Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
10.1109/ACCESS.2017.DOI

Corresponding author: Taufiq Hasan (e-mail: taufiq@bme.buet.ac.bd).

# Heart Sound Classification Considering Additive Noise and Convolutional
Distortion

FARHAT BINTE AZAM1 MD. ISTIAQ ANSARI1
IAN MCLANE2 AND TAUFIQ HASAN1 1mHealth Laboratory, Department of Biomedical
Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka
- 1205, Bangladesh.
2Sonavi Labs Inc., Baltimore, MD 21230, USA.

###### Abstract

Cardiac auscultation is an essential point-of-care method used for the early
diagnosis of heart diseases. Automatic analysis of heart sounds for
abnormality detection is faced with the challenges of additive noise and
sensor-dependent degradation. This paper aims to develop methods to address
the cardiac abnormality detection problem when both types of distortions are
present in the cardiac auscultation sound. We first mathematically analyze the
effect of additive and convolutional noise on short-term filterbank-based
features and a Convolutional Neural Network (CNN) layer. Based on the
analysis, we propose a combination of linear and logarithmic spectrogram-image
features. These 2D features are provided as input to a residual CNN network
(ResNet) for heart sound abnormality detection. Experimental validation is
performed on an open-access heart sound abnormality detection dataset
involving noisy recordings obtained from multiple stethoscope sensors. The
proposed method achieves significantly improved results compared to the
conventional approaches, with an area under the ROC (receiver operating
characteristics) curve (AUC) of 91.36%, F-1 score of 84.09%, and Macc (mean of
sensitivity and specificity) of 85.08%. We also show that the proposed method
shows the best mean accuracy across different source domains including
stethoscope and noise variability, demonstrating its effectiveness in
different recording conditions. The proposed combination of linear and
logarithmic features along with the ResNet classifier effectively minimizes
the impact of background noise and sensor variability for classifying
phonocardiogram (PCG) signals. The proposed method paves the way towards
developing computer-aided cardiac auscultation systems in noisy environments
using low-cost stethoscopes.

###### Index Terms:

Additive and convolutional distortion, stethoscope variability, heart sound
classification.

=-15pt

Cardiovascular Diseases (CVDs) pose a significant burden on the public health
sector, causing about 17.9 million deaths every year, which is 31% of all
deaths worldwide [1]. According to the Center for Disease Control (CDC), in
the US alone, one person dies of CVDs every 36 seconds [2]. With the shortage
of trained physicians and scarcity of diagnostic equipment, the burden of CVDs
is much higher in the low- and medium-income countries [1]. Since early
diagnosis is the key to reducing the burden of CVDs, low-cost screening tools
such as digital stethoscopes with automatic murmur analysis algorithms are
becoming more widely available [3]. With the recent advancement in embedded
systems, it is now possible to incorporate complex machine learning models
within built-in microprocessors within the stethoscope [4, 5]. However,
distortions introduced by the stethoscope sensor (e.g., diaphragm, amplifier)
and background noise are of particular concern in designing computer-aided
cardiac auscultation frameworks, especially in the underserved communities.

A considerable amount of research has been performed in the area of automatic
heart sound analysis for the detection of CVDs. Publicly available datasets
[6, 7] have accelerated the progress of research in this area, in particular
the 2016 Physionet/CinC Challenge [8, 9] dataset. This dataset provides an
archive of 4430 PCG recordings acquired using seven different
stethoscopes/sensors and are annotated as either physiological (normal) or
pathological (abnormal). Various approaches have already been attempted for
heart sound abnormality detection using this dataset. A diverse set of front-
end features have been examined including, time, frequency and statistical
features [10], Mel-frequency Cepstral Coefficients (MFCC) [11, 12, 13, 14],
and Continuous Wavelet Transform (CWT) [15, 16] features. Time-frequency based
features including MFCC and Mel-Spectrograms are most commonly being used in
recent studies. A wide array of classifiers have been attempted including the
k-Nearest Neighbor (k-NN) [12], Support Vector Machine (SVM) [17], Random
Forest [10], Multilayer Perceptron (MLP) [16], [18], deep learning approaches
with 1D & 2D CNNs [19, 20, 21, 22, 23], and Recurrent Neural Network (RNN)
[24]. While [20] addressed the issue of domain variability for heart sound
classification, the issue of additive noise was not addressed. A summary of
recent research works relevant to the proposed method are provided in Table I.
Note that different authors used different train-test splits using the
PhysioNet data, thus, the results are not comparable in most cases.

TABLE I: Summary of recent research works on heart sound classification using
2016 PhysioNet/CinC Database [9]

Author | Year |  Features |  Classifier | Sen. | Spe. | MAcc. | Acc. |  Remarks
---|---|---|---|---|---|---|---|---
Potes et al.[19] | 2016 |  Raw waveform |  Branched 1D-CNN | 0.88 | 0.82 | 0.85 | - |  Top scoring system in [8]. In-house test performance reported.
Rubin et al.[11] | 2016 |  MFCC |  2D-CNN | 0.765 | 0.931 | 0.848 | - |  Official test set results are reported (not publicly available).
Bozkurt et al.[13] | 2018 |  MFCC |  2D-CNN | 0.845 | 0.785 | - | 0.815 |  Noise and/or sensor variability effects not considered.
Ren et al.[15] | 2018 |  Scalogram |  Pre-trained 2D-CNN | 0.246 | 0.878 | 0.562 | - |  Noise and/or sensor variability effects not considered.
Noman et al.[14] | 2019 |  MFCC |  1D-CNN, 2D-CNN | 0.8994 | 0.8635 | 0.8815 | 0.8922 |  Custom data split used. Domain variability or noise not considered.
Humayun et al.[20] | 2020 |  Raw waveform |  Learnable filter & 1D-CNN | 0.8695∗ | 0.7602∗ | 0.8149∗ | - |  Addressed domain variability. Did not consider additive noise.
Deng et al.[25] | 2020 |  MFCC |  Recurrent 2D-CNN | 0.9866 | 0.9801 | - | 0.9834 |  10-fold cross-validation used which shows overoptimistic results.

