lapped with background noise. Therefore, it is difficult to enhance the noisy bowel sounds by using precise digital filters. In this study, a higher order statistics (HOS)-based radial basis function (RBF) network was proposed to enhance noisy bowel sounds. An HOS technique provides the ability of suppressing Gaussian noises and symmetrically distributed non-Gaussian noises due to their natu-ral tolerance. Therefore, the influence of additional noises on the HOS-based learning algorithm can be reduced effectively. The sim-ulated and experimental results show that the HOS-based RBF can exactly provide better performance for enhancing bowel sounds under stationary and nonstationary Gaussian noises. Therefore, the HOS-based RBF can be considered as a good approach for enhancing noisy bowel sounds.
Index Terms—Bowel sound, Gaussian noise, higher order
statis-tics (HOS), radial basis function (RBF) network.
I. INTRODUCTION
G
ASTROINTESTINAL motility is closely related to gas-trointestinal problems, and the auscultation of bowel sounds is usually used for the diagnosis in internal medicine and postsurgery. However, the auscultation of bowel sounds re-quires clinical experiences of physicians and is easily affected by environmental noise [1]. Therefore, the quantitative and qual-itative evaluations of bowel sounds for gastrointestinal diseases still encounter some difficulties.Manuscript received July 12, 2012; revised December 17, 2012; accepted January 25, 2013. Date of publication February 1, 2013; date of current version May 1, 2013. This work was supported by the National Science Council of Taiwan under Grant NSC 100-2221-E-009-007 and Grant NSC 100-2622-E-009-012-CC3.
B.-S. Lin is with the Institute of Imaging and Biomedical Photonics and Biomedical Electronics Translational Research Center, National Chiao Tung University, Hsinchu 300, Taiwan, and also with the Department of Medical Research, Chi Mei Medical Center, Tainan 710, Taiwan (e-mail: borshyhlin@ gmail.com).
M.-J. Sheu is with the Division of Gastroenterology and Hepatology, Chi Mei Medical Center, Tainan 710, Taiwan, and also with the Department of Medicinal Chemistry, Chia Nan University of Pharmacy and Science, Tainan 717, Taiwan. C.-C. Chuang is with the Institute of Imaging and Biomedical Photonics, National Chiao Tung University, Hsinchu 300, Taiwan.
K.-C. Tseng is with the Division of Gastroenterology and Hepatology, Chi Mei Medical Center, Tainan 710, Taiwan.
J.-Y. Chen is with the Department of Anesthesiology, Chi Mei Medical Cen-ter, Tainan 710, Taiwan, and also with the Department of the Senior Citizen Service Management, Chia Nan University of Pharmacy and Science, Tainan 717, Taiwan.
Digital Object Identifier 10.1109/JBHI.2013.2244097
using precise digital filters. Several studies utilized the adap-tive filtering technique to enhance noisy bowel sounds. In 1997, Mansy and Sandler used an adaptive noise canceller with the Widrow–Hoff least-mean-square (LMS) algorithm to reduce the distortion of gastrointestinal acoustic phenomena due to heart sounds [2]. Abdominal sounds are usually nonlinear, and thus, a great number of filter taps are usually required to effectively en-hance nonlinear signals. In order to effectively enen-hance nonlin-ear signals, using neural network filters [3]–[5], which can well approximate any continuous nonlinear function with a small amount of training data and much fewer filter taps, may be a good alternative. In 1997, Gandhi and Ramamurti used a three-layer neural network to detect non-Gaussian noise [3]. How-ever, the learning of multilayer perceptron (MLP) network is slow and global, and the estimate of MLP network easily traps at a local minimum during the learning procedure. In 1995, Billings and Fung used a recurrent radial basis function (RBF) network to cancel noise [4]. Cha and Kassam used the RBF net-work to eliminate interference [5]. However, additional noise usually affects the adaptation of weights in the RBF network. Therefore, reducing the influence of additional noise on the performance of enhancing bowel sounds for RBF network is important.
