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Separation and Analysis of Fetal-ECG Signals From
Compressed Sensed Abdominal ECG Recordings
Giulia Da Poian∗ , Riccardo Bernardini, and Roberto Rinaldo
Abstract—Objective: Analysis of fetal electrocardiogram
(f-ECG) waveforms as well as fetal heart-rate (fHR) evaluation provide important information about the condition of the fetus during
pregnancy. A continuous monitoring of f-ECG, for example using the technologies already applied for adults ECG tele-monitoring (e.g., Wireless Body Sensor Networks (WBSNs)), may increase
early detection of fetal arrhythmias. In this study, we propose a
novel framework, based on compressive sensing (CS) theory, for
the compression and joint detection/classification of mother and
fetal heart beats. Methods: Our scheme is based on the sparse
representation of the components derived from independent component analysis (ICA), which we propose to apply directly in the
compressed domain. Detection and classification is based on the
activated atoms in a specifically designed reconstruction dictionary. Results: Validation of the proposed compression and detection framework has been done on two publicly available datasets,
showing promising results (sensitivity S = 92.5%, P += 92%, F1
= 92.2% for the Silesia dataset and S = 78%, P += 77%, F1 =
77.5% for the Challenge dataset A, with average reconstruction
quality PRD = 8.5% and PRD = 7.5%, respectively). Conclusion: The experiments confirm that the proposed framework may
be used for compression of abdominal f-ECG and to obtain realtime information of the fHR, providing a suitable solution for real
time, very low-power f-ECG monitoring. Significance: To the authors’ knowledge, this is the first time that a framework for the
low-power CS compression of fetal abdominal ECG is proposed
combined with a beat detector for an fHR estimation.
Index Terms—Compressive sensing, fetal ECG, independent
component analysis.
I. INTRODUCTION
SSESSMENT of fetal health conditions through electrocardiography is a useful clinical diagnostic method, which
allows to discover possible distress or congenital heart defects
in early stages of pregnancy and during delivery [1]. Fetal heartrate (HR) monitoring and detection of the fetal electrocardiogram (f-ECG) may be able to provide early detection of fetal
arrhythmias, making it possible to treat them with drug administration or to preschedule the delivery.
In abdominal f-ECG recording, the electrical signal generated
by the fetal heart is measured by noninvasive electrodes placed
on the mother’s abdomen surface. This kind of measurement is
A
Manuscript received May 29, 2015; revised July 29, 2015, September 14,
2015, and October 13, 2015; accepted October 13, 2015. Date of publication
October 26, 2015; date of current version May 18, 2016. Asterisk indicates
corresponding author.
* G. Da Poian is with the Department of Electrical, Management and Mechanical Engineering, University of Udine, Udine 33100, Italy (e-mail: dapoian.
giulia@spes.uniud.it).
R. Bernardini and R. Rinaldo are with the Department of Electrical, Management and Mechanical Engineering, University of Udine.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBME.2015.2493726
Fig. 1. Two abdominal recordings from the Physionet Challenge dataset A. In
(a) trace 1 of signal a32 of the dataset, the f-ECG cannot be eye spotted, while
in (b), trace 1 of signal a22, the f-ECG is clearly visible (box). It is also clear,
from record a22, that different sources of noise may affect the signals.
clearly suitable for long-term observation as well as for at-home
monitoring during all pregnancy. However, the f-ECG signal
acquired from the mother’s abdomen is typically characterized
by a very low SNR. In fact, signals recorded by this method
are always a mixture of noises generated, for instance, by fetal
brain activity, myographic signals (both from the mother and
the fetus), movement artifacts, and maternal ECG. Moreover,
the fetal component is usually smaller compared to the maternal
one, since the fetal heart is smaller than the adult, and is typically
attenuated by tissues in the path to the measuring electrodes.
Advanced techniques are required for abdominal fetal ECG
signals analysis due to the typical complexity and variability
of recorded signals. Fig. 1 shows two abdominal recordings
from the Physionet Challenge database [2], [3]. In Fig. 1(a), the
fetal heart beat is barely visible, while it can be seen clearly in
Fig. 1(b). The duration, amplitude, and morphology of the fetal
QRS complex is similar to the maternal one, but with a smaller
amplitude and QRS width. Moreover, fetal and maternal beats
may overlap in time, making even harder to detect the fetal
QRS complexes. Signal processing techniques for noninvasive
f-ECG are still an active field of research, as reported in [4].
The possibility to obtain clean f-ECG signals by noninvasive
abdominal measurements has been demonstrated in [5]. It has
been shown that the use of signal processing techniques [4], [6]
may improve the quality of f-ECG waveforms from abdominal
recordings and make it comparable to that achievable through
the use of a scalp electrode.
Combining advanced signal processing techniques and noninvasive acquisition of f-ECG through abdominal electrodes may
allow at-home continuous monitoring using technologies such
as wireless body-sensor networks (WBSNs), which have been
recently proposed for adult monitoring of physiological signals during everyday activities [7], [8]. A WBSN is composed
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Fig. 2.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 63, NO. 6, JUNE 2016
Proposed framework.
of a varying number of sensors which measure and compress
physiological signals (e.g., the ECG signal). Signals are then
typically sent to a nearby smartphone to allow its transmission
to a remote terminal via the Internet. WBSN sensors have typically many constraints, one of which is low energy consumption. Moreover, since ultralow-power radio devices, with low
communication capacity, are commonly used for transmission,
another constraint is that the transmitted physiological signal
should be largely compressed.
Compressive sensing (CS) [9]–[11] is a recently introduced
sensing/sampling technique that allows to recover sparse signals from fewer samples than the Shannon sampling theorem
would typically require. It is based on the assumption that a
small collection of linear projections contains enough information to allow the reconstruction of sparse signals. Combining
the acquisition and compression stages, CS is a very promising
technique to develop ultralow-power wireless bio-signal monitoring systems.