∗This study uses a balanced test data across domains and pathology class using
the 2016 PhysioNet validation set. This allows for better evaluation of the
performance across different data subsets. However, the results are not
comparable with other studies using different data-splits or a 10-fold cross
validation.

Figure 1: Schematic model showing the sources of additive noise and
convolutional distortion during cardiac auscultation.

A major limitation of the previous approaches is that while only sensor
variability was addressed in [20], none of the works have considered the
simultaneous presence of channel/sensor and additive noise distortion for this
task. Sensor/channel variability affects the signal through time-convolution,
whereas additive noise affects the signal linearly. Thus it is very difficult
to disentangle the two components of distortion. Traditional signal processing
methods have addressed mainly the channel distortion issue through the log-
filterbank analysis, where the convolutional distortion becomes additive [26].
This also explains the effectiveness of MFCC features for the heart sound
classification task. Previous work on addressing simultaneous presence of
additive and convolutional noise has been mainly focused on speech processing
applications [27, 28, 29]. However, this issue is yet to be addressed for
heart sound analysis in the literature.

In the case of heart sounds, the major sources of signal degradation are: (i)
the variability due to stethoscopes/sensor [20] affecting the PCG as a
convolutional degradation (channel distortion), and (ii) the effect of
additive noise (e.g., from the environment or the patient). These effects are
depicted in Fig. 1. In particular, noise is a major problem in automatic
assessment of cardiac diseases using stethoscopes, especially in low-resource
hospitals. In [20], it was shown that the state-of-the-art algorithms for
heart sound classification are not capable of providing a consistent
performance when different stethoscopes are encountered in the test data.
While the overall performances were impressive, the algorithms easily overfit
to the data recorded using the most prevalent stethoscope. This is the reason
why 10-fold cross-validation [25], frequently performed on this dataset,
provides overoptimal performance as the test sets cannot provide sufficient
variability due to the severe domain imbalance present in the Physionet data
(Fig. 6). In [20], a mini-batch balancing method was proposed to address the
performance issue due to domain variability, and consistent improvement of
performance across different domains was found on a domain and class balanced
test set. However, this dataset also contains additive noise due to human
speech, environmental sounds, stethoscope motion, breathing, intestinal
activity, etc. [9], which was not considered in [20].

This paper aims to address the simultaneous presence of additive noise and
convolutional distortion for the heart sound classification problem. In the
case of cardiac auscultation, additive noise mainly includes respiratory
sounds and environmental noise. The convolutional distortion represents the
transduction effect of the stethoscope sensor. The main contributions of this
paper are:

  * •

We introduce a model of the acoustic environment during auscultation,
considering the additive and convolutional distortions present in the system.

  * •

Perform analysis of additive and convolutional distortion on heart sounds in
the linear and logarithmic filterbank domain and show that both distortions
can be converted into an additive distortion.

  * •

Analyze the effect of additive uncorrelated random noise in the first layer of
a conventional CNN model.

  * •

Proposed a simple feature fusion technique combining linear and logarithmic
filterbank features to simultaneously address additive noise and convolutional
distortion.

  * •

Experimentally validate that the proposed feature fusion scheme can
effectively improve heart sound classification performance compared to
existing methods using a deep residual network.

The remainder of this paper is organized as follows. In Section I-II we
elaborate on our motivation and implementation details of our proposed method.
Section III describes the datasets used, different experiments performed,
analysis of the results obtained by the proposed method and performance
comparisons. Finally, in Section IV and V, we discuss the limitations of our
method, future directions and summarize our findings.

Figure 2: Parametric model of the PCG signal acquisition process showing
additive noise and convolutional distortion.

##  I Background

###  I-A Additive and convolutional distortion

Inspired by [27], we consider a parametric model of the stethoscope as shown
in Fig. 2. This assumes that the original PCG signal and an uncorrelated noise
component are first added before being processed through a time-convolution
operation due to the stethoscope’s impulse response. For a given short-time
segment of length $N$, we assume that the clean PCG, noisy PCG, additive noise
and stethoscope impulse response are given by, $s[t]$, $x[t]$, $n[t]$ and
$h[t]$, respectively. According to the parametric model of Fig. 2,

$x[t]=\Big{(}s[t]+n[t]\Big{)}*h[t].$ (1)

Note that we assume the stethoscope impulse response is independent of the
short-time segment as it is a time-invariant property of the device. We also
assume that the impulse response $h[t]$ has a length less than $N$. Expressing
(1) in the Discrete Fourier Transform (DFT) domain, in each segment, using the
convolution property of DFT, we obtain

$X[k]=\Big{(}S[k]+N[k]\Big{)}H[k].$ (2)

