P and T Wave Detection in Electrocardiogram (ECG) Signals

P and T Wave Detection inElectrocardiogram (ECG) Signals

Chao Lin

Seminar SC, June 2011

1 / 53P and T Wave Detection in Electrocardiogram (ECG) Signals

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Outline

1 Context

2 Literature review

3 The proposed Bayesian methodProblem formulationBayesian modelBlock Gibbs samplerSimulation results

4 Application: TWA detection

5 Conclusion and future works

6 Appendix


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Context

Outline

1 Context

2 Literature review




6 Appendix


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Context

Electrocardiogram (ECG)

A recording of the electrical activity of the heart over time

3 distinct waves are produced during cardiac cycle

P wave caused by atrial depolarizationQRS complex caused by ventricular depolarizationT wave results from ventricular repolarization and relax

Wave shapes and interval durations indicate clinically usefulinformation


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Context

ECG delineation

Delineation: determination of peaks and boundaries of the waves

P and T wave delineation−a challenging problem

Low slope and low magnitude

Presence of noise, interference and baseline fluctuation

Lack of universal delineation rule

Waveform estimation


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Literature review

Outline

1 Context

2 Literature review




6 Appendix


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Literature review

Existing methods

Filtering techniques: nested median filtering, adaptive filtering,low-pass differentiation (LPD)


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Literature review

Existing methods


Basis expansions: Fourier transform, discrete cosine transform,wavelet transform (WT)


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Literature review

Existing methods



Classification and pattern recognition: fuzzy theory, hidden Markovmodels, pattern grammar


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Literature review

Existing methods



Classification and pattern recognition: fuzzy theory, hidden Markovmodels, pattern grammar

Bayesian inference: extended Kalman filter


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Literature review

Low-pass differentiation (LPD)

low-passfilter G1(z)ECG

derivativefilter G2(z)

wavedelineation

G1(z) =1 − z−8

1 − z−1, G2(z) = 1 − z−6

Advantages: simple to implement, robust to waveform variations

Drawbacks: sensitive to noise, arbitrary thresholds

P. Laguna et al., New algorithm for QT interval analysis in 24 hour Hotler ECG:

Performance and applications. Med. Biological Eng. and Comput., 1990


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Literature review


0 50 100 150 200 250 300 350 400

−0.1

0

0.1

0.2

k

Amplitude

ecg(k)

y(k)Tpic

Ti

T2

Ht

y(Ti)


N

Literature review


s 4 . 0 4 . 2 4 . 4 4 . 7 4 . 9 5 . 1 5 . 3 5 . 6 5 . 8

ECGDER

(c)

(b)

ECGPB

(a)

ECG

1 m v

R

Pb

P

Pe

QRSb

Q SQRSe

Tb

T

Te


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Literature review

Wavelet transform (WT)

preprocessingECGwavelet

transform

wavedelineation

WT of a signal x (t):

Wax(b) =1√a

∫ +∞

−∞

x (t)ψ

(t − b

a

)dt, a > 0

Discretization of the dilatation factor a = 2k and the translationparameter b = 2k l to form a discrete wavelet transform (DWT):

ψk,l(t) = 2−k/2ψ(2−kt − l), k , l ∈ Z+


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Literature review


Figure: (a) Mallat’s algorithm.(b) DWT without decimation.

Figure: Prototype wavelet ψ(t),which is a quadratic spline andsmoothing function θ(t).

J. P. Martınez, et al., A Wavelet-based ECG delineator: Evaluation on standard

databases. IEEE Trans. Biomed. Eng., 2004


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Literature review



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Literature review


Advantages:

suitable to locate differentwaves with typicalfrequency characteristics

Drawbacks:

require a priori informationon the waveform and widthrigid arbitrary thresholds todetermine the significanceof the wave components


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Literature review

Pattern Recognition

primitivepattern

extractionECG

attributegrammarevaluator

syntactic andsemantic descrip-tion of the ECG

wavedelineation

Advantages: syntactic approach, simple to implement

Drawbacks: insufficient delineation accuracy, sensitive to noise

P. Trahanias et al., Syntactic Pattern Recognition of the ECG. IEEE Trans. Pattern

Anal. Mach. Intell., 1990


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Literature review

Extended Kalman filter

phasecalculation

ECGextended

Kalman filter

wavedelineation

A dynamic Gaussian mixture model to fit ECG:

θk+1 = θk + ωδ

zk+1 = −∑

j∈P,Q,R,S ,T

αjωδ

b2j

∆θj exp

(−

∆θ2j

2b2j

)+ zk + ηk

O. Sayadi et al., A model-based Bayesian framework for ECG beat segmentation. J.

Physiol. Meas., 2009


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Literature review

Extended Kalman filter

Advantages:

sequential Bayesianapproachlight computational load

Drawbacks:

number of Gaussian kernelsknown a priori

difficulties on handlingabnormal rhythms


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The proposed Bayesian method

Outline

1 Context

2 Literature review




6 Appendix


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Signal model for the non-QRS intervals

(c)

(b)

(a) QRS QRS QRS

N NNNN

N

J JJ

JJ

JD

D

D

P,DT,D

P,DT,D

1

1

1

P,1T,1

P,1T,1

2


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P

ECG Signal T−wave

Local baseline P−wave

(c)

(b)

(a) QRS QRS QRS

PT T

N NNNN

N

J JJ

JJ

J

aa

a

a

bb bb

D

D

D

P,DT,D

P,DT,D

1

1

1

P,1T,1

P,1T,1

2

T,i

T,i

T,m

T,m

P,j

P,j

P,n

P,n=1=1 =1=1


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non-QRS signal components within a D-beat window

xk =

L/2∑

l=−L/2

hT,luT,k−l +

L/2∑

l=−L/2

hP,luP,k−l + ck + wk , k∈J ∗,

uT,k = bT,kaT,k : unknown “impulse” sequence indicating T wavelocations and amplitudes,

uP,k = bP,kaP,k : unknown “impulse” sequence indicating P wavelocations and amplitudes,

hT = (hT,−L/2 · · · hT,L/2)T : unknown T waveform,

hP = (hP,−L/2 · · · hP,L/2)T : unknown P waveform,

ck : baseline sequence, wk : white Gaussian noise


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Representation of the P and T waveforms by a Hermite basisexpansion

hT = HαT , hP = HαP ,

H is a (L +1) × G matrix whose columns are the first G Hermitefunctions with G ≤ (L +1)αT and αP are unknown coefficient vectors of length G

Modeling of the local baseline within the n-th non-QRS interval bya 4th-degree polynomial

cn = Mnγn ,

Mn is the known Nn× 5 Vandermonde matrixγn = (γn,1 · · · γn,5)

T is the unknown coefficient vector


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vector representation of the non-QRS components

x = FTBTaT + FPBPaP + Mγ + w , (1)

bT, bP, aT, and aP denote the M × 1 vectors corresponding tobT,k , bP,k , aT,k , and aP,k , respectively.

BT ,diag(bT) and BP ,diag(bP),

FT and FP are the K × M Toeplitz matrices with first row(hT

1 αT 0TM−1) and

(hT

1 αP 0TM−1), respectively.

M, and γ are obtained by concatenating the Mn and γn, forn = 1, . . . ,D.


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Model parameters

Bayesian estimation relies on the posterior distribution

p(θ|x) ∝ p(x|θ)p(θ)

θ = (θTT θT

P θTcw)T are the unknown parameters resulting from (1)

θT , (bTT aT

T αTT)T and θP , (bT

P aTP αT

P)T are T and P waverelated parameter vectors,

θcw , (γT σ2w )T are baseline and noise parameters.

Likelihood function

p(x|θ) ∝ 1

σKw

exp

(− 1

2σ2w

‖x − FTBTaT − FPBPaP − Mγ‖2

),

where ‖ · ‖ is the ℓ2 norm, i.e., ‖x‖2 = xTx.


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Location prior

T wave indicator prior: block constraint

p(bJT,n) =

p0 if ‖bJT,n‖ = 0

p1 if ‖bJT,n‖ = 1

0 otherwise,

Assuming independence between consecutive non-QRS intervals,the prior of bT is given by

p(bT) =D∏

n=1

p(bJT,n) .


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Amplitude and waveform priors

T wave amplitude prior

p(aT,k |bT,k =1) = N (aT,k ; 0, σ2a)

aT,k are only defined at time instants k where bT,k =1,

uT,k =bT,kaT,k is a Bernoulli-Gaussian sequence with blockconstraints.

T waveform coefficients prior

p(αT) = N (αT; 0, σ2αIL+1)

The priors of the P wave parameters bP, aP and αP are defined ina fully analogous way!


