![Given two dictionaries such that D=[D1 D2] represent an
observed signal x as a superposition of few atoms from
D1 and few atoms from D2, find the corresponding
vectors and .
Ideally we want to solve:
Since this is an NP-hard problem we try to solve its convex relaxation:
which can be solved using linear programming or greedy algorithms like the
Orthogonal Matching Pursuit (OMP).
Objective
↵2↵1
Sparse Approximation
Each ECG cycle can be seen as a linear combination of few Gaussian functions with
appropriate shift and shape parameters [3]:
x(t) =
1X
i= 1
↵i'i(t)
'i
↵
Sparse signal representation [2] aims to decompose complex signals using elementary
functions which are then easier to manipulate.
For an over-complete dictionary D of functions we can always find a representation
sequence , but it is not unique.
We can use sparse representation for source separation into two or more signal components
using a combination of different dictionaries.
x ↵
= Dm Df
gm
gf
↵m
↵f
Fig2. Overcomplete Gaussian Dictionary for the
sparse approximation of fetal and maternal ECG.
Shape parameter s can discriminate mother’s or fetal
beats;
Shift parameter p gives information about time location.
[4] G. Da Poian et al., “Gaussian dictionary for compressive sensing of the ECG signal,” in BIOMS
Proceedings, 2014 IEEE Workshop on. IEEE, 2014, pp. 80–85.
[5] Abdominal and direct fetal ECG,” URL http://physionet.org/physiobank/database/adfecgdb/
[6] Noninvasive fetal ECG: the PhysioNet/computing in cardiology challenge 2013,” URL http://
www.physionet.org/challenge/2013
Dictionary for abdominal fECG
Conclusions
Results
QRS Detection
For multi leads fetal ECG, selection of the channel with the best RR detected series is
based on the computation of RR first and second difference, giving a figure of merit emix.
If emix is higher then a threshold, we can apply Template Subtraction (TS), based on found
maternal QRS complexes (no real-time) and Independent Component Analysis (ICA).
If emix >Th (Th=200 in our experiments) we apply
TS - ICA:
We proposed a new method for the detection of fetal beats exploiting information from the
sparse representation.
Simulations using real data from two public datasets demonstrate the effectiveness of this
method, which is suitable for real-time implementation (with a delay of 2 s), thanks to its low
complexity.
Fig 5. Time-atoms representation. The horizontal axis
represents time, the vertical axis corresponds to the scale
parameters si ∈ Df . Activated atoms with the highest values
correspond to R waves of fetal ECG.
Fig. 1 Abdominal ECG
recordings.
S P+
%
40
60
80
100
(a)
S P+
%
40
60
80
100
(b)
Fig. 5. Fetal QRS detection performance of the proposed method on
Challenge dataset A. (a) Distribution of sensitivity and positive predictivity
for all the signals. (b) Distribution of sensitivity and positive predictivity when
only the sparse representation based method has been used (27 signals).
TABLE II. RESULTS FOR DETECTION ON SINGLE CHANNELS (FIRST
MINUTE OF SIGNALS FROM DATASET [7].)
Channel 1 Channel 2 Channel 3 Channel 4
r01 𝑆 93.80 99.22 99.22 99.22
𝑃 + 89.63 93.43 99.22 100
r04 𝑆 45.60 92.00 76.00 81.60
𝑃 + 37.75 93.50 73.64 76.11
r07 𝑆 39.37 89.76 85.83 83.46
𝑃 + 39.37 93.44 80.15 80.30
r08 𝑆 89.39 96.97 98.45 99.24
𝑃 + 86.76 92.75 99.24 98.49
r10 𝑆 90.63 92.97 51.56 81.25
𝑃 + 86.58 82.64 56.41 78.20
sampled at 1 kHz, but using a variety of instrumentation with
different frequency responses, resolution and configuration.