In this paper, we propose a novel framework for the CS of
abdominal multichannel f-ECG recordings jointly with the detection and classification of fetal and maternal beats. The proposed method is summarized in the block diagram of Fig. 2.
Extending our previous study [12], to overcame the limitations
of classical CS framework for f-ECG signals, we introduce a
new universal dictionary that permits to successfully increase
compression while maintaining a reconstruction quality which
does not affect the detection performance. The dictionary comprises two classes of Gaussian-like functions [13], modeling
the fetal and mother ECG. fHR estimation requires to separate
the fetal and maternal beats from the acquired ECG signals.
We model the recorded ECG signals as a mixture of independent components (ICs) given by the mother’s and fetal heart
beat signals, as well as other noise sources. We show that it
is possible to perform independent component analysis (ICA)
[14] directly in the compressed sensed domain with no performance loss than using the original signals. Our scheme operates
on small blocks of compressed coefficients, and estimates the
compressed ICs, thus, reducing computational complexity and
permitting low delay detection and reconstruction. Finally, from
the compressed ICs, we separate the maternal and fetal beats by
checking the activated atoms during reconstruction within the
CS framework. Although the focus of this paper is the design
of a low-power and low-complexity acquisition/detection realtime system, the performance loss with respect to nonreal-time
procedures, which apply off-line postprocessing techniques and
several detection refinement stages, is acceptable, besides the
fact that the proposed approach does not require training, it is
completely automatic and can be used for real-time analysis
with a small delay.
II. RELATED WORK
Recently, several signal processing techniques have been proposed for the extraction of fetal ECG from abdominal recordings
[4], [6]. Various methods have been proposed for maternal ECG
subtraction, including adaptive filtering techniques [15], which
use one or more maternal ECG reference signals, or template
subtraction [16], [17]. Linear decomposition techniques, such
as matching pursuit [18], have been investigated for fetal ECG
separation and enhancement. The wavelet transform has been
used in [19] to locate the fetal QRS complex from abdominal
f-ECG mixture signals.
Blind and semiblind signal separation techniques for fetal
ECG extraction have also been proposed in the literature. The
idea behind the proposed procedures is that signals, in a multichannel abdominal recording, are mixtures of uncorrelated independent sources corresponding to the mother’s heart beat, the
fetal one, and noise. Two of the most commonly applied blind
source separation techniques are the ICA [20] and the principal component analysis (PCA). PCA allows to find statistically
uncorrelated components, which do not necessarily represent
independent sources. Due to the significant noise usually affecting the signals, ICA and PCA have some limitations when
used alone, and other pre/postsignal processing techniques have
to be adopted. For instance, ICA has been used together with
the wavelet decomposition in [21]. In [22], the authors report
the results relative to a wide variety of standard state-of-theart methods, evaluated on the Challenge dataset A. They also
propose to use a combination of the methods and automatically
select the best result.
CS has been used for adult ECG compression in WBSN applications showing promising results. A first study on the usability
of block sparse Bayesian learning for CS reconstruction of fECG has been investigated in [23] by Zhang et al., discussing its
possible application for telemonitoring purposes. In [23], it is
shown that the current CS framework, using linear sparsifying
bases, generally fails to recover the signal at high compression
ratios, making the reconstructed electrocardiogram nonsuitable
for diagnostic purposes. However, the use of specifically designed overcomplete dictionaries, like the one we propose in
this paper, may improve the reconstruction quality. After signal
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DA POIAN et al.: SEPARATION AND ANALYSIS OF FETAL-ECG SIGNALS
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reconstruction, the method proposed in [23], requires to apply
some classical separation techniques, i.e., ICA, to perform extraction of the f-ECG in order to find the fetal QRS complexes,
and thus, estimate the fHR. To compare results, FastICA is performed both on the reconstructed and original signals. Using the
scheme proposed in [23], the authors report that compression
ratios up to 60% allow the extraction of f-ECG signals without
significative performance loss with respect to using the original
noncompressed signals.
III. COMPRESSIVE SENSING
CS, first proposed in [9] and [11], is a recently introduced
signal processing technique, usually applied as a compression
scheme, which provides a framework for sparse representation
of signals.
The CS problem formulation can be written using matrix
notation as
y = Φx
(1)
where y ∈ RM is the compressed signal, x ∈ RN is a block
of the original signal, and Φ is an M × N measurement (or
sensing) matrix with M N . The sensing matrix does not
depend on x, so the process is nonadaptive and makes the acquisition/compression procedure very simple and universal.
The key concept of CS theory is sparsity. In particular, from
measurements (1), we can recover the original signal if it is
possible to find a sparse representation of x in a proper basis or
redundant dictionary Ψ = {ψ i }, ψ i ∈ RN , i.e.,
ui ψ i .
(2)
x = Ψu =
i
Sparsity of a signal x ∈ RN means that only k of the dictionary coefficients ui are nonzero, where k < M N . In other
words, if u = {ui } is the sparse representation of x, we have
u0 := card(supp(u)) ≤ k, where .0 is a pseudo-norm.
Since the number of taken measurements is M N , the recovery of x at the reconstruction device is an ill-posed problem.
However, it can be shown that, if the unknown signal x has
a k−sparse representation, it is possible, for suitable M > k
and Φ, to recover x by solving the following l0 minimization
problem [24]
min u0 subject to y = ΦΨu, (P0).
ui
(3)
However, since the objective function .0 is nonconvex,
problem (P0) in (3) results to be NP hard. For this reason,
instead of considering (P0), one can solve its convex relaxation
min u1 subject to y = ΦΨu, (P1)
ui
(4)
where .1 represents the l1 -norm. This approach is the basis
pursuit (BP) principle, and it can be solved via linear programming with reasonable complexity [25].
