transform (CWT) is defined as the convolution between the original signal s(t) and a wavelet Ψa,b (t).
where s(t) is the input signal; 'a' is the scaling factor; 'b' is the translation parameter; and Ψ(t) is the transforming function, called mother wavelet. The wavelet function is given by
The Discrete Wavelet Transform (DWT) coefficients are usually sampled from the CWT on a dyadic grid, choosing parameters of translation b = n*2 m and scale a = 2 m . The wavelet function in DWT is defined as
DWT analyzes the signal by decomposing it into its coarse and detail information, which is accomplished by using successive high-pass and low-pass filtering operations, on the basis of the following equations:
where y high ( k ) and y low ( k ) are the outputs of the high-pass and low-pass filters with impulse response 'h' and 'g', respectively, after upsampling by 2.
In DWT the original signal 's' is decomposed into approximation and detail coefficients at the first stage; while in the remaining stages, the decomposition is performed on the approximation coefficients only, as shown in [Figure 1], thus achieving the multi-resolution analysis (MRA). This is called the Mallat algorithm or Mallat-tree decomposition. Its significance lies in the manner it connects the continuous-time multi-resolution to discrete-time filters. In this figure, the signal is denoted by the sequence s(n), where 'n' is an integer. The low-pass filter is denoted by G o while the high-pass filter is denoted by H o . At each level, the high-pass filter produces detailed information, cD; while the low-pass filter associated with scaling function produces coarse approximations, cA.
With the application of this approach, the time resolution becomes arbitrarily good at high frequencies, while the frequency resolution becomes arbitrarily good at low frequencies. The filtering and decimation process is continued until the desired level is reached.
After wavelet decomposition, the noise in a signal can be further removed by wavelet de-noising. There are two methods which can be adopted to remove the noise using wavelet de-noising. The first method is forced de- noising. This method turns selected high-frequency coefficients to zero in wavelet decomposition structure. After reconstruction, the results of this method are smooth. But there is a chance of losing the useful high-frequency parts of the original signal. The second method is threshold de-noising. This method gives the value of threshold based on various thresholding algorithms like universal threshold, rigorous SURE threshold and minimax threshold . The threshold-based de-noising improves the de-noised results significantly. These de- noised decomposition coefficients are then reconstructed using wavelet reconstruction.
[Figure 2] shows the reconstruction of the original signal from the wavelet coefficients. Basically, reconstruction is the reverse process of decomposition. For reconstruction purposes, at each level, after upsampling, the approximation coefficients are convolved with a low- pass reconstruction filter G 1 to obtain the reconstructed approximation A i , while the detail coefficients are convolved with a high-pass reconstruction filter H 1 to obtain the reconstructed detail D i . The low- and high-pass decomposition filters together with the low- and high-pass reconstruction filters are called quadrature mirror filters (QMFs). This process is continued through the same number of levels as in the decomposition process to obtain the original signal ,,, .
| 3. De-Noising Algorithms|| |
Three steps are required for de-noising of signals: Decomposition, thresholding and reconstruction  . The first and last steps are performed with the selection of suitable wavelet family and mother wavelet. The thresholding step is the selection of threshold level for de-noising of the signals. The thresholding algorithms commonly employed for de-noising of the fPCG signals are -
- universal threshold
- minimax threshold
- rigorous SURE threshold
These de-noising algorithms can be divided into linear and nonlinear methods. The linear method is independent of the size of empirical wavelet coefficients, and therefore the size of the coefficient by itself is not taken into account. It assumes that signal noise can be found mainly in fine-scale coefficients and not in coarse scales. The nonlinear method is based on the idea that the signal noise can be found in every coefficient and is distributed over all scales. It can be applied in two ways: Hard thresholding rule and soft thresholding rule. In hard thresholding, if the value of the coefficient is less than the defined value of threshold, then the coefficient is scaled to zero; otherwise, the value of the coefficient is maintained as it is. In soft thresholding, if the value of the coefficient is less than the defined value of threshold, then the coefficient value is scaled to zero; otherwise, the value of coefficient is reduced by the amount of defined value of threshold  .
3.1 Universal Threshold
The universal threshold de-noising algorithm is also known as VisuShrink. It uses a fixed threshold form given by
where 'n' denotes the length of the signal and σ is the standard deviation. This threshold was determined in an optimal context for soft thresholding with random Gaussian noise. This scheme is very easy to implement but typically provides a threshold level larger than other thresholding algorithms, therefore resulting in smoother reconstructed data. Also, such estimation does not take into account the content of the data but only depends on the data size.
3.2 Minimax Threshold
The minimax threshold de-noising algorithm consists of an optimal threshold that is derived from minimizing the constant term in an upper bound of the risk involved in the estimation of the signal. This threshold level depends on the noise and signal relationships in the input data, and it is given by
where λn is determined by a minimax rule such that the maximum risk of estimation error across all locations of the data is minimized.