Results form this dataset (discarding records a38, a47, a52,
a54, a71, a74 with inaccurate annotations) are summarised in
Fig. 5(a). The boxplot reports the obtained distributions for the
sensitivity and positive predicivity values, with median values
for sensitivity equal to 𝑆 = 97.5% and for positive predictivity
𝑃+ = 96.2%, while the average values are 𝑆 = 91.5% and
𝑃+ = 91%. For comparison, similar complexity procedures
evaluated in [2], and using Template Subtraction techniques or
ICA, followed by a standard peak detector, achieve sensitivity
values 𝑆 = 82%, and 𝑆 = 69.1%, respectively. The proposed
method with no 𝑇𝑆 − 𝐼𝐶𝐴 was able to directly detect fetal
beats in 27 out of 69 traces, with average 𝑆 = 96% and
𝑃+ = 95.5% on this subset, Fig. 5(b).
Application to single trace signals has been also investi-
Fig. 11 Distribution of S and P+ for all the signals.
(b) Distribution of S and P+ when only the sparse
representation based method has been used (27
signals).
S % P+ % F %
multi
leads
off line 93.5 85.4 89.5
with TS-ICA 95 94.3 94.7
real time 92.5 85.4 89
single
lead
off line 85 82 83.5
Fig. 7 Abdominal ECG where fECG cannot be
eye spotted.
1. Use the detected maternal QRS complexes
from sparse representation;
2. Apply Template Subtraction (TS);
3. Apply ICA;
4. Use sparse decomposition to identify fetal
QRS’s and to select the best IC.
(2)
Fig. 8 Abdominal ECG after Template Subtraction.
Fig. 9 ICs after TS.
On the “Challenge” Dataset A [6] the proposed
method using TS-ICA achieves S = 91.5% and P +
= 91%.
In 27/69 signals we had emix <Th with S = 96% and
P + = 95.5.
Fig. 10 Single lead Sensitivity detection.
We tested our method on signals from the “Silesia”
dataset [5], for single channel detection and real-time
analysis with small delay.
Maternal
QRS
IC corresponding to
fetal ECG
(1)
(3)
g(p,s) =
1
p
2⇡s
e
(x p)2
2s2
min
↵
k↵k0 s.t.kx D↵k2 ✏
min
↵
k↵k1 s.t.kx D↵k2 ✏
CONTACTS: dapoian.giulia@spes.uniud.it, bernardini@uniud.it, rinaldo@uniud.it
Sparse Representation for Fetal QRS Detection
Giulia Da Poian, Riccardo Bernardini and Roberto Rinaldo
DIEGM, University of Udine, Italy
IEEE INTERNATIONAL CONFERENCE E-HEALTH AND BIOENGINEERING -
“EHB 2015”, IASI, ROMANIA, NOVEMBER 19-21, 2015
Maternal coefficients Fetal coefficients Maternal coefficients Fetal coefficients
We proposed an over-complete dictionary of Gaussian-like functions [4] for sparsification
and separation of mother’s and fetal beats;
The dictionary is separated into two sub-dictionaries, D𝑚 and D𝑓:
Improved Detection Method
Sparse source separation problem
in Abdominal ECG Recordings
s𝑖 ∈ {6.3,7,8,9,10,12,15} to build the maternal dictionary D𝑚
s𝑖 ∈ {2, 3.5, 4, 4.5, 4.7} for the fetal D𝑓 dictionary
Fig. 3 Fetal (red) and Maternal (blu) QRS complexes
and their correspondent sparse representation in
the proposed dictionary.
(a) (b)
-4
-2
0
2
4
Samples
200 400 600 800 1000 1200 1400 1600 1800 2000
Atoms
1
2
3
4
0.1
0.2
0.3
0.4
0.5
0.6
DIPARTIMENTO DI INGEGNERIA ELETTRICA GESTIONALE E MECCANICA
Corso di dottorato in
Ingegneria Industriale e dell’Informazione
AREA TECNICO SCIENTIFICA
pressed domain to
el abdominal fECG.
Validation of the proposed method [5] on two public datasets shows a
mean sensitivity for beat detection S=78% for the Challenge dataset and
S=92.5% for the Silesia dataset.