In a realistic situation, the measurement vector y is only an
approximation of the vector ΦΨu, and we have
y = ΦΨu + n.
In this case, the distance between the original vector and the
reconstructed one is controlled by the measurement error n.
The convex optimization problem (P1) can be replaced by the
following optimization problem [25]:
min u1 subject to y − ΦΨu2 ≤ , (P1,)
ui
(5)
where is a bound on the measurement noise energy, i.e.,
n2 ≤ . The principle to solve (P1,) is called the quadratically constrained BP, and there is a choice of algorithms to
perform the task, e.g., the BP denoising algorithm.
There are other algorithmic approaches to solve the CS recovery problem. These are based on greedy algorithms such as
orthogonal matching pursuit [26], Iterative Thresholding [27],
compressive sensing matching pursuit [28].
Independently from the approach, the structure of the measurement matrix Φ used to sense the signal is not arbitrary and
should be appropriately designed in order to ensure successful
recovery. In particular, to guarantee robust and efficient recovery of the sparse signal, the sensing matrix must satisfy the
restricted isometry property [29]. It has been proven that for
a random matrix Φ with i.i.d Gaussian entries with zero mean
and variance 1/M , bound M ≥ C k log(N/k) is achievable and
can guarantee the exact reconstruction of x with overwhelming
probability [29].
One of the major advantages of the CS is that the same sensing
matrix may be used to sense different classes of signals, independently of the selected reconstruction method. The compression procedure, is therefore, universal, only requiring that the
signal is compressible. Note that knowledge of the sparsifying
dictionary is required only at the receiver and at reconstruction
time. Moreover, employing sensing matrices with entries from
the bipolar set {−1, +1} or binary set {0, 1} may dramatically
reduce the sensing complexity, thus, making CS suitable for
applications in WBSNs [23], [30]. In this paper, we perform
compressed sensing using a sparse binary matrix, suitable for
hardware implementation. Each column of the binary sensing
matrix has only few nonzero entries, and the position of nonzero
entries is randomly chosen [31].
The reconstruction algorithm used for this paper is the
smoothed l0 SL0 algorithm, proposed by Mohimani et al. [32],
which has a fast implementation. This approach tries to directly
minimize the l0 norm of the solution. The basic idea of SL0 is
to solve the reconstruction problem by optimizing continuous
cost functions approximating the l0 norm of a vector.
IV. GAUSSIAN DICTIONARY FOR F-ECG SPARSIFICATION
CS is typically used combined with an orthogonal basis for
signal sparsification, such as the discrete wavelet transform or
the discrete cosine transform. However, the use of an appropriate
overcomplete dictionary may lead to a sparser representation of
signals, improving compression as well as the identification of
signal patterns matched to the dictionary atoms.
Following the ideas of using a Gaussian-like functions dictionary for the sparsification of the adult ECG [12] and the ECG
signal approximation introduced by McSharry et al. [13], we
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propose the use of an appropriate overcomplete Gaussian dictionary D for the abdominal fetal ECG signals sparsification.
In the design of the proposed dictionary, we take into account
not only the aspects of efficient signal representation for compression purposes, but also the possibility to help the separation
between maternal and fetal beats. As a matter of fact, if atoms in
the dictionary approximate different characteristics of the two
signal classes, fetal and maternal, it is possible to separate them
by considering which class of atoms are activated during reconstruction. The proposed dictionary is composed of K unit norm
vectors ψ k 1 = 1, D = {ψ k }k ∈Γ , such that each f-ECG signal
can be sparsely approximated by a subset of vectors {ψ k }k ∈Λ
in D. Defining L = |Λ|, the best L-term approximation xΛ of x
requires L dictionary functions
uk ψ k .
(6)
xΛ =
Fig. 3. Proposed overcomplete dictionary D represented as an N × K matrix
with columns ψk , and split into three parts, for maternal, noise, and fetal waves
approximation. In this model, any sparse set of atoms (columns in gray) can be
selected.
be sufficient to detect the fetal beats. We therefore preprocess the
compressed measurements y as explained in the next section.
k ∈Λ
Vectors ψ k are Gaussian-shaped with elements
2
n − ak
ψ k (n) = Ck exp
σk
V. SOURCE SEPARATION IN CS DOMAIN
(7)
where Ck is a normalization constant, and σk is a shape (or scale)
parameter, which is chosen to give an efficient approximation
of typical ECG waves, such as the P, Q, R, S, and T waves. Note
that the dictionary is universal, and it can be used to represent
different kinds of beats (normal and abnormal) as reported in
our previous study [12].
We use a total of 17 different shape parameter, 11 of them
are used for maternal waves approximation, 4 for fetal ECG
waveforms approximation, and 2 for noise.
Different sets of values of the scale parameter and different
number of atoms have been tested for dictionary construction,
in order to model the maternal and fetal ECGs. In particular,
for the type of recordings considered in the experiments, which
are multichannel ECG traces sampled at 1 kHz, we observed
that scale parameters σk ∈ {5, 6, 7, 8, 9, 10, 12, 15, 20, 30, 50},
ensure a good approximation of both symmetric (Q, R, S)
and asymmetric (P and T) maternal waves. For fetal ECG
approximation, atoms are computed using scale parameters
σk ∈ {2.5, 3, 3.5, 4}. For the noise components, we use σk ∈
{1.6, 2}. For each σk , all the possible shift parameters values
ak within the signal segment x are considered. In the proposed
scheme, since signal segments x with a duration of N = 250
samples are not synchronized with heart beats, the atoms corresponding to waves close to the segment boundaries are built
using windowed Gaussian functions. Fig. 3, reports the resulting
partitioning of the proposed over-complete dictionary.