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Baseline and noise variance priors

Baseline coefficient prior

p(γ)=N (γ; 0, σ2γI5D)

Noise variance prior

σ2w =IG

(σ2

w ; ξ, η)

Conjugate priors for simplicity

Posterior distribution

p(θ|x) ∝ p(x|θ)p(θ) = p(x|θ)p(θT)p(θP)p(θcw)

Complex distribution


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Block Gibbs sampler

- In a D-beat processing window, for each non-QRS interval:

Sample the T indicator block bJT,n

For the k where bT,k =1, sample the T amplitudes aT,k

Sample the P indicator block bJP,n

For the k where bP,k =1, sample the P amplitudes aP,k

- Sample P and T waveform coefficients αT and αP

- Sample baseline coefficients γ

- Sample noise variance σ2w


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Simulation parameters

Preprocessing: QRS complexes detection using the algorithm ofPan et al. (IEEE Trans. Biomed. Eng., 1985),

Processing window length: D = 10,

For each estimation, the 40 first iterations are disregarded (burn-inperiod) and 60 iterations are used to compute the estimates.

Real ECG datasets from the QT database.

Computation time: 8 seconds to run 100 iterations on a 10-beatECG block (Matlab implementation).

C. Lin et al., P and T wave delineation in ECG signals using a Bayesian approach and

a partially collapsed Gibbs sampler, IEEE Trans. Biomed. Eng., 2010

C. Lin et al., P and T wave delineation and waveform estimation in ECG signals using

a block Gibbs sampler, IEEE ICASSP, 2011


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Typical examples

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

0

0.4

0.8

ECG signal: dataset sele0136(a

)

1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

0.5

1

time(sec)

(b)

Posterior distributions of the P and T−wave indicator locations

0 10 20 30 40 50 60 70

0

0.5

1T−waveform estimation (normalized)

Samples

(c)

0 10 20 30 40 50 60 70

0

0.5

1P−waveform estimation (normalized)

Samples

(d)


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Typical examples

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)

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0.5

1

time(sec)

(b)


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0.5


Samples

(c)

0 10 20 30 40 50 60 70

0

0.5


Samples

(d)

T

T

PTPPP PT T T

P


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Typical examples

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)

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Samples

(c)

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Samples

(d)

T

T

PTPPP PT T T

P


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Typical examples

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)

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time(sec)

(b)


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Samples

(c)

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Samples

(d)

T

T

PTPPP PT T T

P


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Typical examples

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)

1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

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time(sec)

(b)


0 10 20 30 40 50 60 70

0

0.5


Samples

(c)

|peak

|onset

|end

0 10 20 30 40 50 60 70

0

0.5


Samples

(d)

|peak

|onset

|end

T

T

PTPPP PT T T

P


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Typical examples

0 1 2 3 4 5 6 7 8

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(a)

time (s)

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(b)

time (s)


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Typical examples

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(a)

time (s)

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(b)

time (s)


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Typical examples

0 1 2 3 4 5 6 7 8

0

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(a)

time (s)

ECG signalestimated P and T wavesestimated baseline

0 1 2 3 4 5 6 7 8

0

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0.6

(b)

time (s)


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Typical examples

0 1 2 3 4 5 6 7 8

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(a)

time (s)

ECG signalestimated P and T wavesestimated baseline

0 1 2 3 4 5 6 7 8

0

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0.6

(b)

time (s)


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Premature ventricular contraction ECG

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

0

0.5

1

ECG signal: dataset sel803(a

)

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 100

0.5

1

time(sec)

(b)


0 10 20 30 40 50 60

0

0.5


Samples

(c)

|peak

|onset

|end

0 10 20 30 40 50 60

0

0.5


Samples

(d)

|peak

|onset

|end

P P P P PT T T T T T

T P


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Premature ventricular contraction ECG

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

0

0.5

1

Am

p.(m

v)

time(sec)

ECG signalestimated P and T−wavesestimated baseline

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

0

0.5

1

Am

p.(m

v)

time(sec)


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biphasic T wave ECG

4 5 6 7 8 90

0.5

1ECG signal: dataset sele0607

(a)

4 5 6 7 8 90

0.5

1

time(sec)

(b)


10 20 30 40 50

−0.50

0.51

T−waveform estimation (normalized)

