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 Dfgm 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 onChallenge dataset A. (a) Distribution of sensitivity and positive predictivityfor all the signals. (b) Distribution of sensitivity and positive predictivity whenonly the sparse representation based method has been used (27 signals).

TABLE II. RESULTS FOR DETECTION ON SINGLE CHANNELS (FIRSTMINUTE OF SIGNALS FROM DATASET [7].)

Channel 1 Channel 2 Channel 3 Channel 4r01 ! 93.80 99.22 99.22 99.22

"+ 89.63 93.43 99.22 100r04 ! 45.60 92.00 76.00 81.60

"+ 37.75 93.50 73.64 76.11r07 ! 39.37 89.76 85.83 83.46

"+ 39.37 93.44 80.15 80.30r08 ! 89.39 96.97 98.45 99.24

"+ 86.76 92.75 99.24 98.49r10 ! 90.63 92.97 51.56 81.25

"+ 86.58 82.64 56.41 78.20

sampled at 1 kHz, but using a variety of instrumentation withdifferent frequency responses, resolution and configuration.Results form this dataset (discarding records a38, a47, a52,a54, a71, a74 with inaccurate annotations) are summarised inFig. 5(a). The boxplot reports the obtained distributions for thesensitivity and positive predicivity values, with median valuesfor sensitivity equal to ! = 97.5% and for positive predictivity#+ = 96.2%, while the average values are ! = 91.5% and#+ = 91%. For comparison, similar complexity proceduresevaluated in [2], and using Template Subtraction techniques orICA, followed by a standard peak detector, achieve sensitivityvalues ! = 82%, and ! = 69.1%, respectively. The proposedmethod with no $! − %&' was able to directly detect fetalbeats in 27 out of 69 traces, with average ! = 96% and#+ = 95.5% on this subset, Fig. 5(b).

Application to single trace signals has been also investi-gated, using each lead signal belonging to dataset [7]. Resultsreported in Tab. II show an average sensitivity of about 85%,which is less than the sensitivity obtained with the multi-channel procedure (! = 92.45% ) due to the poor qualityof some signals (e.g., r07, Channel 1).

Finally, we applied the proposed technique to dataset [7] byusing 2 s long observation windows, considering multi-channeldetection without $!−%&'. In Tab. III, we report the averagesensitivity and positive predictvity values for all signals, aswell as the average computation time for each window (about0.17 s, on an Intel Core i7 processor, equipped with 16 GBmemory, simulations in Matlab). The results are comparableto those obtained with 1 min long windows, and show thatreal-time implementation with a small 2 s delay is possible.

V. CONCLUSIONIn this paper, we proposed a new method for the de-

tection of fetal beats exploiting information from the sparse

TABLE III. SENSITIVITY AND POSITIVE PREDICTIVITY VALUES FORTHE REAL-TIME IMPLEMENTATION OF THE PROPOSED METHOD WITHIN

THE FIRST MINUTE OF SIGNALS FORM DATASET [7]. TIME REQUIRED BYTHE ALGORITHM FOR BEATS DETECTION EVERY 2 S.

mean ! mean "+ mean time% % s

r01 98.63 95.25 0.167r04 85.25 82.22 0.169r07 88.60 85.63 0.169r08 98.90 98.22 0.168r10 87.06 84.39 0.168

representation onto an over-complete Gaussian Dictionary.The proposed method allows to identify beats belonging tothe fetal signal and to distinguish them from the mother’sones. Results of simulations using real data from two publicdatasets have been presented to demonstrate the effectivenessof the proposed methods. Unlike more accurate frameworksthat achieve sensitivity values up to 95.6% [2] working off-line, the one proposed in this paper is suitable for real-time implementation (with a delay of 2 s), thanks to its lowcomplexity.

REFERENCES[1] R. Sameni and G. D. Clifford, “A review of fetal ECG signal processing;

issues and promising directions,” The open pacing, electrophysiology &therapy journal, vol. 3, p. 4, 2010.

[2] J. Behar et al., “Combining and benchmarking methods of foetal ecgextraction without maternal or scalp electrode data,” Physiologicalmeasurement, vol. 35, no. 8, p. 1569, 2014.

[3] R. Almeida et al., “Fetal qrs detection and heart rate estimation: awavelet-based approach,” Physiological measurement, vol. 35, no. 8, p.1723, 2014.

[4] S. Puthusserypady, “Extraction of fetal electrocardiogram using hadaptive algorithms,” Medical & biological engineering & computing,vol. 45, no. 10, pp. 927–937, 2007.

[5] H. Zhang et al., “Semi-blind source extraction algorithm for fetalelectrocardiogram based on generalized autocorrelations and referencesignals,” Journal of Computational and Applied Mathematics, vol. 223,no. 1, pp. 409–420, 2009.