Thus, the atoms used for reconstruction using the proposed
dictionary provide information about the location and nature
of ECG waveforms, which can be used for classification, as
detailed in Section VI. As a matter of fact, one would expect that
the reconstruction of a fetal or mother’s ECG waveform would
use only atoms from the corresponding section of the dictionary.
Of course, an abdominal ECG signal of a pregnant woman
requires a set of atoms (columns in gray in Fig. 3) belonging to
all three sections, so additional processing is needed. Fig. 1 also
shows that direct analysis of the reconstructed signals may not
Among the different approaches proposed for f-ECG extraction from multichannel recordings, blind source separation techniques, such as the ICA, combined with other methods (e.g.,
maternal QRS cancellation), seem to allow reliable results [33].
In the following, we summarize the ICA technique and propose
its application in the domain of compressed signals y.
A. ICA of the ECG signal
Let xi (k), i = 1, . . . , P be one of the multichannel recorded
signals. In the framework of ICA, xi (k) is modeled as a linear combination of independent processes corresponding to P
unknown sources, i.e.,
xi (k) = ai1 s1 (k) + ai2 s2 (k) + . . . + aiP sP (k).
(8)
Each sample xi (k) is therefore an instance of a random variable
xi =
P
aij sj
(9)
j =1
where sj are assumed to be independent and non-Gaussian (except for one of the variables at most). By collecting variables
(9) in vector xm = [x1 , . . . , xP ]T , we can write the ICA model
in matrix-vector notation as
xm = As
(10)
where xm are the observed linear mixtures, s = [s1 , . . . , sP ]T
are the hidden source signals and A is the unknown mixing
matrix.
ICA algorithms estimate matrix W = A−1 and obtain the ICs
s = Wxm . ICA is based on the fact that according to the central
limit theorem, each variable xi , since it is a linear combination
of independent variables, tends to have a Gaussian distribution opposite to the distribution of the source components sj .
According to this observation, separation algorithms for ICA estimation are based on the maximization of the non-Gaussianity
of wT xm , which allows us to find one row wT of matrix W.
This gives one of the ICs. The other ICs can be estimated by
finding all the local maxima of the optimization problem in the
P -dimensional space of vectors w. In our application of the ICA
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DA POIAN et al.: SEPARATION AND ANALYSIS OF FETAL-ECG SIGNALS
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Fig. 4. (a) First 2 s of original four channels abdominal fetal ECG record a32 of the Challenge dataset A. (b) k = 8 consecutive blocks of compressed sensed
measurements of each channel (record a32), corresponding to the first 2 s. The compression ratio is CR = 75%. (c) Estimated four ICs, which are still a compressed
version of the original ICs. (d) Reconstructed ICs from the compressed ICs. (e) ICs corresponding to ICA applied to the original signal.
method in the CS domain, which we analyze in the next section,
we preprocess the data through centering and whitening [14].
elements of Φh , one row of the sensing matrix Φ, are i.i.d. normalized Gaussian random variables. Then, given sj , variable ysj
is Gaussian with variance
B. ICA in the Compressed Domain
Define xi = [xi (k0 ), . . . , xi (k0 + N − 1)] as a block of N
consecutive samples of the ith multichannel recorded signal.
According to (8), we can write
T
xi = ai1 s1 + · · · + aiP sP
(11)
where sj = [sj (k0 ), . . . , sj (k0 + N − 1)]T . With the help of a
random sensing matrix Φ, the CS framework computes measurements for a block as
yi = Φxi = ai1 Φs1 + · · · + aiP ΦsP .
(12)
Across various blocks, the statistics we observe allow to model
the elements of yi as samples of a process
yi (h) = ai1 Φh s1 + . . . + aiP Φh sP
(13)
where Φh is one row of the random matrix Φ, and sj is an
N −dimensional random vector of samples sj (k). Each sample
yi (h) is therefore an instance of a random variable
yi =
P
aij ysj
(14)
j =1
where variables ysj = Φh sj obtained by sensing the unknown
sources, can be supposed to be independent, since they are functions of the independent source processes. Moreover, variables
ysj are in general non-Gaussian. Assume for instance that the
σ2 =
k 0 +N
−1
s2j (k).
k =k 0
However, the distribution of ysj is obtained by averaging
over the distribution of sj , and is given by a non-Gaussian
linear superposition of Gaussian components. Of course, nonGaussianity arises also when Φ is generated with distributions
other than Gaussian.
In summary, according to (14), we can write in matrix notation y = Ays i.e., the measurements can be expressed as a
combination, with the same mixing matrix of the original model,
of non-Gaussian ICs, obtained as CS measurements of the unknown sources. We can, therefore, use ICA to estimate W and
the compressed sensed unknown sources, in order to apply the
separation procedure within the CS reconstruction framework.
As an example, Fig. 4(a) shows the first 2 s of record a32 of the
four-channel abdominal recordings from the Physionet Challenge dataset. The signals sampled at 1 kHz are divided into
blocks of length N = 250 samples. Fig. 4(b) shows the corresponding CS measurements, consisting of eight consecutive
blocks yi of length M = 62 (75% compression ratio). Fig. 4(c)
shows the ICs ysj of the measurements, which are estimated by
performing ICA in the compressed domain. Finally, Fig. 4(d)
shows the signal ICs after CS reconstruction. It may happen that
ICA fails to separate the mother’s and fetal components exactly.
The typical situation is that one of the ICs reveals the mother’s
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Fig. 5. Absolute value of atoms activated during reconstruction of one IC
of signal a23 of the Physionet challenge database, in the dictionary section
corresponding to maternal ECG approximation.
beat, while one of the others is still a mixture of the mother’s
and fetal ECG, the other components corresponding to noise.