Samples

(c)

|peak

|onset

|end

10 20 30 40 50

−0.50

0.51

P−waveform estimation (normalized)

Samples

(d)

|peak

|onset

|end

P

P

T

T T

T

TT T T T TP P P P P P P P


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biphasic T wave ECG

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

0

0.2

0.4

0.6

Am

p.(m

v)

time(sec)


3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

0

0.2

0.4

0.6

0.8

Am

p.(m

v)

time(sec)


N


Absence of P wave

1 2 3 4 5 6 7 8 9 10

−0.6−0.4−0.2

00.2


)

1 2 3 4 5 6 7 8 9 100

0.5

1

time(sec)

(b)


0 10 20 30 40 50 60 70 80 90 100

0

0.5


Samples

(c)

|peak

|onset

|end

0 10 20 30 40 50 60 70 80 90 100

0

0.5


Samples

(d)

|peak

|onset

|end

P

P P

P

PT T T T T T T

T P


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Absence of P wave

2 3 4 5 6 7 8 9 10 11

−0.2

0

0.2

0.4

Am

p.(m

v)

time(sec)


2 3 4 5 6 7 8 9 10 11−0.4

−0.2

0

0.2

0.4

Am

p.(m

v)

time(sec)


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Evaluation on QTDBTable: Delineation and detection performance for QTDB

Parameter Proposed alg. LPD WT

bP: Se (%) 99.60 97.70 98.87

Onset-P: µ± σ (ms) 1.7 ±10.8 14.0 ±13.3 2.0 ±14.8

Peak-P: µ± σ (ms) 2.7 ±8.1 4.8 ±10.6 3.6 ±13.2

End-P: µ± σ (ms) 2.5 ± 11.2 −0.1 ±12.3 1.9 ±12.8

bT: Se(%) 100 97.74 99.77

Onset-T: µ± σ (ms) 5.7 ±16.5 N/A N/A

Peak-T: µ± σ (ms) 0.7 ±9.6 −7.2 ±14.3 0.2 ±13.9

End-T: µ± σ (ms) 2.7 ± 13.5 13.5 ± 27.0 −1.6 ±18.1


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Application: TWA detection

Outline

1 Context

2 Literature review




6 Appendix


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T-wave alternans (TWA) detection

TWA: a consistent fluctuation in the T waves on anevery-other-beat basis

a challenging problem: non-visible (microvolt-level) TWA detection


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Spectral methods (SM):

Consider an aligned ST-T complexes matrix of a 2D-beat window:

T =

T1(1) T1(2) . . . T1(N)

......

. . ....

T2D(1) T2D(2) . . . T2D(N)

Spectral analysis by using periodogram:

Sn(f ) =1

2D|TF(Tk(n))|2 , k = 1, . . . ,D

1

N

N∑

n=1

Sn(0.5) − µ

σ

H1

≷H0

γ

Drawbacks: large window size (2D ≥ 128), sensitive to noise


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Statistical test (ST):

T-wave amplitudes are estimated as follows:

ai = max(Ti (1),Ti (2), . . . ,Ti (N))

µodd =1

D

D∑

n=1

ai , i = 1, 3, . . . , 2D − 1

µeven =1

D

D∑

n=1

ai , i = 2, 4, . . . , 2D

The statistical test can be formalized as:

H0 : µodd = µeven, H1 : µodd 6= µeven

Drawbacks: rough amplitude estimation, strong hypothesis on thedistribution, analysis window size


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Signal model for TWA detection

2D

ECG Signal

Local baseline

odd T−wave

even T−wave

(c)

(a)QRS QRS QRS

J JJ

(b)

QRS

J

o,iae,ja o,ia

e,ma ae,q

N1

o,1 e,1 o,2 e,D

QRS

Je,2

NT,1

1 2 3 4

Figure: (a) T-wave search intervals within the 2D-beat processingwindow. (b) T waves within each non-QRS region. (c) T-waveamplitudes. Here we set NT,n = Nn/2.


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Bayesian TWA detection

Different statistical tests can be carried out on the T-waveamplitudes generated by the proposed sampler.

The two-sample Kolmogorov-Smirnov (KS) test:

H0 : Fo = Fe, H1 : Fo 6= Fe

Fo and Fe are the cumulative distribution functions of the odd andeven T-wave amplitude samples.The KS test statistic is defined as:

s(i) = supx

∣∣∣F (i)o (x) − F (i)

e (x)∣∣∣ (2)

F(i)o and F

(i)e are the empirical distribution functions of a

(i)o and a

(i)e .