In this step, we assume a $K$-point DFT with $k=0,1\cdots,K$ representing the
frequency indices, whereas $X[\cdot]$, $S[\cdot]$, $N[\cdot]$ and $H[\cdot]$
represent the DFT coefficients of the corresponding time-domain signals. Note
that the convolutional distortion $H[k]$ due to the stethoscope transfer
function has now become multiplicative. Next, we estimate the power spectrum
of this short-time PCG segment by squaring the absolute value of the DFT
coefficients and obtain

$\begin{split}\left|X[k]\right|^{2}&=\Big{(}|S[k]|^{2}+|N[k]|^{2}\Big{)}|H[k]|^{2}\\\
&+2\mbox{Re}\\{S[k]H[k]N[k]^{*}H[k]^{*}\\}.\end{split}$ (3)

###  I-B Linear filterbank energy analysis

Audio signals can be conveniently analyzed in different frequency bands by
using a filterbank. Let us assume a pre-defined filterbank of $M$ filters and
denote the $i$-th filter energy coefficient of the noisy PCG signal as $X[i]$.
We assume that the filterbank-energy term $X[i]$ is related to $X[k]$ by the
expression

$|X[i]|^{2}=\mathbb{E}^{i}_{k}\Big{(}|X[k]|^{2}\Big{)}.$ (4)

Here, $\mathbb{E}^{i}_{k}$ indicates that the expected value operation is
performed over the $k$ frequency indices that belong to the $i$-th filter.
Substituting the values from (3) we obtain,

$\displaystyle|X[i]|^{2}$ $\displaystyle=$
$\displaystyle\mathbb{E}^{i}_{k}\Big{(}|S[k]|^{2}|H[k]|^{2}+|N[k]|^{2}|H[k]|^{2}$
(5) $\displaystyle+2\mbox{Re}\\{S[k]H[k]N[k]^{*}H[k]^{*}\\}\Big{)}.$

Statistically, heart sound $s[t]$ and additive noise $n[t]$ are independent
and uncorrelated, and therefore the expected value of the last term of (5) can
be approximated to be zero. According to this assumption and using the
definition of filterbank energy, we simplify (5) to obtain a similar
expression derived in [27] given by

$|X[i]|^{2}=(|S[i]|^{2}+|N[i]|^{2})|H[i]|^{2}.$ (6)

Here, $S[i]$, $N[i]$ and $H[i]$ represent the filterbank-energy values
obtained from the corresponding DFT coefficients. Thus, according to (6), the
background noise component $N[i]$ is additive to the signal component $S[i]$
whereas the channel distortion component $H[i]$ is multiplicative in the
filterbank energy domain.

###  I-C Log-filterbank energy analysis

In filterbank analysis, logarithm operation is usually performed on the energy
coefficients to increase the dynamic range and transform multiplicative
operation into addition. Taking natural logarithm over (6) we obtain

$\log|X[i]|^{2}=\log|H[i]|^{2}+\log\Big{(}|S[i]|^{2}+|N[i]|^{2}\Big{)}.$ (7)

As expected, (7) reveals that in the log-filterbank domain, the channel or
transducer/sensor distortion becomes additive while the heart sound signal and
background noise becomes non-linear functions of the output log-energy
coefficient. This was one of the motivations of Cepstral analysis to separate
the channel effect from the signal [26, 30]. We may write (7) to express the
log-energy vectors for each frame using matrix notation as

$\mathbf{E}_{X}=\mathbf{E}_{H}+\mathbf{E}_{S+N},$ (8)

where

$\displaystyle\mathbf{E}_{X}$ $\displaystyle=$
$\displaystyle\Big{[}\log|X[1]|^{2},\log|X[2]|^{2}\cdots\log|X[M]|^{2}\Big{]}^{T},$
$\displaystyle\mathbf{E}_{X}$ $\displaystyle=$
$\displaystyle\Big{[}\log|H[1]|^{2},\log|H[2]|^{2}\cdots\log|H[M]|^{2}\Big{]}^{T},\mbox{
and}$ $\displaystyle\mathbf{E}_{S+N}$ $\displaystyle=$
$\displaystyle\left[\begin{array}[]{c}\log(|S[1]|^{2}+|N[1]|^{2})\\\
\log(|S[2]|^{2}+|N[2]|^{2})\\\ \vdots\\\ \log(|S[M]|^{2}+|N[M]|^{2})\\\
\end{array}\right].$ (13)

In (8), each vector consists of $M$ elements obtained from the individual
front-end filters. To summarize our analysis on filterbank and log-filterbank
energy analysis, when both additive and convolutional distortion is present,
it is not possible to decompose them into additive terms in the feature
domain. However, noise component as in (6) or the convolutional distortion
component as in (7) can become additive separately. A static additive
distortion component from features can be easily reduced by mean normalized
which was the original motivation for the traditional Cepstral mean
normalization (CMN) [31] used for robust speech recognition.

###  I-D cepstral feature domain analysis

MFCC features are frequently utilized in speech and audio processing. After
the extraction of log-filterbank features, an additional step of Discrete
Cosine Transform (DCT) is applied to obtain the well-known MFCC coefficients
[26]. The DCT step is performed to reduce the correlation among the different
filterbank energy coefficients and compress the overall energy of the features
to the leading few components. Therefore, after this step, the higher-order
DCT coefficients are usually eliminated, and thus, the feature dimensionality
is reduced. Since DCT is a linear operation, it follows from (8) that the
convolutional distortion component will still be an additive component after
this operation. Thus we have

$\mbox{DCT}\left(\mathbf{E}_{X}\right)=\mbox{DCT}\left(\mathbf{E}_{H}\right)+\mbox{DCT}\left(\mathbf{E}_{S+N}\right)$
(14)

Similarly, we can easily show that by removing the higher order DCT
coefficients, (14) still holds for the remaining coefficients. However, the
PCG signal and additive noise is still entangled within the component
$\mathbf{E}_{S+N}$ where their relationship is non-linear.

