Online exercise ECG signal orthogonalization

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Online exercise ECG signal orthogonalization

Conference Paper

· October 1996

DOI: 10.1109/CIC.1996.542517 · Source: IEEE Xplore CITATIONS

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Onlline Exercise ECG Signal Orthogonalization

Rurali Acar arid

TIayrettin

Kiiymeri

Billieiit Uiiiversity, Dept. of Electrical

and

Electronics Engineering, Ankara

,

Tuxltey

Abstract

Iii t h i s p a p e r a n e f i c i e n t m e i h o d of m a k i n g use oj -the reduii,daiecy in s t a n d a r d 12 lead ECG sigiials t o e l i m i n a t e n o i s e is described. T h e naelhod i s based o n o r t h o g o n a l i z a t i o n v i a o n l i n e S i n g a l a r V a l u e D e c o m p o - s i t i o n (SVD). Its a p p l i c a t i o n as a f i l t e r t o r e m o v e F M C

n o i s e aiid b a s e l i n e w a n d e r a r e e x p l a i n e d . il coinparu- % w e s t u d y of ST a i d y s i s resudts of o r i g i n a l a n d p r o - cessed exercise EGG d a t a is r e p o r t e d .

1.

hit

roductioii

Exercise electrocardiogram

(ECG)

is cont,ainiiiat,cd by

EMG

iioisc aiid Ixseline wander

(BW).

Storage oE

data constitutes a. prohlem because this requires high storage capacity.

Several techniques were reported in the literature t o enhance t h e exercise ECG signals [l]. All o l them are based on solme sort of composite heat, formation.The iiiaiii object,ive iii thest: a.pproaclies is t o disregard the outliiier sample values a n d filter out t h e noise which i s assumed to b e stationary and uncorrelated with t h e sig- nal. Averaging a n d median filtering are two basic tecli- niques applied with this objective. However these as-

suniptioiis are t o o restrictive and usually rnost of them are coiri[,irl,atioiially involved.

Our algorit,hin

[a],

ton the otlier hand

,

is a recur-

sive one which approxiinates Singular Valuc? Decoinpo- sit,ion (SVD) first proposed by Vnnderscliool et.al. [3], t,o seperate fetal ECG from inaternal ECG signals. 'This approach is employed jii tlie presented work t o reiliovc redunda.ncy by t h e ort,hogorralizatiorl of input s i g n d s . Thus all the information conta.ined in t h e input sig- nals is represented in a, fewer iiumber of output signals. Since these signals are orthogoiial t o each other, no

redundancy exists in the o u t p u t signal set.

2 .

Basis Of

The

Algorithm

T h e d g o r i t h m is based on t h e online approximation

oi SVD of a matrix

.

M E R F x " . SVD of M is given in [4] as

U'MV x: (1)

U U T = U V J = I ,

,

VV'=I,, (2)

from which we can establish tlic relation 1xtwec.n S V D

of M a n d eigenvalue decoiupositioii ol' MMT as

where

r = rcln.k(lM) (12)

( 1 3 )

U = [UrllTn]. (14)

B = [SI . . . s,.O.. .O]

n

Zeros i n

W

are subst~itut~cd for noise c,haniiels.

IS,.

cor- responds

-

t o Iiigh singular vallles u i d slmiis thc signal space. U,, is its orthogoiml coitirp1eiiit:nt ant1 slia..iis tlie noise space. Q; is the Giveii's Rotkition niat,rix t h a t makes an off diagonal element of B; zero

[4].

l h e max- iinurn off dia.gona1 element of B; is chosen tmo he inade zero a t each stcp in the above algorithm. inti is t h e input signal vector at, h i e instant i . s f corresponds t o the decomposed signal set at t h a t instant. mi is

thc reconstructed signal set. Figure 1 shows t h e input and the decomposed signal sets. The first r channels ( = 2 in the example ) are t h e projections of input channels onto the subspacc spmiierl b y U,. (st:e Q u a , -

tion l4).'l'hese iiialte t i p t h e signal space. T h e rest of the tlecoiriposccl sigrials-a.rc t h c project,ions onto t h e noise space spanned b y Upl.

-

3.

Noise

Eliiiiiiiatioii

INPUT

In t,he following describe our online noise detection algorithm developed aiid tested on real d a t a .

In geucral, t h e algorithm is capable o f mapping noise a n d ECG onto orthogonal subspa.ces, the signal space aiid the noise space as mentioned before. However in some ca.ses shift#s between t h e two subspaces can occur a n d noise can be seen in t h e signal space. T h e rea,son for this differs.