The next section describes the proposed procedure to detect the
two signals during the reconstruction process. In Fig. 4(e), we
also show the result of ICA on the original signals. It can be seen
that apart from the different order and possible sign changes, the
signals are almost identical to those in Fig. 4(d), thus, confirming that the proposed component analysis can be safely applied
in the compressed domain.
VI. DETECTION AND CLASSIFICATION OF FETAL AND
MATERNAL BEATS
The final step of the proposed approach involves the detection
of the maternal and fetal QRS complexes and their classification.
The reconstruction process is based on the assumption that the
ICs, resulting from the ICA analysis, share the same structure
of the original signals, i.e., they are sparse in the Gaussian
dictionary used for approximation.
Two assumptions have been made for the localization of maternal beats. The first one is that at least one of the ICs contains
maternal beats. The second one is that these components are
reconstructed using atoms mainly belonging to the maternal
dictionary section. Fig. 5 shows the atoms in the maternal dictionary activated during reconstruction of one IC of signal a23
of the Physionet challenge database. Based on the sparse representation, only atoms with a nonnegligible magnitude in the
maternal dictionary are considered as potential maternal QRS
complexes. Note that fetal QRS complexes, clearly visible in
Fig. 5, do not significantly activate atoms from the maternal
dictionary. Within a signal block of 2 s, an R peak position
candidate p at time t is selected if the corresponding atom magnitude |ui | (see (6)) is greater than a threshold T = αAmax ,
where Amax is the maximum atom magnitude in the current
signal segment. In the experiments, we set α = 0.75. If two detected atoms correspond to time positions less than 0.3 s apart,
the one with smaller |ui | is discarded, since they are supposed
to be redundant.
Detection is performed on three of the four channels simultaneously. The channel with the lowest kurtosis is supposed to
be noise and is not considered. For beat position detection, we
select the channel with the largest absolute ui value.
The detection of fetal beats is carried out in a similar way
as for maternal detection, but considering the dictionary section used for fetal approximation. However, in this case, some
Fig. 6. One of the IC’s of signal a22. (a) Absolute value of atoms activated in
the fetal dictionary. (b) Absolute value of atoms resulting after attenuation.
of the atoms activated during reconstruction might be related
to the mother’s beats. Not considering the atoms located in
correspondence of the previously detected mother’s beats is not
efficient, since maternal and fetal beats may overlap in time.
A possible solution is the attenuation of these values by multiplying them by a constant value 0 < β < 1. For simulations,
we set this constant equal to β = 0.25. This ensures that when
there is a time overlap between the fetal and maternal beats, we
are still able to detect the fetal one (see Fig. 6).
The threshold value used for the detection of fetal QRS complexes should take into account the lower power of the fetal
signal, and it is set at T = 0.5Amax in the experiments. The time
interval used to classify close peaks as redundant is reduced to
0.25 s, given that the fetus heart rate is faster than the maternal
normal sinus rhythm (i.e., about 110 to 160 beats per minute
(bpm) [34]). We compute the time differences between the detected atom positions in the three channels, and select the one
with the lowest difference variance, corresponding to the most
regular beat rate.
VII. EXPERIMENTAL SETUP AND METHODS
Fig. 2 summarizes the approach implemented for this study,
which consists of five main steps, namely, 1) compression of the
raw abdominal ECG signals using CS, 2) application of ICA on
the compressed measurements, 3) reconstruction of the ICs via
their sparse representation, 4) detection of the maternal beats,
5) detection of the fetal beats.
Before calculating the CS measures, raw signals are preprocessed using a zero phase high-pass Butterworth digital filter for
baseline wander removal, with cut-off frequency equal to 2 Hz.
To remove power-line interference, a second-order notch filter
at 50 or 60 Hz is applied, depending on the fact that signals come
from European or US recordings. Original signals are sampled
at 1 kHz.
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DA POIAN et al.: SEPARATION AND ANALYSIS OF FETAL-ECG SIGNALS
CS is applied on signal blocks of length N = 250 samples,
using a sparse sensing matrix Φ, with only two nonzero elements
in each column, whose row position is randomly chosen. This
class of sensing matrices is particularly interesting for lowpower applications and allows an efficient implementation in
hardware. In the experiments, we consider signal blocks of N =
250 samples, and take M = 62 measurements, corresponding
to a compression ratio CR = 75%. With a 63 × 250 sensing
matrix, we require 437 additions. The choice of a compression
ratio of 75% is based on the results reported in [12], where it
has been shown that it is the maximum CR that ensures a good
reconstruction quality of the signals. However, for the sake of
completeness, in Section VIII, we evaluate the performance of
the proposed framework at different CRs. Compressed data are
represented with 16 bits.
In the proposed framework, we reconstruct signal ICs and
not the original mixed signals. However, these can be recovered
by simply multiplying the estimated mixing matrix and the reconstructed ICs. As mentioned in this study, we use the reconstruction algorithm proposed in [32], the Smoothed l0 (SL0)
algorithm, which allows real-time implementation. Detection
and classification are applied on the sparse representation and
the fHR is computed every 2 s.
A. Datasets
Validation of the proposed compression and detection framework has been done on three datasets. The first one is the Abdominal and Direct f-ECG Database [3], [35] denoted as the
Silesia dataset. It contains five multichannel f-ECGs, obtained
from five different women, each one consisting of four abdominal f-ECG recordings as well as one f-ECG recording taken directly from a scalp electrode and used as reference. The position
of the electrodes was constant during all recordings. The sampling rate is 1 kHz with a resolution of 16 bits. For this dataset,
data are already preprocessed by digital filtering for removal of
power-line interference and baseline drift. The R-wave locations
were automatically determined in the direct f-ECG signal and
these locations were verified by a group of expert cardiologists.