###  I-E Additive distortion in a CNN model

Although CNNs are primarily used for image classification, in many 1D signal
processing applications, 2D spectrogram-images are used as input features to
CNN models for classification [32]. In addition, previous methods have
utilized additive noise in training for data augmentation that generally
improves the robustness of the models [33, 34]. In this sub-section, we
perform a mathematical analysis of the CNN input layer when an additive noise
component is present in the input feature data.

In the $0^{th}$ (first) layer of a CNN model, for a 2D input feature matrix
$\mathbf{F}_{cn}$ and the $j$-th 2D kernel $\mathbf{K}_{j}$, the output $j$-th
feature map before the nonlinear activation layer is given by

$\mathbf{G}_{j}=\mathbf{F}_{cn}\otimes\mathbf{K}_{j}.$ (15)

Here, $\otimes$ represents the correlation operation performed in a CNN layer.
Eq. (15) can be expressed for each individual matrix elements of row $m$ and
column $n$ as,

$\displaystyle G_{j}[m,n]$ $\displaystyle=$ $\displaystyle F_{cn}\otimes
K[m,n]$ (16) $\displaystyle=$
$\displaystyle\sum_{\alpha=-l}^{l}\sum_{\beta=-l}^{l}F_{cn}[m+\alpha,n+\beta]K_{j}[\alpha,\beta].$

Here, we assume a kernel size of $(2l+1)\times(2l+1)$, and $\alpha$ and
$\beta$ are dummy variables. When spectrogram images from heart sounds are
considered, $m$ represent the short-time frame index whereas $n$ represent the
frequency-band index.

Let us now assume that the input feature matrix $\mathbf{F}_{cn}$ can be
expressed as

$\mathbf{F}_{cn}=\mathbf{F}_{c}+\mathbf{F}_{n}$ (17)

where $\mathbf{F}_{c}$ is dependent on the class $c\in\mathcal{C}$ where
$\mathcal{C}$ defines the set of disease classes, and $\mathbf{F}_{n}$ is an
additive noise component independent and uncorrelated to $\mathbf{F}_{c}$ (and
thus independent of $c$). The source of $\mathbf{F}_{n}$ may environmental
noise or sensor degradation. Considering the presence of this additive
distortion, we obtain from (15)

$\displaystyle\mathbf{G}_{j}$ $\displaystyle=$
$\displaystyle(\mathbf{F}_{c}+\mathbf{F}_{n})\otimes\mathbf{K}_{j}$ (18)
$\displaystyle=$
$\displaystyle\mathbf{F}_{c}\otimes\mathbf{K}_{j}+\mathbf{F}_{n}\otimes\mathbf{K}_{j}.$

Assuming that the model has converged after being trained on a sufficiently
large amount of data, we may compute the expected value of the feature map as

$\displaystyle\mathbb{E}\\{\mathbf{G}_{j}\\}$
$\displaystyle=\mathbb{E}\\{\mathbf{F}_{c}\otimes\mathbf{K}_{j}\\}+\mathbb{E}\\{\mathbf{F}_{n}\otimes\mathbf{K}_{j}\\}.$
(19)

At this stage, we will make a few simplifying assumptions. Since CNN models
are trained using a loss-function that minimizes the classification error, it
can be expected when trained on sufficient training data, the model parameters
will be dependent on the disease classes $c$. In contrast, the additive
component $\mathbf{F}_{n}$ by definition is independent and uncorrelated of
$\mathbf{F}_{c}$ and thus the disease class $c$. Therefore, we may assume that
after the training is converged,
$\mathbb{E}\\{\mathbf{F}_{n}\otimes\mathbf{K}_{j}\\}\approx 0$ and (18) can be
written as

$\displaystyle\mathbb{E}\\{\mathbf{G}_{j}\\}\approx\mathbb{E}\\{\mathbf{F}_{c}\otimes\mathbf{K}_{j}\\}.$
(20)

Thus, we may conclude that in case of an additive uncorrelated noise present
in the data, CNN model parameters can be assumed to be independent of the
noise when sufficient training data is present. In contrast, for
multiplicative noise in the feature matrix, it is obvious from (16) that a
decomposition similar to (19) will not be possible and the learning of the
network will be directly affected by the distortion.

###  I-F Fusion of linear and logarithmic features

It is clear that linear filterbank energy features are linearly affected by
the additive noise and non-linearly affected by channel/sensor noise, as shown
in (6). In contrast, logarithmic filterbank energy features are linearly
affected by channel/sensor noise and non-linearly affected by additive noise,
as demonstrated in (7). Thus, in this respect, the linear and logarithmic
filterbank energy features are complimentary. However, if we concatenate the
two types of features, both additive noise and convolutional distortion can be
separated as an additive component in the fused feature space. As shown in
(20), a CNN model is less affected by additive distortion during
classification, assuming that the noise is independent and uncorrelated with
the signal component. However, in the proposed fused feature space, both noise
and channel distortion components become additive. Therefore, we hypothesize
that the fused feature set will provide improved performance in the presence
of both additive and convolutional/channel noise. The following sections of
this paper will focus on designing the relevant features and validating this
hypothesis through experimental evaluation.