Positive predictivity mean values are P+=78% and P+=91.6%.
Compression ratios up to CR=75% allow to achieve
good reconstruction quality.
Results are comparable with state-of-the-art methods, beside the fact that
our scheme allows very low-power compression and real-time
classification
Samples
200 300 400 500
nciple that a small
capture all the
ion and enable its
veSensingofFetalECG
he CS domain
rough electrocardiography allows to discover
ts during pregnancy [1].
for the compression and analysis of the
(fECG) using Compressive Sensing (CS),
pplied in the compressed domain and sparse
es.
Low complexity
Low power
Time [s]
0 10 20 30 40 50 60
FetalHR[bpm]
100
110
120
130
140
150
160
Estimated fetal HR
True fetal HR
RESULTS
CONCLUSIONS
compression of abdominal fECG recordings jointly with real time beat detection and
at the proposed framework may be used for compression of abdominal f-ECG and to obtain
providing a suitable solution for low-power telemonitoring applications.
Sparsifiying
dictionary
se Binary
ng matrix
For the reconstruction of the independent components we exploit the
signal sparsity using an overcomplete dictionary of Gaussian like
functions [4]. This representation allows further separation of
maternal and fetal beats.
Classification is based on
the sparse representation of
independent components.
Reconstructed ICs
BEATS CLASSIFICATION
-5
0
5
-5
0
5
-2
0
2
Samples
0 500 1000 1500 2000
-2
0
2
REFERENCES
[1] R.G. Kennedy, ”Electronic fetal heart rate monitoring: retrospective reflections on a twentieth-century technology." Journal of the Royal
Society of Medicine 91.5 (1998): 244.
[2] D.L. Donoho, ”Compressed sensing." Information Theory, IEEE Transactions on 52.4 (2006): 1289-1306.
[3] A. Hyvärinen and O. Erkki, "Independent component analysis: algorithms and applications." Neural networks 13.4 (2000): 411-430.
[4] G. Da Poian, R. Bernardini and R. Rinaldo. "Gaussian dictionary for Compressive Sensing of the ECG signal." Biometric Measurements
and Systems for Security and Medical Applications (BIOMS) Proceedings, 2014 IEEE Workshop on. IEEE, 2014.
[5] G. Da Poian, R. Bernardini and R. Rinaldo. “ Separation and Analysis of Fetal-ECG Signals from Compressed Sensed Abdominal ECG
Recordings.” Submitted to IEEE Transactions on Biomedical Engineering.
-100
0
100
-100
0
100
-50
0
50
Time [s]
0 0.5 1 1.5 2 2.5 3 3.5
-50
0
50
Distribution of S and P+ values
for the Challenge dataset.
S P+
20
30
40
50
60
70
80
90
100
andBeyond
Example of fetal heart rate estimation.
x = D u
Abdominal fECG recordings
Non-invasive fetal ECG (fECG) extraction from abdominal recordings is a well-known problem
since the fECG is unfortunately contaminated by maternal ECG, maternal electromyogram
(EMG), and noise [1].
Non-invasive extraction of fECG from abdominal
recordings of a pregnant woman using:
an array of electrodes placed on the abdomen
without maternal ECG reference;
a single electrode on the abdomen.
Real-time implementation.
Off-line implementation.
References
[1] G. D. Clifford et al., “Non-invasive fetal ECG analysis,” Physiol. Meas., vol. 35, no. 8, pp.1521, 2014
[2] M. Elad,‘Sparse and Redundant Representations’, Springer, 2010
[3] P. E. McSharry et al., “A dynamical model for generating synthetic electrocardiogram signals,”
Biomedical Engineering, IEEE Transactions on, vol. 50, no. 3, pp. 289–294, 2003.
The procedure to identify fetal beats is based on the atoms s𝑖 ∈ D𝑓 used to approximate
the beats in the sparse decomposition.