The second and the third datasets we consider are set A
and set B of the Physionet challenge dataset. Both consist of
1-min-long four-lead abdominal f-ECG recordings. Set A has
75 records while set B has 100 records. These datasets contain
signals belonging to different databases, all sampled at 1 kHz
with a resolution of 16 bit, but with different instrumentation
and unknown electrode position. Reference positions of fetal
QRS complexes are available for all the files in set A, while the
reference annotations for dataset B are not public. Due to the
inaccuracy of reference annotations, records a38, a46, a52, a54,
a71, a74 of dataset A are discarded, as suggested in [22].
B. Evaluation Metrics
For the evaluation of the proposed scheme, we use classical
performance figures usually applied for the assessment of QRS
detection algorithms, i.e., sensitivity (S) and positive predictivity
(P+). According to the American National Standard [36] S and
1275
P+ are computed as
S=
TP
100,
TP + FN
P+ =
TP
100
TP + FP
(15)
where TP is the number of true positives, FP of false positives,
and FN of false negatives. A detected beat is considered to
be true positive if its time location differs less than 50 ms from
the reference markers (within a window of 100 ms centered
on the reference marker). The algorithm accuracy can be also
evaluated using the F1 measure, proposed in [37],
F1 = 2
TP
S P+
100 = 2
100.
S + P+
2TP + FN + FP
(16)
Additionally, we apply the scoring methods proposed in [4],
using two metrics, i.e., fHR measurement and RR interval measurement. The first one, denoted here as HRmeas (bpm2 ), is used
to assess the ability of the algorithm to provide valid fHR estimation. It is based on the squared difference between matched
reference (fHR) and detected fHRd measurements every 5 s (12
instances for 1-min-long signals)
1 (fHRi − fHRdi )2 .
12 i=1
12
HRmeas =
(17)
To assess the ability of the algorithm to extract the correct fetal
QRS locations with respect to the reference markers, the RR
measure metric is used, which is calculated from the differences
between matched reference RR and test RRd intervals. This
metric is denoted here by RRmeas (ms)
1 I −1
(RRi − RRid )2
(18)
RRmeas =
i=1
I −1
where I is the total number of fetal QRS complexes in the reference. These measures correspond to the Physionet challenge
scores and were obtained with the same code used by the Challenge scorer.
Since we are applying a compression technique (CS), reconstruction quality is evaluated using the PRD metric, defined as
− x̂(n))2
n (x(n)
× 100
(19)
PRD(%) =
2
n x(n)
where, x(n) and x̂(n) are the original (after baseline wander
removal and notch filtering) and reconstructed signals, respectively. This value is computed for each reconstructed segment
of every channel and then the average value is calculated. According to [38], reconstructions with PRD values between 0%
and 2% are qualified to have “very good” quality, while values
between 2% and 9% are categorized as “good”.
Finally, we consider the total time required by the algorithm
for beat classification, including reconstruction of all the four
channels, in order to assess the possibility to implement the proposed framework in a real-time application. The average time
required by the algorithm, for a 1-min-long signal, is approximately 3.7 s. The reconstruction program is written in Matlab,
running on an Intel Core i7 processor, equipped with 16 GB
memory.
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1276
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 63, NO. 6, JUNE 2016
TABLE I
RESULTS, AFTER ONE MINUTE AND AFTER FIVE MINUTES, FOR SIGNALS
FROM THE ABDOMINAL AND DIRECT FETAL ECG DATASET (SILESIA)
Record
t
r01
1’ 129 0 0
5’ 628 21 15
1’ 110 17 15
5’ 508 142 123
1’ 122 3 5
5’ 5721 63 55
1’ 123 10 9
5’ 638 18 12
1’ 109 20 19
5’ 519 154 117
r04
r07
r08
r10
TP
FP FN
S
%
P+
%
F1
%
mean PRD
%
HRmeas
(bpm2 )
RRmeas
(ms)
100
98
88
80
96
91
93
98
85
82
100
97
87
78
97
90
92
97
84
77
100
97.5
87.5
79
96.5
90.5
92.5
97.5
84.5
79.5
9.85
10.29
5.52
5.93
6.20
5.21
10.24
10.60
10.55
10.24
0.0048
22.1578
23.6373
75.9085
14.7479
33.0583
0.0038
7.2327
13.30
129.4236
1.49
13.10
12.30
22.21
14.74
16.04
12.03
10.12
20.98
20.92
The same sensing matrix has been used to sense all signals.
VIII. EXPERIMENTAL RESULTS
A. Results for Detection Performance
Table I reports a full evaluation of the proposed framework
in terms of the number of correctly found beats (TP), sensitivity
S, positive predictivity P+, and F1 measures, for all the five
records in the Silesia dataset. The compression ratio resulting
from CS is 75%, since we take 63 measurements every 250
signal samples at 1 kHz. For each signal, the first row of the
table shows results obtained within the first minute, whereas
the second row shows results for the whole 5-min-long signals.
The same randomly selected sparse sensing matrix has been
used for all traces and signal segments. For this dataset and the
selected sensing matrix, the average value for sensitivity is S =
92.5% within the first minute, and S=90% for the 5-min-long
signals. The positive predictivity average values are P += 92%
and P += 88% within the first minute and for 5 min, respectively.
Average HRmeas and RRmeas values within the first minute are
10.34 bpm2 and 12.33 ms, respectively. For 5-minlong signals, we obtain HRmeas = 53.55 bpm2 and
RRmeas = 16.48 ms.
Evaluation of the proposed detection method on the dataset
A, using a fixed randomly selected sparse sensing matrix ΦA
for all the signals of the dataset, gives an average sensitivity S
= 78% and an average positive predicitivity value P += 77%.