3.3 Rigorous SURE Threshold
The de-noising algorithms described previously use global thresholds, that is, the computed threshold is applied to all wavelet coefficients. The rigorous SURE threshold algorithm describes a scheme that uses a threshold value λj at each resolution level 'j' of the wavelet coefficients. This algorithm is also known as SureShrink, and it uses the Stein's unbiased risk estimate (SURE) criterion to get an unbiased estimate.
| 4. Comparisons and Results|| |
The fPCG signals are recorded from the maternal abdominal surface using a highly sensitive and inexpensive data-recording module (DRM)  . The block diagram of the DRM is shown in [Figure 3].
The output of the sensor is fed to a separate pre-amplifier, which provides high amplification and better noise rejection. These signals are then low-pass filtered with the help of an active low-pass filter. A power amplifier further strengthens the output signal from the filter. The recordings are obtained from pregnant women with gestation age between 36 and 40 weeks. The signals are recorded with a sampling frequency of 8000 Hz, 16-bit resolution, and saved in a personal computer for further processing. [Figure 4] shows the waveform of one of these fPCG signals.
All the three de-noising algorithms are simulated in Matlab® for de-noising of the fPCG signals. The mean-squared error (MSE) is used to evaluate the performance of the presented approach for the selection of appropriate de-noising algorithm. It can be obtained using the following expression:
where 'n' denotes the length of the signal, 's' represents the original signal and s e is the estimated signal obtained from the de-noised wavelet coefficients. [Figure 5] is a test signal generated by adding simulated random noise in the original fPCG signal, which is shown in [Figure 4]. This simulated random noise is analogous to the noise produced because of maternal organ sounds, fetal movement effects and ambient noise  .
The wavelet analysis of this signal is performed with five levels of decomposition using fourth-order Coiflets wavelet. This selection of mother wavelet is random and based on the fact that it possesses all the properties needed for analysis of the fPCG signals. All the three algorithms with soft or hard thresholding rule are applied for de-noising of the fPCG signal  . [Figure 6] shows the waveforms of the fPCG signal obtained using these optimal wavelet functions.
Finally, the efficacy of the method is evaluated using fPCG signals (S1-S5) recorded from five different subjects. All the de-noising algorithms are applied for de-noising of these fPCG signals using selected mother wavelets, and the respective results generated are depicted in tabular form [Table 1] below.
[Table 1] shows a comparison among three de-noising algorithms with soft or hard thresholding rule. The rigorous SURE threshold algorithm with soft thresholding rule yields the best estimation with considerably smaller MSE as compared to other algorithms for de-noising of fPCG signals.
| 5. Conclusion|| |
Wavelet transforms have become a well-known useful tool for various biomedical signal processing. This paper presents an approach to select the appropriate de-noising algorithm for de-noising of the fPCG signals. The performances of universal threshold, minimax threshold and rigorous SURE threshold algorithms along with soft and hard thresholding rules have been compared for de-noising of the fPCG signal. The comparison is based on evaluating the MSE of the original signal and the estimated signal. The performance of the system is validated using fPCG signals recorded from five different subjects. The results show that the rigorous SURE threshold algorithm with a soft thresholding rule has the best performance for de-noising of fPCG signals when using fourth-order Coiflets wavelet. The proposed approach is simple and proves to be effective when applied for the selection of de-noising algorithm for the fPCG signals. The main object is to improve the SNR of the fPCG signals for accurate determination of FHR and further diagnostic applications.
| 6. Acknowledgement|| |
The fetal heart sound recordings were taken at the District Government Women Hospital. The authors of this paper thank Dr. Shirish Ratnaparkhi (gynecologist) and Dr. (Mrs.) Megha Ratnaparkhi (obstetrician) for their support in taking the records with the help of developed prototype instrument. The authors also thank the pregnant ladies who volunteered to participate in the clinical test.
Vijay Chourasia graduated in Electronics Engineering from RTM Nagpur University, Nagpur. He is pursuing his Master of Engineering (By Research) from RTM Nagpur University, Nagpur. He is Senior Lecturer in the Department of Electronics Engineering in Manoharbhai Patel Institute of Engineering & Technology, Gondia, India. He has more than 15 years experience in the field of academics and has about 10 research publications in various national and international conferences and journals. His area of research is Biomedical Instrumentation, Biomedical Signal Processing and Soft Computing.