##  II Proposed Method

In this section, we discuss the development of the proposed feature extraction
method and the CNN architecture for effective classification of heart sounds,
considering both additive and convolutional distortions.

###  II-A Pre-processing and segmentation

The heart-sound segments are first re-sampled to $1000$Hz, followed by band-
pass filtering between $25$-$400$Hz, and cardiac cycle segmentation according
to [35]. In the next step, we ensure that each heart sound training segment
consists of a single cardiac cycle of a fixed duration of $2.5$s. Zero-padding
is applied if the cardiac cycle is shorter than $2.5$s.

###  II-B Feature extraction framework

In order to validate our hypothesis, we needed to extract four different
varieties of filter-bank based acoustic features from the PCG signal segments.
These are based on equations (6), (7) and (14). The features can be
effectively extracted using a unified framework outlined in Fig. 3. The
extraction procedure is detailed below.

First, the PCG signal segments are divided into short-time frames of length
$0.5$s with a hop size $0.01$s between successive frames. Filterbank analysis
is performed on the $0.5$s segments using $26$ mel-scaled filters. The
features extracted from these segments are summarized in Table II.

TABLE II: Description of acoustic features

Name |  Feature description | Dimension
---|---|---
Fbank |  Filterbank energy features as shown in eq. (6) | 26
Log-Fbank |  Log-filterbank energy features as shown in eq. (7) | 26
MFCC-26 |  MFCC retaining all coefficients after DCT compression | 26
MFCC-13 |  MFCC retaining 13 coefficients after DCT compression | 13

To validate our hypothesis, it is essential to perform classification
experiments on all these features for the following reasons. According to (6),
the _Fbank_ features should be able perform better in case of additive noise.
In the case of _Log-Fbank_ , we can expect better results in case of
convolutional distortion as per our analysis in (7). Since CNN models are able
to model the correlation among the input features, it is unclear if the DCT
step will improve the performance in our case. For this reason, we retain both
_MFCC-13_ and _MFCC-26_ variants of the traditional MFCC features to observe
the effect of DCT in the classification performance.

###  II-C Preparing 2D feature matrices

From each $2.5$s segment, the extracted feature (column) vectors are stacked
horizontally to form a 2D feature matrix (input) for classification using our
CNN model. Each of these input feature matrices has a dimension of $d\times
246$, where $d$ represents the acoustic feature dimension. The four features
as described in Table II are visualized in Fig. 4. Before feeding into the CNN
model, features from each cardiac cycle are normalized by subtracting the mean
of the full cycle and dividing by their standard deviation (STD).

Figure 3: A flow diagram of the acoustic features extraction framework.
Different features are extracted from different stages as depicted. Figure 4:
2D visualization of the acoustic features as input to the proposed CNN model.
(a) Filterbank energy (Fbank), (b) Log-Filterbank energy (log-Fbank), (c)
Full-dimension MFCC (MFCC-26), (d) Dimension reduced MFCC (MFCC-13). Figure 5:
Residual model architecture used for heart sound abnormality detection.

###  II-D Model architecture

A residual neural network (ResNet) architecture based on [36] is used as the
classification model. The model is modified to fit the proposed input
features. The model has four resnet layers, each containing two residual
blocks, the first block is with down-sampling, and the latter is with direct
skip connection. Fig. 5 shows the model architecture used. Each residual block
generally consists of two convolution blocks, which also perform the down-
sampling operation. Each convolution block has one convolutional layer of
kernel size $3$, followed by a 2D batch normalization layer and Rectified
Linear Unit (ReLU) activation functions. Weights of each convolutional layer
have are initialized using the Xavier method [37]. The number of filters of
these four resnet layers is $16$, $32$, $64$, $128$. The input feature matrix
goes through a convolutional block with a max-pooling of $2$ before the resnet
layer. Extracted features from the fourth resnet layer are then flattened, and
two neurons are added with softmax activation for binary classification
(normal and abnormal PCG). The code is available online at
https://github.com/mHealthBuet/CepsNET.

##  III Experiments and results

###  III-A Dataset

We use the 2016 PhysioNet/CinC Challenge Database [9] for our experiments. It
is an archive of PCG recordings from both clinical and non-clinical
environments. It consists of a total of 3,157 recordings from 764 patients and
contains a total of 84,425 cardiac cycles ranging from heart rates 35 to 159
beats-per-minute (bpm). The PCG recordings have been collected from seven
different research groups denoted as {a-g,i}. A brief summary of this dataset
is shown in Table III. Among seven categories, six {a-f} sets are distributed
in training data, which is publicly available. The recordings generally have a
duration between 5–120 seconds. Metadata of recording quality, annotations for
the onset of S1, S2, systole, diastole are also provided.

As shown in Table III, this dataset is unbalanced both in terms of pathology-
class (normal vs. abnormal) and the data subsets/domains ({a-f}). We use 2,856
(90.47%) for training and the remaining 301 (9.53%) for test. This test set is
based on the original Physionet challenge validation set which is domain and
class balanced [20]. The train-test split is also patient independent by
design. The class imbalance, variability of stethoscope sensors, and noisy
environment are all challenging issues to be addressed in this dataset, making
it suitable for experimental validation of the proposed approach.

TABLE III: Data distribution of PhysioNet/CinC Challenge Database.