Concerning the scoring method proposed by the Physionet challenge the average HRmeas, for the same sensing matrix ΦA ,
is 138.65 bpm2 and the RRmeas is 20.92 ms. Since the Challenge dataset contains signals from different databases, recorded
using different instrumentations and methods, results have an
inhomogeneous distribution. Therefore, we analyzed the distribution among the signals of the dataset, obtaining a minimum
value for sensitivity equal to 15% (signal a18) and a maximum
value 100% (signal a32), while positive predictivity values range
from 21% up to 99%. The median value of the sensitivity distribution is about 87.7%, while the positive predictivity median
value is 85.5%. Median value for the HRmeas and RRmeas are
31.58 bpm2 and 17.96 ms, respectively.
To assess the influence of different sensing matrices on the
ability to correctly classify the fetal beats, we tested 50 different
sensing matrices on the Challenge dataset A, for a compression
Fig. 7. (a) and (b)—Reconstruction of 1 s of record a21, channel 1, of Challenge A dataset for the same compression ratio CR = 75%. In (a), a wavelet
basis is used (PRD = 28.19%), while in (b) the Gaussian overcompelete dictionary is used (PRD = 5.48%). (c) Reconstruction of record a21, channel 1, with
compression ratio CR = 90% and the Gaussian Dictionary, PRD = 29.25%.
ratio CR = 75% and the entire dataset. Average results obtained
for sensitivity are S = 78 ± 1 % and for positive predictivity P
+= 77 ± 1 %. Again using 50 different sensing matrices, the
values for HRmeas are 133.16 ± 9.04 bpm2 and 21.41 ± 0.6
ms for RRmeas. The influence of the sensing matrix appears to
be moderate.
Finally, we tested the proposed framework on dataset B of
the Challenge. Also for this dataset, the proposed method has
been tested using 50 different sensing matrices. The scores are
HRmeas = 188 ± 13 bpm2 and RRmeas = 24.52 ± 0.26 ms.
To allow the comparison with some off-line methods considered in Section IX, we add a limited complexity postprocessing
stage after real-time detection, in order to correct the estimated
fHR and RR time series (we call this variation of the proposed
method smoothed in Section IX). It operates on 1-min-long
blocks of the detected fetal channel and consists in the removal
of beats that are too short to be physiologically possible. It also
checks for missed beats, using an approach similar to the one
proposed in [17]. After this postprocessing stage, the average
scores obtained using dataset B, with 50 randomly chosen sensing matrices, are 136 ± 11 bpm2 and 17,23 ± 0,41 ms for
HRmeas and RRmeas, respectively.
B. Effects of Compression Ratio
Fig. 7 shows a comparison between the reconstruction
obtained with the proposed Gaussian dictionary and a
wavelet-based sparsifying basis, as commonly adopted for CS
implementation [30]. In accordance with the results presented
in [12], relative to standard ECG traces and a simpler dictionary,
the use of the proposed Gaussian dictionary for mother and
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DA POIAN et al.: SEPARATION AND ANALYSIS OF FETAL-ECG SIGNALS
1277
IX. DISCUSSION AND RELATION TO OTHER F-ECG
EXTRACTION METHODS
Fig. 8. Average reconstruction performance (i.e., average PRD (a) and reconstruction time (b) values) at six different compression ratios ranging from 60%
to 90%, for dataset A; (c) HRmeas and (d) RRmeas at different CRs. Error bars
indicate standard deviation.
fetal ECG compression allows a great improvement in the
reconstruction quality (on average, about 75% CR with the
Gaussian dictionary against a smaller 50% CR with wavelets, for
a “good” reconstruction quality PRD = 9%). On an average, the
proposed dictionary seems to ensure good reconstruction quality
for signals in the Silesia dataset (see Table I), with a mean PRD
value of 8.5%. Even if some signals have a PRD greater than 9%,
the ability of the algorithm to correctly detect and classify the
fetal beats does not seem to be affected. Concerning the reconstruction quality on the Challenge dataset A, results show a mean
PRD value of 7.5 %, satisfying the reconstruction requirements
for diagnostic purposes. In Fig. 8, the performance of our framework at six different compression ratios, ranging from 60% to
90%, are reported. Results are averages of the performance for
the entire dataset A, using 50 different sensing matrices at each
compression ratio. Both mean and standard deviation values are
shown for each CR. As it can be seen in Fig. 8(a), the reconstruction quality changes with the CR, as well as the reconstruction
time, from 6.7 ms for a CR = 60% to 4.6 ms when the CR is 90%,
see Fig. 8(b).
The detection performance in term of sensitivity, positive
predictivity, HRmeas, and RRmeas shows a negligible variation when the reconstruction ensures a good quality (i.e., for
CR<75%), as shown in Fig. 8(c) and (d) for HRmeas and
RRmeas. In particular, the average sensitivity value ranges from
79%, for CR = 65%, to 76% for CR = 80%. The positive predictivity value shows a similar trend. Also HRmeas and RRmeas
show small variations (i.e., a variation of 3 bmp2 for HRmeas,
and less than 1 ms for RRmeas). Higher compression ratios
(CR>80%) cause a loss of detection performance, both in terms
of S and P+ and in terms of HRmeas and RRmeas. At CR =
90%, sensitivity decreases to 61% and P+ decreases to 59%,
while HRmeas and RRmeas increase to 225 bpm2 and 28 ms,
respectively.
Unlike others methods proposed in the literature, which are
designed for offline analysis after preprocessing of the signal, our framework allows detection of fetal beats, as well as
maternal beats, by processing short 2-s signal blocks during signal reconstruction within the CS framework. Due to its relatively
low complexity, the proposed procedure can be implemented in
real time at the receiver. From the best of our knowledge, this is
the first time that a framework for the low-power CS compression of fetal abdominal ECG is proposed combined with a beat
detector for fHR estimation.