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Bayesian TWA detection

The two-sample Student’s t-test:

H0 : µo = µe, H1 : µo 6= µe

µo and µe are the means of the odd and even T-wave amplitudesamples.The t-test statistic can be computed as follows:

t(i) =a(i)o − a(i)

e

S(i)eo

√2D

(3)

a(i)o =

1

D

D∑

j=1

a(i)o,j, a(i)

e =1

D

D∑

j=1

a(i)e,j and

S (i)eo =

√√√√√ 1

2D − 2

D∑

j=1

(a(i)o,j − a(i)

o

)2

+D∑

j=1

(a(i)e,j − a(i)

e

)2

.


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Synthetic TWA signals for evaluation

“ma” noise: muscular activity artifact

“em” noise: electrode motion artifact


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Estimation results

2 4 6 8 10 12 14

−0.1

0

0.1

0.2

0.3

(a)

Am

p.(m

v)

time(sec)

ECG signal estimated odd T−waves estimated even T−waves estimated baseline

0 20 40 60 80−0.1

−0.05

0

0.05

0.1

0.15odd T−wave estimation

Samples

(b)

Am

p.(m

v)

0 20 40 60 80−0.1

−0.05

0

0.05

0.1

0.15even T−wave estimation

Samples

(c)

Am

p.(m

v)


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Test decisions for each iteration

0

0.2

0.4

0.6

0.8

1

ks−t

est d

ecis

ions

(a)

τ = 0, null hypothesis accepted

0

0.2

0.4

0.6

0.8

1

(b)

τ = 0.93, null hypothesis rejected

0

0.2

0.4

0.6

0.8

1

(c)

τ = 1, null hypothesis rejected

0

0.2

0.4

0.6

0.8

1

t−te

st d

ecis

ions

(d)

τ = 0, null hypothesis accepted

0

0.2

0.4

0.6

0.8

1

(e)

τ = 0.82, null hypothesis rejected

0

0.2

0.4

0.6

0.8

1

(f)

τ = 1, null hypothesis rejected

H0

H1

H0

H1

H1

H0

H1

H0

H1

H0

H1

H0

Figure: The KS-test (top) and the t-test (bottom) decisions made forthree different 16-beat windows: (1) no synthetic TWA and SNR=10dB.(2) synthetic 35µv TWA and SNR=5dB. (3) synthetic 35µv TWA andSNR=10dB.


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Detection performance comparison

−15 −10 −5 0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

Det

ectio

n pr

obab

ility

TWA detection rate on real ECG signals with synthetic TWA Valt

=35 µ v

BGS−KS (ma noise)BGS−KS (em noise)BGS−T (ma noise)BGS−T (em noise)ST (ma noise)ST (em noise)SM (ma noise)SM (em noise)

C. Lin et al., T-wave Alternans Detection Using a Bayesian Approach and a Gibbs

Sampler, IEEE EMBC, 2011, to appear


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Conclusion and future works

Outline

1 Context

2 Literature review




6 Appendix


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Conclusion

A Bayesian model for the non-QRS intervals of ECG signals

Gibbs-type samplers for joint delineation and waveform estimationof P and T waves

Evaluation on the QTDB is promising

TWA detection: Bayesian test

Prospects

Exploitation of the waveform estimation, ex., arrhythmia detection

Beat-to-beat / sequential delineation


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Thank you for your attention!


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Appendix

Outline

1 Context

2 Literature review




6 Appendix


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Appendix

Time-shift and scale ambiguities

Issue: No unique solution for a convolution model

Scale ambiguity: h ⋆ u = (ah) ⋆ (u/a), ∀a 6= 0,

Time-shift ambiguity: h ⋆ u = (dτ ⋆ h) ⋆ (d−τ ⋆ u), ∀τ ∈ Z.

Solution: Hybrid Gibbs sampling

Metropolis-Hastings within Gibbs after sampling waveformcoefficients,

Deterministic shifts after sampling waveform coefficients:

Time-shifts to have h′

0 = max |h|,Scale-shifts to have h′

0 = 1,

C. Labat et al., Sparse blind deconvolution accounting for time-shift ambiguity,ICASSP, 2006


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Documents

P and T Wave Detection in Electrocardiogram (ECG) Signals