Subset |  Total Subject |  Normal recordings |  Abnormal recordings | Used device
---|---|---|---|---
a | 121 | 117 | 292 | Welch Allyn Meditron
b | 106 | 385 | 104 | 3M Littmann E4000
c | 31 | 7 | 24 | AUDIOSCOPE
d | 38 | 27 | 28 | Infral Corp. Prototype
e (Norm.) | 174 | 1867 | 0 | MLT201/Piezo
e (Abn.) | 335111We only used 151 usable abnormal recordings from ’e’ subset and the rest are removed due to data errors [20]. | 0 | 151 | 3M Littmann
f | 112 | 80 | 34 | JABES

###  III-B Training regime

In the training-set, the e-subset has the highest number of recordings (about
68%) as can be seen in Fig. 6. Thus we use the domain balance training (DBT)
method that prepares mini-batches of data that are balanced for both class and
domain [20]. This method was found to be effective in case of domain
variability and data imbalance. We also apply shifting on both right and left
directions to avoid the effect of segmentation errors.

To examine the effect of the input feature variation on classification
performance, we perform our experiments in two steps. First, we use 2D
matrices extracted from the individual features described in Table II as input
to our model. The first three features (Fbank, Log-Fbank, MFCC-26) in Fig. 4
are of shape $(246,26)$ whereas the fourth feature (MFCC-13) is of the shape
$(246,13)$. The proposed model is designed to be able to handle different
input dimensions. The overall results of the experiments are shown in Table
IV. In the second step, we used multiple feature combination of the four
selected features (Fig. 4) for performance analysis. In this case, individual
features are vertically concatenated, which increases the height of the input
(minimum 26 to maximum 65) to our model.

Figure 6: Distribution of sensor-dependent subsets of the PhysioNet heart
sound data.

###  III-C Optimization and hyperparameter tuning

We use the cross-entropy loss from the final softmax layer output and perform
optimization by stochastic gradient descent (SGD) using the Nesterov momentum
method [38]. We also use a cyclic learning rate (CLR) scheduler to change the
learning rate in a triangular shape with the same height. Hyper-parameters of
the scheduler, which includes minimum and maximum learning rate and step size,
are calculated according to [39]. The model generally converges to the optimal
point within 50-60 epochs while trained using these parameters. Majority
voting is used to obtain the final abnormality prediction of the heart sound
recordings obtained from individual 2.5s segments.

###  III-D Performance metrics

The final decision provided by the network is used to compute the following
performance matrices: AUC, F1-score, and modified accuracy (Macc)[20]. The
Macc value is obtained by averaging sensitivity and specificity [9], and thus
can be considered a reliable metric for the overall system performance.

In addition, we also calculate the mean and STD of the accuracy metric for
each system within individual data subsets {a-f} [9] distributed as shown in
Fig. 5. These data subsets are collected in different environmental locations
(varying noisy conditions) and using different stethoscopes/sensors (varying
convolutional channel effect) [9] and are summarized in Table III. This
subset-wise performance evaluation is essential as it shows if the overall
performance is being skewed towards a specific subset due to data imbalance as
seen in Fig. 5. The mean and STD accuracy over the subsets measure the
robustness and consistency of the performance across different domains.

TABLE IV: Experimental results of the baseline and proposed systems for the
heart sound abnormality detection task.

Method | AUC | F1 Score | Macc | Accuracy in data subsets / domains | Domain avg. acc.
---|---|---|---|---|---
a | b | c | d | e
1D-CNN based End-to-End systems
Potes-CNN [19] | 79.50 | 74.99 | 73.50 | 60.00 | 63.26 | 71.43 | 40 | 100 | 66.94$\pm$21.80
Potes-CNN DBT [20] | 84.20 | 80.67 | 79.79 | 71.25 | 70.41 | 85.71 | 66.66 | 97.5 | 78.31$\pm$12.95
Humayun _tConv_ -CNN DBT [20] | 83.04 | 81.91 | 81.49 | 76.25 | 71.43 | 71.42 | 80 | 97.75 | 79.37$\pm$9.73
2D-CNN (ResNet) based systems using spectro-temporal features
Fbank | 89.33 | 82.18 | 82.72 | 71.25 | 76.53 | 71.43 | 90 | 100 | 81.84$\pm$11.36
Log-Fbank | 90.37 | 84.40 | 84.55 | 76.25 | 77.55 | 85.71 | 80 | 100 | 83.90$\pm$8.68
MFCC-26 | 87.82 | 79.54 | 81.15 | 77.50 | 69.39 | 85.71 | 80 | 100 | 82.52$\pm$10.20
MFCC-13 | 89.07 | 84.07 | 83.63 | 73.75 | 76.53 | 85.71 | 80 | 100 | 83.20$\pm$9.30
MFCC-13+$\Delta$ | 89.53 | 80.30 | 81.56 | 71.25 | 72.45 | 85.71 | 90 | 100 | 83.88$\pm$10.87
MFCC-13+$\Delta$+$\Delta\Delta$ | 87.51 | 78.29 | 80.09 | 72.50 | 68.37 | 85.71 | 80 | 100 | 81.32$\pm$11.10
2D-CNN (ResNet) based systems using feature-level fusion (Proposed)
Fbank & Log-Fbank | 90.67 | 83.22 | 83.18 | 72.50 | 75.51 | 85.71 | 90 | 100 | 84.74$\pm$9.96
Fbank & MFCC-13 | 91.36 | 84.09 | 85.08 | 78.75 | 76.53 | 85.71 | 90 | 100 |  86.20$\pm$8.42
Log-Fbank & MFCC-13 | 89.93 | 82.53 | 83.37 | 73.75 | 76.53 | 85.71 | 80 | 100 | 83.20$\pm$9.30
Fbank, Log-Fbank & MFCC-13 | 90.61 | 82.84 | 83.71 | 77.50 | 75.51 | 85.71 | 80 | 98.88 | 83.52$\pm$8.41

###  III-E Baselines methods and implementation

In this work, we use the best performing system in the Physionet 2016 CinC
Challenge developed by Potes et al. [19]. This branched CNN model (Potes-CNN)
is implemented as described in [19] and with the addition of the proposed DBT
training scheme to address the domain variability present in the dataset. The
network uses a set of finite impulse response (FIR) filters as a filterbank
front-end and provides inferences for each segmented cardiac cycle [20]. The
branched CNN model [19] with including the DBT method to handle domain
variability is denoted as the Potes-CNN-DBT method. The results of these
systems are summarized in Table IV.