See also:
http://ieeexplore.ieee.org/document/7305770/
http://www.mdpi.com/1424-8220/17/1/9/htm
See also:
http://ieeexplore.ieee.org/document/7305770/
http://www.mdpi.com/1424-8220/17/1/9/htm](https://image.slidesharecdn.com/ehbconference2015-170130220015/85/Sparse-Representation-for-Fetal-QRS-Detection-in-Abdominal-ECG-Recordings-1-320.jpg)
Sparse Representation for Fetal QRS Detection in Abdominal ECG Recordings
- 1. Given two dictionaries such that D=[D1 D2] represent an observed signal x as a superposition of few atoms from D1 and few atoms from D2, find the corresponding vectors and . Ideally we want to solve: Since this is an NP-hard problem we try to solve its convex relaxation: which can be solved using linear programming or greedy algorithms like the Orthogonal Matching Pursuit (OMP). Objective ↵2↵1 Sparse Approximation Each ECG cycle can be seen as a linear combination of few Gaussian functions with appropriate shift and shape parameters [3]: x(t) = 1X i= 1 ↵i'i(t) 'i ↵ Sparse signal representation [2] aims to decompose complex signals using elementary functions which are then easier to manipulate. For an over-complete dictionary D of functions we can always find a representation sequence , but it is not unique. We can use sparse representation for source separation into two or more signal components using a combination of different dictionaries. x ↵ = Dm Df gm gf ↵m ↵f Fig2. Overcomplete Gaussian Dictionary for the sparse approximation of fetal and maternal ECG. Shape parameter s can discriminate mother’s or fetal beats; Shift parameter p gives information about time location. [4] G. Da Poian et al., “Gaussian dictionary for compressive sensing of the ECG signal,” in BIOMS Proceedings, 2014 IEEE Workshop on. IEEE, 2014, pp. 80–85. [5] Abdominal and direct fetal ECG,” URL http://physionet.org/physiobank/database/adfecgdb/ [6] Noninvasive fetal ECG: the PhysioNet/computing in cardiology challenge 2013,” URL http:// www.physionet.org/challenge/2013 Dictionary for abdominal fECG Conclusions Results QRS Detection For multi leads fetal ECG, selection of the channel with the best RR detected series is based on the computation of RR first and second difference, giving a figure of merit emix. If emix is higher then a threshold, we can apply Template Subtraction (TS), based on found maternal QRS complexes (no real-time) and Independent Component Analysis (ICA). If emix >Th (Th=200 in our experiments) we apply TS - ICA: We proposed a new method for the detection of fetal beats exploiting information from the sparse representation. Simulations using real data from two public datasets demonstrate the effectiveness of this method, which is suitable for real-time implementation (with a delay of 2 s), thanks to its low complexity. Fig 5. Time-atoms representation. The horizontal axis represents time, the vertical axis corresponds to the scale parameters si ∈ Df . Activated atoms with the highest values correspond to R waves of fetal ECG. Fig. 1 Abdominal ECG recordings. S P+ % 40 60 80 100 (a) S P+ % 40 60 80 100 (b) Fig. 5. Fetal QRS detection performance of the proposed method on Challenge dataset A. (a) Distribution of sensitivity and positive predictivity for all the signals. (b) Distribution of sensitivity and positive predictivity when only the sparse representation based method has been used (27 signals). TABLE II. RESULTS FOR DETECTION ON SINGLE CHANNELS (FIRST MINUTE OF SIGNALS FROM DATASET [7].) Channel 1 Channel 2 Channel 3 Channel 4 r01 𝑆 93.80 99.22 99.22 99.22 𝑃 + 89.63 93.43 99.22 100 r04 𝑆 45.60 92.00 76.00 81.60 𝑃 + 37.75 93.50 73.64 76.11 r07 𝑆 39.37 89.76 