As explained in the previous sections, lung sound analysis has been of interest for its diagnostic values for pathology of the lung and airways assessment. Most of the lung sounds energy is concentrated in the frequencies below 200 Hz, which has an overlap with the main frequency components of heart sounds. The heartbeat is an unavoidable source of interference for lung sound recording that when it occurs it changes both frequency and time characteristics of the lung sounds.
Physicians may try to ignore the heart sounds during auscultation or when assessing the recorded lung sounds remove the parts that include heart sounds. Since heart sounds occur regularly, the removal of heart sound included portions of the recorded sound signal causes artifacts and click sounds in those locations; hence making the signal unusable for any automatic analysis or even listening to the entire signal. Since both heart and lung sounds have major components in the frequency range below 200 Hz, a simple filtering cannot remove the effect of heart sounds. Hence, several researchers employed different methods to reduce or eliminate the effect of heart sounds in lung sounds recordings. The heart sound reduction methods can be divided in two groups: the methods that apply a filter to the entire lung sound record and reduce the heart sounds effect and the methods that remove the heart sound included portion of the lung sound record and then estimate the signal in the gaps. The recent methods developed for heart sound reduction are described below. Among these methods the wavelet denoising, adaptive filtering and independent component analysis belong to the first group of heart sound reduction methods, while the rest belong to the second group.
Wavelet denoising. Wavelet transform (WT) is a useful tool when dealing with signals that have some nonstationary parts. Therefore, some researchers have tried to develop filters based on wavelet transform. The WT-based adaptive filtering was first proposed in  to separate discontinuous adventitious sounds from vesicular sounds based on their nonstationary characteristics assuming that nonstationary parts of a signal in the time domain produce large WT coefficients (WTC) over many wavelet scales, whereas for the stationary parts the coefficients die out quickly with the increasing scale. Therefore, it is possible to apply a threshold to the WTC amplitudes to detect the most significant coefficients at each scale representing the nonstationary parts of the signal in the time domain; hence, the rest of the WTC correspond to stationary parts of the signal. Consequently, a wavelet domain separation of WTC corresponds to the time domain separation of stationary and nonstationary parts of the signal. This method was applied for heart sound separation (reduction) from lung sounds by a few researchers [24,25]. The desired lung sounds and unwanted heart sounds portions of a signal were separated through iterative multiresolution decomposition and multiresolution reconstruction based on hard thresholding of the WTC. While the WT-based filters do reduce the heart sounds effect on the lung sound record, however, according to the reported results, some audible heart sounds still remained in the lung sound record.
Adaptive filtering. Linear adaptive filtering (usually with the least mean squares (LMS) or recursive least squares (RLS) algorithms for adaptation) has been used widely for canceling power-line noise in biological signals successfully. The technique is to use the original signal including the noise as one of the inputs and a copy of the noise signal as another input in which the filter tries to find the components in the main signal that match with the copy of the noise and finally after the filter coefficients are optimized by an algorithm, i.e., LMS or RLS, the adapted-to-noise output is subtracted from the signal; hence the remaining is supposedly the noise-free signal.
This technique works well if the signal and noise are uncorrelated as it is an assumption in the design of linear adaptive filters. This assumption holds true for the power-line noise and biological signals. However, in applying this technique to separate heart and lung sounds from each other, the main problem is how to provide a copy of the noise, i.e., heart sounds in this case, that is uncorrelated to the main signal, i.e., lung sounds. Even if we assume that the heart and lung sounds are uncorrelated in their source of generation, they become correlated when we record them on the surface of the chest wall as they both pass through the same medium.
Two groups, who applied adaptive filtering for heart sound reduction, used ECG signals instead of the heart sound as the copy of the noise input [26, 27]. This is highly questionable as the ECG signal is not the noise of the lung sound record and hence even if the filter tries to adapt itself to the ECG signal, the results will not be meaningful. Two other groups used the heart sounds recorded over the heart of the subjects as the reference signal for the adaptive filtering with the LMS algorithm [28, 29]. However, the heart sound signal recorded over the chest wall inevitably includes lung sounds as well.
In order to eliminate the need of the reference signal for the adaptive filter, some researchers proposed a single recording technique based on the modified version of the adaptive LMS algorithm by adding a low-pass filter with a cut-off frequency of 250 Hz in the error signal path to the filter . However, their results showed that heart sounds were still clearly audible due to the improper identification of the heart sound segments within the long sound record.
As it can be deduced from the above review, the reference signal plays a key role in the successful noise reduction in the output of the linear adaptive filter. In one of the successful and most recent studies using adaptive filtering, the reference signal was constructed by first detecting the heart sounds locations in the bandpass filtered version of the original record using an old method introduced in  and then replacing all the components of the bandpass filtered original signal by zero except for the heart sound included parts. The resulted impulse-like signal was used as the reference signal for the adaptive noise cancelation using the RLS algorithm. The results were evaluated both quantitatively and qualitatively. The average power spectral densities of unfiltered signals over four frequency bands in areas including and excluding heart sounds were compared with those of the filtered recordings. Also a panel of researchers experienced in lung sound auscultation provided qualitative analyses of the filtered signals, which was favorable for significant heart sound reduction .
Spectrogram-independent component analysis. Blind source separation (BSS) is a method to recover independent source signals while only a linear mixture of the signals is available, in which the sources and the way they have been mixed is unknown; hence the term "blind" in the method. Independent Component Analysis (ICA) is a technique used to solve BSS problems. ICA finds a linear coordinate system such that the recovered signals are statistically independent .