Recently, a higher order statistics (HOS) technique has been developed and applied for signal enhancement [6]–[13]. HOS techniques provide the ability of suppressing Gaussian noise and symmetrically distributed non-Gaussian noise due to their natural tolerance [14], [15]. In this study, the HOS-based RBF network was proposed to enhance noisy bowel sounds. Bowel sounds usually contain high non-Gaussianity due to the fea-ture of explosive sounds [16]. By using HOS techniques, the non-Gaussian property of bowel sounds can be enhanced ef-fectively. Here, an adaptive line enhancement (ALE) scheme, which uses the delayed input signal as the reference signal, is utilized, and only single channel of bowel sounds is re-quired for signal enhancement. The performance of enhanc-ing noisy bowel sounds under different noise state was inves-tigated, and finally, the HOS-based RBF was tested and vali-dated at Chimei Medical Center. This paper is organized as fol-lows. The basic schemes of RBF network and HOS-based RBF for signal enhancement are introduced in Section II. The per-formance of enhancing bowel sounds using different methods is investigated in Section III. In Section IV, conclusions are drawn.
Fig. 1. Basic scheme of RBF network for signal enhancement.
II. METHODS
A. RBF Network for Signal Enhancement
RBF was first derived by Broomhead and Lowe in 1988 [17]. It is a special three-layer network containing an input layer, a hidden layer, and an output layer. The hidden layer performs a nonlinear transformation role which maps the input space onto the output space. Therefore, by using RBF network, the surface in a multidimensional space, which provides a best fit to training data, can be found out [18], [19].
The basic scheme of RBF network for signal enhancement is shown in Fig. 1. Let the desired signal d(t) be
d(t) = s(t) + ns(t) (1)
where s(t) and ns(t) denote the noise-free bowel sound and additional noise at the iteration t, respectively. Based on the scheme of ALE [20], the delayed version of d(t) can be used as the reference signal r(t) and is given by
r(t) = d(t− Δ). (2)
Here, the prediction depth Δ is usually selected by the unit of sampling period. Let N0and N1denote the number of the input
and hidden nodes, respectively; the estimate ˆs(t) of s(t) can be calculated by
ˆ
s(t) = δ(t)Tw(t) (3)
where δ(t) = [δ1(t), δ2(t), ..., δN1(t)]
T denotes the output vec-tor of the hidden nodes, generated by Gaussian basis function, and w(t) = [w1(t), w2(t), ..., wN1(t)]T denotes the weight
vec-tor connecting the hidden nodes with the output node. The output of Gaussian basis function in the kth hidden node can be defined by δk(t) = exp −r(t) − vk(t)2 2ρ2(t) (4) where · denotes the Euclidean norm, r(t) = [r(t), r(t− 1), ..., r(t − N0+ 1)]T is the vector of the input nodes,
and vk(t) denotes the center in the kth hidden node. In
addi-tion, ρ(t) denotes the width of the centers and can be defined as the variance of the input vector. The center vk(t) can be
obtained by the k-means clustering algorithm [21], which is a self-organized learning procedure, and the weight vector w(t)
Fig. 2. Basic scheme of higher order statistics-based RBF network for signal enhancement.
is commonly adapted by the normalized LMS algorithm [20]. The weight vector can be adapted by
w(t + 1) = w(t) +
μw
(1+ δT(t)δ(t))
δ (t)(d(t)− ˆs(t)) (5)
where μwdenotes the learning rate. Obviously, adapting weights is easily affected by additional noise ns(t) due to that e(t) is correlated with additional noise ns(t), i.e., e(t) = d(t)− ˆs(t) =
s(t) + ns(t)− ˆs(t).