###  III-F Performance of individual features

First, we look at the performance of the individual features in the second
section of Table IV. The best performing individual feature is the Log-Fbank
with AUC, F1-score, and Macc values of $90.37\%$, $84.40\%$, and $84.55\%$,
respectively.

Figure 7: Comparison of performance between Fbank and Log-Fbank features
depicting the effect of logarithm operation on the features.

We hypothesized the logarithm operation on the Fbank features would improve
the system performance since it can express the sensor variation as an
additive component in the feature space. Observing the results of the Fbank
and Log-Fbank features separately in Fig. 7, we indirectly validate this
hypothesis as the logarithm operation provides an overall improvement in the
classification performance while also improving the robustness of the system
across the data subsets (increase in average domain-wise accuracy and reducing
the STD). It should be emphasized that both the features Fbank and Log-Fbank
carry the same information content since logarithm is a one-to-one function.
Therefore, we assume the improvement is due to the model’s ability to fit the
data better.

Next, we analyze the performance of the system after the DCT operation leading
to MFCC-26, and later MFCC-13 due to dimensionality reduction. The DCT
operation is generally used in feature dimensionality reduction as it performs
compression of the data into a few coefficients and also de-correlates them.
In theory, deep learning architectures should be able to model complex
relation among the input features and thus decorrelating the features using a
data-independent linear transformation, i.e. DCT, should not have an impact.
However, in practice we observe that most of the performance metrics drop due
to the DCT operation without dimensionality reduction. The performance of Log-
Fbank and MFCC-26 are graphically compared in Fig. 8 where we can better
observe the performance difference.

The performance drop from Log-Fbank to MFCC-26 may be explained as follows.
Since the DCT operation performs feature compression, the high frequency DCT
coefficients should be of of negligible value and carry very little
information about the PCG signal [30]. Although the 26 components of Log-Fbank
and MFCC-26 theoretically contain the exact same information, since the
features are normalized before being fed in to the ResNet model, it is
possible that these insignificant frequency components are being amplified out
of proportion and confusing the model. This is consistent with our observation
that by removing the 13 higher order coefficients from MFCC-26, we improve the
performance as evident from the results of the MFCC-13 feature vector. This
feature set provides the best overall performance among the individual
features with a sensitivity, specificity, F1-score and Macc values of
$89.86\%$, $77.40\%$, $84.07\%$, and $83.63\%$, respectively. The performance
of MFCC-13 closely follows as expected since this feature configuration widely
validated in speech and audio processing applications [30, 40].

Figure 8: Comparison of performance between Log-Fbank and MFCC-26 features
depicting the effect of DCT operation without dimensionality reduction.

###  III-G Effect of velocity and acceleration

Appending the velocity ($\Delta$) and acceleration features ($\Delta\Delta$)
is very common along with MFCC-13 features, and thus we also examine the
effect of these simple feature modifications. From the results in Table IV and
Fig. 9, we observe that the effect of adding these features do not improve the
performance of the static MFCC-13 coefficients. We presume that since the CNN
model inputs the successive MFCC-13 vectors as a 2D image, it can model the
velocity and acceleration features quite well, and thus the addition of these
features is redundant.

Figure 9: Comparison of performance among MFCC-13, MFCC-13+$\Delta$ and
$\Delta$+$\Delta\Delta$ features depicting the effect of appending velocity
and acceleration features on the heart sound classification task.

###  III-H Feature level fusion

The previous sub-sections analysis reveals that Log-Fbank and MFCC-13 are the
best two features for heart sound abnormality detection for classification
using the ResNet model described. In Sec. I-F we argued that Fbank and Log-
Fbank features have complimentary properties since they can express additive
and convolutional distortions, respectively, as an additive component in the
feature space. Therefore, our hypothesis is that fusion of the Fbank and Log-
Fbank features would significantly improve heart sound classification
performance, particularly on this task since it involves both
stethoscope/sensor and background noise variability in the dataset [9].
However, in practice, the MFCC-13 and MFCC-26 features have the same property
of expressing convolution as a linear operation, as shown in (14), and thus
can be equally effective in the presence of sensor variability.

In this section of our analysis, we discuss our feature-level fusion
experiments, as shown in the third section of Table IV. These experiments use
several combinations of Fbank, Log-Fbank, and MFCC-13 features, being the most
promising individual feature sets. The results show that, indeed, the feature-
level fusion of Fbank and MFCC-13 provides the overall best results and the
domain-wise performance. This configuration yields an Macc score of $85.08\%$
which shows an absolute gain of $5.29\%$ and $11.58\%$ over the Potes-CNN [19]
and Potes-CNN DBT [20] baseline systems, respectively. In terms of domain-wise
performance, it performs better in almost all of the data subsets {a-e} with a
mean accuracy of $86.2\%(\pm 8.42\%)$. Thus, the average accuracy over
different domains has increased, but the STD of the accuracy is also reduced
compared to individual spectro-temporal features. This validates our
hypothesis that this particular feature combination is complementary and
effectively addresses the issues of convolutional (sensor variability) and
additive distortion (noise) components.