However, in some cases the signals are not linearly mixed but are convolved due to transmission through one or more mediums with unknown transfer functions. Therefore only mixed and distorted versions of the signals are available. Applying ICA on the spectrograms of the mixed signals has been suggested as an alternative solution to this kind of problem .
In the case of lung and heart sounds, since both sounds pass through fat, skin and lung tissues, it makes sense that the signals are a convolutive mixtures. This technique has been applied for separating speech signals  and for heart sound reduction . The assumption in applying this method is that the source signals are originally statistically independent and at least one of them has the Gaussian distribution. At least two versions of the mixed signals are required although the more the better the performance of separations, which is also at a much higher computational cost.
In  lung sounds were recorded from two sensors on the chest wall to provide two mixed signals, and then ICA was applied on the spectrograms of the signals. In general, it is difficult to evaluate the results of ICA as the method's claim is that it recovers the original signals at the source while there is no access to the actual source signals to compare with and evaluate. Therefore, in heart sound cancelation we can only compare it quantitatively using the spectra of the recorded lung sound portions free of heart sound and the resulted signal for any significant changes and also by visual and auditory means. The results of the ICA-based method have been shown to reduce the effect of heart sound while still a weakened heart sound could be heard in the resultant signal. In addition, the lung sounds were heard somewhat different from the original signal . This is expected because the techniques that are applied to the entire signal inevitably change the lung sounds portions free of heart sound too.
Time-frequency filtering. The idea of removing the heart sound portions of the lung sound record and then estimating the missing data was first introduced in , in which the heart sound segments are removed from the lung sound record using time-varying filtering based on the short-time Fourier transform (STFT) of the original signal and then interpolation is used to fill the gaps in the time-frequency plane. Finally, the signal is reconstructed in the time domain. The block diagram in Fig. 5.2 illustrates the necessary steps of this method. The performance of the method is also shown by an example in Fig. 5.3. The result of this method by far has been the best among the other heart sound cancelation methods. It is also computationally efficient.
Multiscale product wavelet filtering and linear prediction. In this method [38, 39] the heart sound segments are detected by multiscale product (described in the next section) and removed from the wavelet coefficients at every scale. After removal of the heart sound included segments, the missing data are estimated by the linear prediction using either auto regressive (AR) or moving average (MA) models. AR and MA models are two common signal processing tools used to predict past or future values of a time-limited signal. The predicted samples are basically weighted linear combinations of the signal known values. A more complete discussion about AR/MA models can be found in .
This idea has been used for interpolation of missing speech segments in audio signals for short periods of time that can be assumed stationary . However, it is too simplistic to assume that lung sounds are stationary during the entire duration of a respiratory cycle (inspiration/expiration) especially in the vicinity of breath onsets. Therefore, correct selection
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FIGURE 5.2: Block diagram of the STFT method. Adopted from  with permission
Reconstructed LS Spectrogram LS Spectrogram after removal of HS corrupted segments
FIGURE 5.3: Performance of the STFT method for a typical lung sound record
Reconstructed LS Spectrogram LS Spectrogram after removal of HS corrupted segments
FIGURE 5.3: Performance of the STFT method for a typical lung sound record of the order as well as the type of the linear prediction model (AR or MA) must be done carefully to ensure that the data used for prediction of the gaps are indeed stationary.
The choice of either AR or MA modeling depends on the location of the heart sound segment within the breath cycle. If heart sound occurs close to the vicinity of the onset of the respiratory phase, i.e., inspiration or expiration, the method uses MA modeling to predict the gap with future values, due to the fact that most of the information about the samples in the gap is in the next lung sound segment; otherwise the method uses AR modeling.
The order of either AR or MA model is increased until the energy difference between the original and estimated data is minimum. The order, where the performance of the AR or MA models results in the minimum energy difference between the original and extrapolated data, is chosen as the best order for that portion of the lung sound signal. The performance of this method is comparable with the time-frequency filtering method both quantitatively and qualitatively, but this method is more complex.
Among the heart sound cancelation methods, those that apply a filter to the entire record of lung sound do reduce the heart sound but do not remove their effect completely, while the lung sound also changes slightly as the filter is applied to the entire signal. The time-frequency filtering method, multiscale wavelet filtering method, and linear prediction method perform better compared to the other methods because they remove the entire heart sound included segments and estimate the missing data by either spline interpolation or linear prediction. Therefore, heart sounds are completely removed from the record and the rest of the data remain unchanged. Removal of the heart sound included segments followed by interpolation or linear prediction for the missing data makes the record to be heard unchanged but without heart sounds.
Recurrence time and nonlinear prediction. In this method , the heart sound locations are found by the recurrence time statistic measure (described in Section 5.3), and removed from the original lung sound record like in the previous methods in this group. The missing data are then predicted by a nonlinear scheme. In fact, since the heart sound localization is achieved in state space, the prediction is also in the state space using the six neighboring trajectories to reconstruct the punctured space after removing heart sound portions. Then, the predicted reconstructed data are brought back into the time domain.
The results of this method seem to be reasonable as the reported differences in the spectra of the original lung sound portions free of heart sounds and the predicted lung sounds are less than 3 dB in the frequency ranges below 300 Hz. Since our ear is not sensitive to the differences below 3 dB, it can be concluded that the predicted data with this method are not heard much different from the original lung sounds free of heart sounds. However, the study does not elaborate on the differences at different flow rates and whether the method is successful in high flow rates.
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