[6] J. Jezewski et al., “Determination of fetal heart rate from abdominalsignals: evaluation of beat-to-beat accuracy in relation to the direct fetalelectrocardiogram,” Biomedizinische Technik/Biomedical Engineering,vol. 57, no. 5, pp. 383–394, 2012.

[7] “Abdominal and direct fetal ECG,” URLhttp://physionet.org/physiobank/database/adfecgdb/.

[8] A. L. Goldberger et al., “Physiobank, physiotoolkit, and physionet com-ponents of a new research resource for complex physiologic signals,”Circulation, vol. 101, no. 23, pp. e215–e220, 2000.

[9] “Noninvasive fetal ECG: the physionet/computing in cardiology chal-lenge 2013,” URL http://www.physionet.org/challenge/2013.

[10] Y. C. Pati et al., “Orthogonal matching pursuit: Recursive functionapproximation with applications to wavelet decomposition,” in Signals,Systems and Computers, 1993. 1993 Conference Record of The Twenty-Seventh Asilomar Conference on. IEEE, 1993, pp. 40–44.

[11] G. Da Poian et al., “Gaussian dictionary for compressive sensing of theECG signal,” in Biometric Measurements and Systems for Security andMedical Applications (BIOMS) Proceedings, 2014 IEEE Workshop on.IEEE, 2014, pp. 80–85.

[12] P. E. McSharry et al., “A dynamical model for generating syntheticelectrocardiogram signals,” Biomedical Engineering, IEEE Transactionson, vol. 50, no. 3, pp. 289–294, 2003.

[13] M. Varanini et al., “An efficient unsupervised fetal QRS complexdetection from abdominal maternal ECG,” Physiological measurement,vol. 35, no. 8, p. 1607, 2014.

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 89.5with TS-ICA 95 94.3 94.7real 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) =1p2⇡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 DetectionGiulia Da Poian, Riccardo Bernardini and Roberto RinaldoDIEGM, 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, D! and D":

Improved Detection Method

Sparse source separation problem

in Abdominal ECG Recordings

s# ∈ {6.3,7,8,9,10,12,15} to build the maternal dictionary D!

s# ∈ {2, 3.5, 4, 4.5, 4.7} for the fetal D" dictionary

Fig. 3 Fetal (red) and Maternal (blu) QRS complexes and their correspondent sparse representation in the proposed dictionary.

(a) (b)

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4

Samples200 400 600 800 1000 1200 1400 1600 1800 2000

Atom

s

1

2

3

4

0.10.20.30.40.50.6

DIPARTIMENTO DI INGEGNERIA ELETTRICA GESTIONALE E MECCANICA

Corso di dottorato in Ingegneria Industriale e dell’Informazione

AREA TECNICO SCIENTIFICA

We propose to apply the ICA [3] directly in the compressed domain to extract the source components from the multi-channel abdominal fECG.

• Find Amix and yS with ICA from y • From yS find s by exploiting sparsity

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

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ICA in COMPRESSED DOMAIN

Compressive Sensing theory [2] is based on the principle that a small number of random measurements are sufficient to capture all the information in a signal having a sparse representation and enable its exact reconstruction.

Compressive Sensing of Fetal ECG

dott. Giulia Da Poian Prof. Roberto Rinaldo dapoian.giulia@spes.uniud.it

rinaldo@uniud.it

ICs in the CS domain

CS measurements

Assessment of fetal health conditions through electrocardiography allows to discover possible distress or congenital heart defects during pregnancy [1]. Our project presents a novel system for the compression and analysis of the Abdominal Fetal Electrocardiogram (fECG) using Compressive Sensing (CS), Independent Component Analysis (ICA) applied in the compressed domain and sparse representations in overcomplete dictionaries.

!!! Low complexity !!! Low power

Time [s]0 10 20 30 40 50 60

Feta

l HR

[bpm

]

100

110

120

130

140

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160

Estimated fetal HRTrue fetal HR

COMPRESSIVE SENSING

RESULTS

CONCLUSIONSOur work proposes a novel framework for the compression of abdominal fECG recordings jointly with real time beat detection and classification. 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 fetal heart rate, providing a suitable solution for low-power telemonitoring applications.

Sparsifiying dictionary

Sparse Binary Sensing 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

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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.

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Distribution of S and P+ values

for the Challenge dataset.

S P+

2030405060708090100

Compression and Beyond

Example of fetal heart rate estimation.

Source signalsMixing Matrix

CS

yS = � D u

y = � x

T = � s

TA

TMIX

x = AMIX s

y = � 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 s# ∈ D" 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