85.83 83.46 𝑃 + 39.37 93.44 80.15 80.30 r08 𝑆 89.39 96.97 98.45 99.24 𝑃 + 86.76 92.75 99.24 98.49 r10 𝑆 90.63 92.97 51.56 81.25 𝑃 + 86.58 82.64 56.41 78.20 sampled at 1 kHz, but using a variety of instrumentation with different frequency responses, resolution and configuration. Results form this dataset (discarding records a38, a47, a52, a54, a71, a74 with inaccurate annotations) are summarised in Fig. 5(a). The boxplot reports the obtained distributions for the sensitivity and positive predicivity values, with median values for sensitivity equal to 𝑆 = 97.5% and for positive predictivity 𝑃+ = 96.2%, while the average values are 𝑆 = 91.5% and 𝑃+ = 91%. For comparison, similar complexity procedures evaluated in [2], and using Template Subtraction techniques or ICA, followed by a standard peak detector, achieve sensitivity values 𝑆 = 82%, and 𝑆 = 69.1%, respectively. The proposed method with no 𝑇𝑆 − 𝐼𝐶𝐴 was able to directly detect fetal beats in 27 out of 69 traces, with average 𝑆 = 96% and 𝑃+ = 95.5% on this subset, Fig. 5(b). Application to single trace signals has been also investi- Fig. 11 Distribution of S and P+ for all the signals. (b) Distribution of S and P+ when only the sparse representation based method has been used (27 signals). S % P+ % F % multi leads off line 93.5 85.4 89.5 with TS-ICA 95 94.3 94.7 real time 92.5 85.4 89 single lead off line 85 82 83.5 Fig. 7 Abdominal ECG where fECG cannot be eye spotted. 1. Use the detected maternal QRS complexes from sparse representation; 2. Apply Template Subtraction (TS); 3. Apply ICA; 4. Use sparse decomposition to identify fetal QRS’s and to select the best IC. (2) Fig. 8 Abdominal ECG after Template Subtraction. Fig. 9 ICs after TS. On the “Challenge” Dataset A [6] the proposed method using TS-ICA achieves S = 91.5% and P + = 91%. In 27/69 signals we had emix <Th with S = 96% and P + = 95.5. Fig. 10 Single lead Sensitivity detection. We tested our method on signals from the “Silesia” dataset [5], for single channel detection and real-time analysis with small delay. Maternal QRS IC corresponding to fetal ECG (1) (3) g(p,s) = 1 p 2⇡s e (x p)2 2s2 min ↵ k↵k0 s.t.kx D↵k2 ✏ min ↵ k↵k1 s.t.kx D↵k2 ✏ CONTACTS: dapoian.giulia@spes.uniud.it, bernardini@uniud.it, rinaldo@uniud.it Sparse Representation for Fetal QRS Detection Giulia Da Poian, Riccardo Bernardini and Roberto Rinaldo DIEGM, University of Udine, Italy IEEE INTERNATIONAL CONFERENCE E-HEALTH AND BIOENGINEERING - “EHB 2015”, IASI, ROMANIA, NOVEMBER 19-21, 2015 Maternal coefficients Fetal coefficients Maternal coefficients Fetal coefficients We proposed an over-complete dictionary of Gaussian-like functions [4] for sparsification and separation of mother’s and fetal beats; The dictionary is separated into two sub-dictionaries, D𝑚 and D𝑓: Improved Detection Method Sparse source separation problem in Abdominal ECG Recordings s𝑖 ∈ {6.3,7,8,9,10,12,15} to build the maternal dictionary D𝑚 s𝑖 ∈ {2, 3.5, 4, 4.5, 4.7} for the fetal D𝑓 dictionary Fig. 3 Fetal (red) and Maternal (blu) QRS complexes and their correspondent sparse representation in the proposed dictionary. (a) (b) -4 -2 0 2 4 Samples 200 400 600 800 1000 1200 1400 1600 1800 2000 Atoms 1 2 3 4 0.1 0.2 0.3 0.4 0.5 0.6 DIPARTIMENTO DI INGEGNERIA ELETTRICA GESTIONALE E MECCANICA Corso di dottorato in Ingegneria Industriale e dell’Informazione AREA TECNICO SCIENTIFICA pressed domain to el abdominal fECG. Validation of the proposed method [5] on two public datasets shows a mean sensitivity for beat detection S=78% for the Challenge dataset and S=92.5% for the Silesia dataset. Positive predictivity mean values are