B. HOS-Based RBF Network for Signal Enhancement
The basic scheme of HOS-based RBF network for signal enhancement is shown in Fig. 2. For a set of real stationary variables{zi(t)}, i = 1, 2, 3, ..., the nth-order cross cumulant of{zi(t)} can be defined as follows:
Cz1z2...zn(τ1, τ2, ..., τn−1)≡ Cum[z1(t), z2(t + τ1), z3(t + τ2), ..., zn(t + τn−1)]. (6) Here, Cum[·] denotes the cumulant operator [14]. Under the assumption that the nth-order cumulants (n > 2) of the desired and reference signals exist, they can be represented by
Cdr r...r(τ1, τ2, ..., τn−1)
= Cum[d(t), r(t + τ1), r(t + τ2), ..., r(t + τn−1)]. (7) Since s(t) and ns(t) in the desired and reference signal are independent, and the nth cumulant of Gaussian noises is iden-tically zero, (7) can then be simplified as
Cdr r...r(τ1, τ2, ..., τn−1) = Cum[s(t), s(t + τ1− Δ), ...,
s(t + τn−1 − Δ)] = Css...s(τ1− Δ, τ2− Δ, ..., τn−1− Δ). (8)
Similarly, the nth cumulant of the filtered output signal can also be represented by
Cˆs r r . . . r(τ1, τ2, ..., τn−1) = Cs s s . . . sˆ (τ1− Δ, τ2− Δ, ..., τn−1− Δ). (9)
( τ1, τ2, . . . , τn−1)∈Γ 2 τn−1− Δ) − Cs s . . . s(τ1− Δ, τ2− Δ, ..., τn−1− Δ)]2 = ( τ1, τ2, . . . , τn−1)∈Γ ... 1 2 ⎡ ⎣N1 j = 1 wjCδjr r . . . r(τ1, τ2, ..., τn−1) − Cd r r . . . r(τ1, τ2, ..., τn−1) ⎤ ⎦ 2 . (10)
Equation (10) can be rewritten in a matrix form ξ = 1
2[Cδ rr...rw− Cdrr...r]
2 (11)
Here, Cδ rr...r and Cdrr...r are an NΓ× N1 matrix and an
NΓ× 1 column vector, and NΓdenotes the number of points in
the set Γ. In order to minimize ξ, the gradient-descent method was used. The gradient of ξ is given by
∇w(t)≡ ∂ξ
∂w(t) =−C
T
δ rr...r(t)[Cdrr...r(t)− Cδ rr...r(t)w(t)]. (12) Consequently, the adaptation formula can be given by
w(t + 1) = w(t)− μw
(1 + tr(CT
δrr...rCδrr...r))
∇w(t). (13) Under the assumption that s(t) approximates to ˆs(t), the learning criterion in (10) will be close to optimal. Therefore, by using the HOS-based learning algorithm, the influence of additional noises ns(t) on Cdrr...rcan be eliminated and provide better performance. In this paper, the HOS-based RBF with the third-order statistics was used for enhancing bowel sounds. For a zero-mean signal, the estimate of the third-order cumulant can be recursively computed by
ˆ
Cz1z2z3(t; τ1, τ2) =< z1(t)z2(t + τ1)z3(t + τ2) > . (14)
Here, the operation <· > is defined as follows:
< f (t) >=λ < f(t − 1) > +(1 − λ)f(t) (15) whereλ is a forgetting factor.
III. RESULTS ANDDISCUSSIONS
A. Performance Comparison for Enhancing Bowel Sounds Under Stationary Gaussian Noise
In this section, the performances of enhancing bowel sounds under stationary Gaussian noise by using different methods,
Fig. 3. Noise-free bowel sound, simulated noisy bowel sound with an SNR of –6 dB, and filtered bowel sounds by using different methods.
which include adaptive filter with normalized LMS algorithm (AF-NLMS), adaptive RBF filter with normalized LMS algo-rithm (RBF-NLMS), and the HOS-based RBF, were investi-gated. In this study, ten trials of 1-min bowel sounds (five healthy control cases and five adhesive ileus cases) recorded in the anechoic chamber were used to validate the performance of the proposed methods. The frequency of peristalsis is about 3–15 events/min, and the length of the bowel sound is about 1–3 s. Therefore, in order to clearly present the effect of differ-ent methods on the enhancemdiffer-ent of bowel sounds, one of the peristalsis events from adhesive ileus cases was selected as the pattern of noise-free bowel sounds in this study. The simulated noisy bowel sounds with different signal-to-noise ratio (SNR) were generated for simulations. Here, the definition of SNR is given by SNR = 20 log10 As An (16) where As and An denote the root mean square of noise-free bowel sound and noise, respectively. Fig. 3 shows the noise-free bowel sound, noisy bowel sound with an SNR of –6 dB, and the results of filtered bowel sounds by using 32 filter-order AF-NLMS (μw = 0.8), RBF-NLMS (N0 = 32, N1 = 32, and
μw = 0.8), and HOS-based RBF (N0= 32, N1= 32, μw = 0.8,
andλ = 0.1), respectively. It shows that the SNR of the filtered bowel sound by using AF-NLMS, RBF-NLMS, and HOS-based RBF are about –0.18, 4.76, and 12.18 dB, respectively.