A. K. Mittra graduated in Electrical Engineering from GGD University Bilaspur and Post Graduated in Electronics and Control Engineering from BITS Pilani. He is pursuing his Doctoral Research from RTM Nagpur University, Nagpur. Currently he is an Assistant Professor in the Department of Electronics Engineering in Manoharbhai Patel Institute of Engineering & Technology, Gondia, India. He has a vast experience in academic field and he has more than 25 research publications in various national and international conferences and journals. His area of research is Biomedical Instrumentation, Biomedical Signal Processing and Soft Computing.
| References|| |
|1.||R.K. Freeman, and T.J. Garite, Fetal Heart Rate Monitoring, p. 7-17, Williams and Wilkins, 1981. |
|2.||P. Va´rady, L. Wildt, Z. Benyo, and A. Hein, "An advanced method in fetal phonocardiography," Computer Methods and Programs in Biomedicine , v0 ol. 71, pp. 283-96, 2003. |
|3.||J. Chen, K. Phua, Y. Song, and L. Shue, "A portable phonocardiographic fetal heart rate monitor," Proceedings of the International Symposium of the IEEE on Circuits and Systems , pp. 2141-4, 2006. |
|4.||V. Padmanabhan, R. Fischer, J.L. Semmlow, and W. Welkowitz, "High sensitivity PCG transducer for extended frequency applications," Proceedings of the Annual International Conference of the IEEE on Engineering in Medicine and Biology Society, Images of the Twenty-First Century , v0 ol. 1, pp. 57-8, 1989. |
|5.||F. Kovacs, Cs. Horvath, M. Torok, and G. Hosszu, "Long-term phonocardiographic fetal home monitoring for telemedicine systems," 27 th Annual International Conference of the IEEE on Engineering in Medicine and Biology Society , pp. 3946-9, 2005. |
|6.||J. Nagel, "New diagnostic and technical aspects of fetal phonocardiography," European Journal of Obstetrics, Gynecology and Reproductive Biology , v0 ol. 23, pp. 295-303, 1986. |
|7.||G. Vasios, A. Prentza, D. Blana, E. Salamalekis, P. Thomopoulos, D. Giannaris, and D. Koutsouris, "Classification of fetal heart rate tracings based on wavelet-transform and self-organizing-map neural networks," Proceedings of the 23 rd Annual International Conference of the IEEE on Engineering in Medicine and Biology Society , v0 ol. 2, pp. 1633-6, 2001. |
|8.||X. Yang, P. Li, Z. Xin, Z. Bian, and B. Wang, "De-Noising of the doppler fetal heart rate signal with wavelet threshold filtering based on spatial correlation," The 1 st International Conference of the IEEE on Bioinformatics and Biomedical Engineering, ICBBE 2007, pp. 928-31, 2007. |
|9.||M.R. Raghuveer, and A.S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications, pp. 25-50, Pearson Education Pvt. Ltd., Singapore, Indian Branch , 2002. |
|10.||I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics New York , 1992. |
|11.||S.G. Mallat, A Wavelet Tour of Signal Processing, Academic Press , 1999. |
|12.||S.G. Mallat, "A theory of multiresolution signal decomposition: The wavelet rpresentation," IEEE Transactions on Pattern Analysis and Machine Intelligence , v0 ol. 11, pp. 674-93, 1989. |
|13.||Matlab Wavelet Toolbox User′s Guide, Mathwork Incorporation; www.mathworks.com. |
|14.||M.C.E. Rosas-Orea, M. Hernandez-Diaz, V. Alarcon-Aquino, and L. G. Guerrero-Ojeda, "A comparative simulation study of wavelet based denoising algorithm," Proceedings of the 15 th International Conference of the IEEE on Electronics, Communications and Computers , pp. 125-130, 2005. [PUBMED] |
|15.||V.S. Chourasia, and A.K. Mittra, "Development of data acquisition module for a non-invasive fetal monitoring system," International Journal of Biomedical Signal Processing , in press, 2008. |
|16.||A.K. Mittra, N.K. Choudhary, and A.S. Zadgaonkar, "Development of an artificial womb for acoustical simulation of mother′s abdomen," International Journal of Biomedical Engineering and Technology , v0 ol. 1, n0 o. 3, pp. 315-28, 2008. |
|17.||W.G. Morsi, and M.E. El-Hawary, "The most suitable mother wavelet for steady-state power system distorted waveforms," Canadian Conference of the IEEE on Electrical and Computer Engineering , pp. 17-22, 2008. |
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
|This article has been cited by|
|| De-noising algorithm based on compression of wavelet coefficient for MEMS accelerometer signal
| ||Wu, P., Ge, Y., Chen, S., Xue, B. |
| ||2010 IEEE International Conference on Information and Automation, ICIA 2010. 2010; 5512369: 402-407 |
||A single channel phonocardiograph processing using EMD, SVD, and EFICA
| ||Warbhe, A.D., Dharaskar, R.V., Kalambhe, B. |
| ||Proceedings - 3rd International Conference on Emerging Trends in Engineering and Technology, ICETET 2010. 2010; art(5698392): 578-581 |