Data from this Silesia dataset have been previously used in
[19] for the validation of a wavelet-based method. Sensitivity
values reported in [19] range from S = 85% to S = 95% for
the 5-min-long signals. Instead, when it is evaluated on each
minute, the sensitivity ranges from about 72% up to 98%. From
the results reported in Table I, it is apparent that the proposed
framework allows a similar performance, besides the fact that
it operates on compressed data which are acquired with very
little complexity. The HRmeas and the RRmeas values on this
dataset have been previously reported in [39] using two different
approaches, with average values HRmeas = 122.5 bpm2 and
RRmeas = 31.46 ms for the global approach, and HRmeas =
11.21 bpm2 and RRmeas = 26.64 ms for the time adaptive
approach. Thus, on this dataset, our framework (HRmeas =
53.55 bpm2 and RRmeas = 16.48 ms) outperforms the global
approach proposed in [39] and is comparable with the second
one.
In [22], several techniques have been tested on dataset A of the
Chellenge dataset. One of the methods operates on the full original signals, computes ICA, and uses an adapted version of the
standard Pan and Tompkins QRS detector [40]. Besides baseline
wander removal and notch filtering, the method does not employ additional pre/postprocessing techniques, similarly to what
we do in the proposed approach. Compared to this method, our
solution increases detection performance by 10% for the mean
sensitivity value (reported result for the same dataset is 69.1%).
Moreover, the percentage improvement for the positive predictivity is 18% (reported result, P += 60%). When PCA is used
instead of ICA in [22] our improvement is 21% and 31% for S
and P+, respectively. With respect to the results reported in [22],
the mean HRmeas achieved by the proposed approach outperforms the methods based on ICA and PCA (mean HRmeas value
2852.1 bpm2 for the ICA based method and mean HRmeas value
3892.1 bpm2 for the PCA method). Clifford et al.[4], [22] also
report results obtained with different techniques comprising a
combination of ICA processing stages and template subtraction.
These techniques operate on the full length preprocessed original signals with no compression. Our method has comparable
results with respect to each individual technique considered in
[22], even if the most elaborate, which use a combination of
individual techniques, can achieve considerably better results
than the proposed method.
Methods reviewed in [4] usually follow a four step approach,
which includes preprocessing, estimation of maternal compo-
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 63, NO. 6, JUNE 2016
TABLE II
COMPARISON OF SOME DETECTION METHODS ON DATASET B
Method
ICA-Template
Adaption [41]
FUSE - smooth [22]
ICA-TS-ICA
upsampling [33]
Wiener filter [39]
TS-ICA upsampling
[17]
Proposed method smoothed
Proposed method
ICA-Extended
Kalman [41]
TS and PCA[42]
Wavelet based [19]
TSP C A [22]
HRmeas
bpm2
RRmeas
ms
Realtime
Compression
Execution Time
s
20.4
4.6
NO
NO
N.A.
29.6
34
4.7
5.1
NO
NO
NO
NO
1.8
1.55
124.8
134.5
14.4
12.4
NO
NO
NO
NO
4.8
200
136
17.2
NO
YES
0.64
188
219
24.5
7.7
YES
NO
YES
NO
0.64
N.A.
305.7
513.1
759.42
23.1
35.3
21.86
NO
NO
NO
NO
NO
NO
N.A.
N.A.
1.09
In case of no publicly available implementation, the execution time is set to N.A.
nent and its removal, estimation of fHR and RR time series, and
a postprocessing final stage where detected beats are corrected
based on prior knowledge. Table II summarizes and compares
the performance of some approaches proposed in [4], with respect to the one proposed in this paper, for dataset B. As it can
be seen, the proposed method achieves results comparable to
some off-line methods, even though it works on compressed
signals and, using short signal blocks, can be implemented in
real-time with a short delay. Regarding execution time, as shown
in Fig. 2, the proposed approach includes reconstruction from
compressed samples, according to the fact that the intended
focus of the paper is a low-power and low-complexity acquisition/detection real-time system, while existing algorithms operate on noncompressed data. A fair comparison would need to
include compression/decompression procedures in the existing
schemes. In Table II, we report results by neglecting the time required by the reconstruction stage (see Fig. 2). We evaluate the
CPU execution time of Matlab publicly available implementations, running on an Intel Core i7 processor, equipped with
16 GB memory. For the proposed techniques, we report average
values, using 50 different sensing matrices. To compute ICA in
the compressed domain and to detect the fetal QRS complexes,
the proposed algorithm takes about 0.64 s for a 1-min-long signal, while the total time including reconstruction is about 3.7 s,
as mentioned before.
Preprocessing may increase detection performance, especially when impulsive artifact removal is applied. Impulsive
artifacts may affect the performance of ICA decomposition, and
this may be one of the reasons why the proposed method has
for some signal a worse performance than other methods [22].
Moreover, we believe that the proposed method fails on some
abdominal signals of the Challenge A dataset due to the poor
quality of the signals. As mentioned in [17] and [39], for some
signals, such as a02, a09, a18, or a29, due to the low signal quality, it is not possible to correctly identify the fetal beats obtaining
unreliable results. For practical purposes, the choice of the optimal number and position of electrodes is important since the
efficiency of the signal processing methods strongly depends on
the signal quality and on the number of channels. This observation is confirmed by the different average performance obtained
with the Silesia and Challenge datasets.
X. CONCLUSION
In this paper, a framework for the CS compression of abdominal fetal ECG recordings jointly with real time beat detection and classification has been presented. Evaluation of the
proposed method has been done on three open datasets, showing
promising results for both correct detection of fetal beats (S =
92.5% for Silesia dataset and S = 78% for the Challenge dataset
A) and reconstruction quality (PRD = 8.5% and PRD = 7.5%).
These results allow us to conclude that the proposed framework
may be used for compression of abdominal f-ECG and to obtain
real time information of the fHR, providing a suitable solution
for low-power telemonitoring applications.
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