Next, the effect of selecting the learning rate μωon the perfor-mance was investigated. Fig. 4 shows the comparison between the performances of enhancing bowel sounds corresponding to different learning rate. Obviously, the HOS-based RBF with μω = 1.6 can provide better performance for enhancing bowel sounds. Therefore, by using the HOS technique, the influence of additional noise on adapting weights can be reduced effectively.
Fig. 4. Performance comparison for enhancing noisy bowel sounds corre-sponding to different learning rates by using different methods.
Fig. 5. Performance comparison of enhancing noisy bowel sounds by using different methods under different noise levels.
Next, the performances of enhancing noisy bowel sounds un-der different noise levels were investigated. Here, the simulated noisy bowel sounds with the SNR of –9–0 dB were generated for simulations. Fig. 5 shows the results for the performance of enhancing noisy bowel sounds under different noise level. Both HOS-based RBF and RBF-NLMS can provide better per-formance under different noise level. Obviously, the perfor-mance of enhancing bowel sounds for AF-NLMS rapidly be-comes poorer when the SNR of noisy bowel sounds bebe-comes poorer. However, the performance of enhancing bowel sounds for HOS-based RBF is most insensitive to the noise level.
B. Performance Comparison for Enhancing Bowel Sounds Under Nonstationary Gaussian Noise
The performance of enhancing noisy bowel sounds under nonstationary Gaussian noise was investigated in this section. Here, four types of Gaussian noise, as shown in Fig. 6(a), were used to generate nonstationary noise. Here, the type of additional Gaussian noises was randomly selected and its magnitude was also varied every 25 ms to generate nonstationary Gaussian noises with the SNR of 15–0 dB. Fig. 6(b) shows the results of filtered bowel sounds by using 32 filter-order AF-NLMS (μw = 0.8), RBF-NLMS (N0 = 32, N1 = 32, and μw = 0.8), and HOS-based RBF (N0 = 32, N1 = 32, μw = 0.8, andλ = 0.1). The simulated result shows that AF-NLMS and RBF-NLMS are relatively sensitive to the SNR variation of additional noise, but
Fig. 6. (a) Four types of Gaussian noises used to generate nonstationary noise, and (b) filtered bowel sounds by using different methods.
the influence of the SNR variation of additional noise for HOS-based RBF is negligible. Obviously, the efficiency of HOS-HOS-based RBF for enhancing noisy bowel sounds under nonstationary Gaussian noise is most significant.
Next, the performance of enhancing noisy bowel sounds un-der environment noise for different methods was also inves-tigated. Two types of crowd-indoor sounds from the Sound Ideas [22], as shown in Fig. 7(a), were used to simulate environ-ment noise in the Emergency room or the Intensive Care Unit. Fig. 7(b) and (c) shows the results obtained by AF-NLMS, RBF-NLMS, and HOS-based RBF for two types of crowd-indoor sounds, respectively. In this simulation, the SNR of noisy bowel sounds was set to –3 dB. For case I noise, the SNRs of filtered noisy bowel sound by using AF-NLMS, RBF-NLMS, and HOS-based RBF are about 4.74, 6.23, and 8.55 dB, respectively. For case II noise, the SNRs of filtered noisy bowel sound by using AF-NLMS, RBF-NLMS, and HOS-based RBF are 5.2, 6.27, and 9.02 dB, respectively. From the above simulated results, the HOS-based RBF presented the better performance for enhanc-ing noisy bowel sounds under different environment noise.
C. Performance Evaluation for Enhancing Real Bowel Sounds
In this section, the performance of enhancing real bowel sounds was evaluated by questionnaire test. Twenty trials of bowel sounds with environmental noise (ten healthy control cases and ten adhesive ileus cases) recorded in the com-mon ward were used for test. Here, healthy controls are from health management center. The patient group is from hospi-tal inpatients. They were all in fasting status at least for 6 h. Each bowel sound trial was processed by using AF-NLMS,
Fig. 7. (a) Two types of crowd-indoor sounds: case I and case II, (b) filtered bowel sounds for case I noise, and (c) filtered bowel sounds for case II noise.