We want to point out several other observations from the results in Table IV.
Firstly, the feature level fusion of all three features (Fbank, Log-Fbank,
MFCC-13) does not show any additional benefit, as evident from Fig. IV.
Secondly, a significant improvement in reducing domain-variability is achieved
by introducing the DBT training scheme, which was already noted in [20]. This
is evident from the reduction of STD values in the domain-wise performance
evaluation. The Potes-CNN [19] with and without DBT yields domain-wise
accuracies of $66.94\%(\pm 21.80)$ and $78.31\%(\pm 12.95\%)$, respectively.
Therefore, the results have already been improved by the DBT scheme. However,
the proposed feature fusion scheme provides an additional improvement over the
Potes-CNN DBT system, which further validates the effectiveness of the
proposed method. We have also provided the t-distributed Stochastic Neighbor
Embedding (t-SNE) of the extracted features of our model trained with this
fused feature set in Fig. 11, where we observe that the different domains are
almost indistinguishable in this higher-dimensional space. This depiction is
consistent with the observations presented in [20].

TABLE V: _McNemar’s Chi-squared test_ for statistical significance analysis
compared to the baseline Potes-CNN-DBT [19, 20] system.

Input Feature | $\chi^{2}$ | p-value | Significant
---|---|---|---
($p<0.05$)
Fbank | 24.00 | 0.2892 | No
Log-Fbank | 24.00 | 0.0980 | No
MFCC-26 | 0.28 | 0.5962 | No
MFCC-13 | 21.00 | 0.1690 | No
MFCC-13+$\Delta$ | 0.4464 | 0.5040 | No
MFCC-13+$\Delta$+$\Delta\Delta$ | 0.0167 | 0.8973 | No
Fbank & Log-Fbank | 29.00 | 0.2750 | No
Fbank & MFCC-13 | 18.00 | 0.0365 | Yes
Log-Fbank & MFCC-13 | 19.00 | 0.1524 | No
Fbank, Log-Fbank & MFCC-13 | 18.00 | 0.1114 | No

###  III-I Statistical significance analysis

In this section, we perform statistical significance tests to evaluate if the
improvements obtained by the proposed method is significantly better than the
baseline or not. We use McNemar’s chi-squared test [41] to perform a pair-wise
comparison of the system performances and validate whether the system
performance is significantly different. The results are summarized in Table V.
According to this analysis, it is indeed confirmed that the performance
improvement achieved by the proposed method with fusion of Fbank and MFCC-13
is significant ($p<0.05$) compared to the baseline system Potes-CNN DBT [19,
20]. This feature-fusion combination provides the lowest p-value among all the
other system comparisons and further justifies the effectiveness of the method
in heart sound datasets with sensor and noise variability. The proposed system
also provides an absolute $3.59\%$ improvement in Macc compared to Humayun
_tConv_ -CNN DBT [20]. However, this improvement is not significant according
to the McNemar’s chi-squared test ($p>0.05$).

Figure 10: Improvement obtained by fusing linear and logarithmic features
(Fbank and MFCC-13) in heart sound abnormality detection in the presence of
noise and sensor variation. Figure 11: TSNE visualization of the last layer of
the proposed model showing the distribution of different data subsets. No
meaningful clusters have formed with the features of different source domains.

##  IV Discussion

In this work, we have indirectly validated the hypothesis that feature-level
fusion of filter-bank energy features and log-filter-bank energy features
provide robust performance in the heart sound abnormality detection task in
the presence of noise and sensor variability. However, a major limitation of
the proposed approach is that the validation is empirical by nature. Although
it is known that the Physionet data [9] contains environmental noise, it is
not possible to precisely identify the sensor dependent (convolutional
distortion) and the background noise (additive distortion) components from the
PCG signals. However, since the results achieved are significantly improved
compared to existing methods, especially methods that already deal with
reducing domain-variability [20], the proposed method is promising and
justifies further investigation. A more thorough analysis could have been
performed by artificially generating stethoscope effects using its impulse
response [42] and adding environmental noise to clean heart sound recordings.
In such a scenario, it would have been possible to observe the effect of the
features in the presence or absense of additive and convolutional distortions
more systematically. However, such analysis is outside the scope of this
current work where we focus on a novel feature fusion scheme to handle channel
and noise variability. The proposed method is simple and can also be applied
to other biomedical signal analysis tasks that involve noise and channel
distortion.

##  V Conclusions

This paper has first mathematically analyzed the simultaneous effect of
additive and convolutional distortions for heart sound abnormality detection.
In the context of PCG signals, we have hypothesized that the additive
distortion components represent environmental and other body sounds, whereas
convolutional distortion includes sensor variability and transmission channel
effects. We have shown that effectively designed features using a combination
of filter-bank energy and its natural logarithm can significantly reduce
domain variability due to noise and sensor degradation in a heart sound
classification task. A residual network architecture has been proposed and
evaluated to classify the feature-stream cascaded to form 2D input feature
matrices. Experimental results have demonstrated that the proposed method
achieves a significant ($p<0.05$) absolute improvement of $5.29\%$ in Macc
performance metric compared to a competitive baseline system that utilizes a
domain-balanced training (DBT) scheme.

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