P+=78% and P+=91.6%. Compression ratios up to CR=75% allow to achieve good reconstruction quality. Results are comparable with state-of-the-art methods, beside the fact that our scheme allows very low-power compression and real-time classification Samples 200 300 400 500 nciple that a small capture all the ion and enable its veSensingofFetalECG he CS domain rough electrocardiography allows to discover ts during pregnancy [1]. for the compression and analysis of the (fECG) using Compressive Sensing (CS), pplied in the compressed domain and sparse es. Low complexity Low power Time [s] 0 10 20 30 40 50 60 FetalHR[bpm] 100 110 120 130 140 150 160 Estimated fetal HR True fetal HR RESULTS CONCLUSIONS compression of abdominal fECG recordings jointly with real time beat detection and at the proposed framework may be used for compression of abdominal f-ECG and to obtain providing a suitable solution for low-power telemonitoring applications. Sparsifiying dictionary se Binary ng matrix For the reconstruction of the independent components we exploit the signal sparsity using an overcomplete dictionary of Gaussian like functions [4]. This representation allows further separation of maternal and fetal beats. Classification is based on the sparse representation of independent components. Reconstructed ICs BEATS CLASSIFICATION -5 0 5 -5 0 5 -2 0 2 Samples 0 500 1000 1500 2000 -2 0 2 REFERENCES [1] R.G. Kennedy, ”Electronic fetal heart rate monitoring: retrospective reflections on a twentieth-century technology." Journal of the Royal Society of Medicine 91.5 (1998): 244. [2] D.L. Donoho, ”Compressed sensing." Information Theory, IEEE Transactions on 52.4 (2006): 1289-1306. [3] A. Hyvärinen and O. Erkki, "Independent component analysis: algorithms and applications." Neural networks 13.4 (2000): 411-430. [4] G. Da Poian, R. Bernardini and R. Rinaldo. "Gaussian dictionary for Compressive Sensing of the ECG signal." Biometric Measurements and Systems for Security and Medical Applications (BIOMS) Proceedings, 2014 IEEE Workshop on. IEEE, 2014. [5] G. Da Poian, R. Bernardini and R. Rinaldo. “ Separation and Analysis of Fetal-ECG Signals from Compressed Sensed Abdominal ECG Recordings.” Submitted to IEEE Transactions on Biomedical Engineering. -100 0 100 -100 0 100 -50 0 50 Time [s] 0 0.5 1 1.5 2 2.5 3 3.5 -50 0 50 Distribution of S and P+ values for the Challenge dataset. S P+ 20 30 40 50 60 70 80 90 100 andBeyond Example of fetal heart rate estimation. x = D u Abdominal fECG recordings Non-invasive fetal ECG (fECG) extraction from abdominal recordings is a well-known problem since the fECG is unfortunately contaminated by maternal ECG, maternal electromyogram (EMG), and noise [1]. Non-invasive extraction of fECG from abdominal recordings of a pregnant woman using: an array of electrodes placed on the abdomen without maternal ECG reference; a single electrode on the abdomen. Real-time implementation. Off-line implementation. References [1] G. D. Clifford et al., “Non-invasive fetal ECG analysis,” Physiol. Meas., vol. 35, no. 8, pp.1521, 2014 [2] M. Elad,‘Sparse and Redundant Representations’, Springer, 2010 [3] P. E. McSharry et al., “A dynamical model for generating synthetic electrocardiogram signals,” Biomedical Engineering, IEEE Transactions on, vol. 50, no. 3, pp. 289–294, 2003. The procedure to identify fetal beats is based on the atoms s𝑖 ∈ D𝑓 used to approximate the beats in the sparse decomposition. See also: http://ieeexplore.ieee.org/document/7305770/ http://www.mdpi.com/1424-8220/17/1/9/htm See also: http://ieeexplore.ieee.org/document/7305770/ http://www.mdpi.com/1424-8220/17/1/9/htm