RBF-NLMS, and HOS-based RBF, respectively. For each trial, the results of bowel sound processed by different methods were randomly sorted to avoid the physician recognizing the process-ing methods. A total of 12 physicians from the Division of Gas-troenterology and Hepatology, Chimei Medical Center, Taiwan, who own extensive experience in the auscultation diagnosis of bowel sounds, were invited to attend this questionnaire test. The physicians were instructed to hear the original bowel sound first, and then hear these filtered bowel sounds in sequence to com-pare the efficiency of these unknown methods on enhancing the original bowel sounds. Here, the efficiency of enhancing bowel sounds will be rated in the level range between 1 and 5. Finally, MATLAB was used to perform analysis of variance (ANOVA) analysis of the questionnaire exam.
Fig. 8 shows the questionnaire results for the efficiency level of enhancing bowel sounds. Here, one-way ANOVA was used for analysis, and the sign∗∗ denotes that the efficiency differ-ence is significant (p < 0.01). The mean and standard deviation for the level of enhancing effect by using AF-NLMS, RBF-NLMS, and HOS-based RBF are 1.08 ± 0.33, 3.51 ± 0.83, and 4.62± 0.76, respectively. Obviously, the performance of
RBF-NLMS can also provide a good performance for enhanc-ing bowel sounds. However, the computational complexity of RBF-NLMS is significantly smaller than that of HOS-based RBF.
IV. CONCLUSION
The HOS-based RBF network was proposed for enhancing noisy bowel sounds in this study. Based on the nature tolerance of HOS on suppressing Gaussian noises and symmetrically dis-tributed non-Gaussian noises, the learning criterion designed by using higher order cumulants can reduce the influence of additional noise on adapting weights effectively. Simulated re-sults validated that using the HOS-based RBF can effectively enhance bowel sounds under both stationary and nonstationary Gaussian noises. Finally, the efficiency of enhancing real bowel sounds for different methods was also evaluated by question-naire examination. From the questionquestion-naire result, it shows that both HOS-based RBF and RBF-NLMS can provide good formances for enhancing real bowel sounds. Although the per-formance of HOS-based RBF is better than that of RBF-NLMS, the computational complexity of RBF-NLMS is far less than that of HOS-based RBF. Therefore, both HOS-based RBF and RBF-NLMS can be a preferred solution for enhancing bowel sounds.
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Bor-Shyh Lin (M’02) received the B.S. degree from National Chiao Tung University, Hsinchu, Taiwan, in 1997, and the M.S. and Ph.D. degrees both in elec-trical engineering from National Taiwan University, Taipei, Taiwan, in 1999 and 2006, respectively.
He is currently an Assistant Professor at the Insti-tute of Imaging and Biomedical Photonics, National Chiao Tung University, Hsinchu. His research inter-ests include biomedical circuits and systems, biomed-ical signal processing, and biosensor.
Ming-Jen Sheu received the B.M. degree from Chung Shan Medical College, Taichung, Taiwan, in 1986.
He is currently the Director of the Division of Gas-troenterology, Department of Internal Medicine, Chi Mei Medical Center, Tainan, Taiwan. His research interests include gastroenterology, hepatology, and internal medicine.
Ching-Chin Chuang received the B.S. degree from National Central University, Taoyuan, Taiwan, in 2010, and the M.S. degree from the Institute of Imag-ing and Biomedical Photonics, National Chiao Tung University, Hsinchu, Taiwan, in 2012.
His research interests include biomedical circuits and systems, and biomedical signal processing.
Kuan-Chih Tseng received the B.M. degree from Chung Shan Medical University, Taichung, Taiwan, in 2006.
He is currently a Fellow with the Division of Gastroentero-hepatology, Department of Internal Medicine, Chi Mei Medical Center, Tainan, Taiwan. His research interests are in the areas of gastroen-terology and internal medicine.
Jen-Yin Chen received the M.D. degree from the School of Medicine, China Medical University, Taichung, Taiwan, in 1986, and the Master degree in food science and applied biotechnology from Na-tional Chung Hsing University, Taichung, in 2004.
She is currently an Assistant Professor in the Department of the Senior Citizen Service Manage-ment, Chia Nan University of Pharmacy and Science, Tainan, Taiwan. Her research interests include clini-cal medicine, biostatistics, and nutrition.