It

inay be due to high amplitude noise, low amplitude long lasting noise, noise in the major- ity of input channels, and noise in an important input cha.nne1. Noise det,ection a.nd eliinina.tion is clone t o avoid sucli interferences into t h e signal space.

T w o methods are developed for this purpose. High amplitude noise causes u i ’ s

( i

5

r a n k ( M ) ) which de- fine the projection o€ the input signal set onto si, to

rotate significantly. ‘[’he direction of rotation is such t,liat t,he component of ui corresponding t o the iioisy input channel experiences t h e highest increase in ab- solute value. As a result ui begins to m a p iioise onto the signal space. To preserve orthogonality some

ECG

signal is also mapped onto t h e noise space. Setting

a, rotmation angle threshold for iii’s t h a t span t>he sig- na,l space, we let them rotate within some limits so as

not t o ca.use any interfcreiice bet,ween subspa.ces as ex- pla,iiied above. Whciiever this threshold is violated, the noisy input chaiiiiel is determined for the components

of U;.

Low amplitude noise is directly mapped oiit,o t,lie

noise space. Ilowever if tlie noise in tlie input lasts

€or a long time, the energy colitsent of t h e o u t p u t noise clmnnel begins to increase considerably depending on t,he value of cy. Aft,er a while, tlie diagonal entry of C corresponding to t h a t noise channel reaches a signifi- cant fra,ction of the one corresponding t,o t h e smallest signa.1 cha.iine1. This causes a rotation o f U; sucli t,liat tlie noise is projected onto tlre signal spa.ce. ‘This is a. sirni1a.r result as in high aniplit,ude noise. However, these rot,atioiis a.re slower and ca.nnot be detected by observing t h e rotat,ion angle of iii. Rather, the accu- mulation can he detec,t>ed by observing the dia.goiia1 entries of C . When it is detected, the component of i i i ,

mapping that pa.rticular noise, which is t h e greatest, in absolute value sliows the iioisy input channel.

I h v i n g determined t,he noisy input channel, t h e cor- responding row a n d left niost column of U are deleted together with t h e la.st row and column of C . This cor- responds to excluding t,he noisy input chnnnel froin the input, dat,a set, decrea.sing the dimension by one, disre- garding t h e sinallest

SVD

o u t p u t channel.

These input channels. excluded from the decompo- sition, are clieclted via. c,ross corre1at)ioii of QFLS coni-

Time ( sec ) (a) SVD Decomposition -1500 0 0 5 1 1 5 2 2 5 3 7 5 4 4 5 5 Time ( s e c ) 01)

Figure 1 8 charinel (a)Lnput

,

(b)SVD O u t p u t s

plexes t o detect whether tlie noise has disappeared. T h e segiiieiits of the noisy input channel t o be cross

correlated are chosen from the cleaii input clianiiels’

QRS containing portions by time aligiiinent. If‘ a high correlation occurs then t,lint cliaiiiiel is included in t h e input d a t a set t,o lie decoiiiposed. ’l’his i s done by in- creasing t,lie dimension by recovering old U and C used j u s t before the most recent tliriieiisioii reductlion.

4.

Observatioiis

Exhaustive a,nalysis o f exercise ECC; da.ta records from 23 pa.tient,s showed t,Jiat, rank of M is generally

two a n d in f e w cases a third channel is seen in which colisiderable amount of‘ QR.S iiiformatioii exists.

High noise coizt,aiiiiiiat,ioii of tlir signal cliaiiiiels were observed in case of noisy DII. ‘This indicates t1ia.t DIT

i s the channel tliat is tlie lcast correlated cha.nne1 with

substitutcd by signal content in other channels. This is due t o its spatial position on the body. Recordiiig

DIII independently will help improving this unique de- pendence on DIT and increase the noise imrnuiiity by adding further redundancy t o the input set.

'The f o r g e t h g h c t o r ,

a ,

determines how far the algorithm remembers past d a t a .

It

affects the set- tling time a.nd noise a.ccuniulation. As a gets higher, the probability of passing noise accumulation thresh- old falls, i.e. low power noise is mapped onto the noise space for longer periods. T h e decrease in the adaptive nature of the algorillim is a dra.wbacli for high C Y . As a gets lower, imniunity to noise is lost. If it is too low,

ECG cannot lie preservlxl in the signal space even in the absence of noise. Be'cause the a.lgoritlim cmiiot re- member past d a h at a.11 and is extraordinarily seiisitive t o the input. As a. result, Q R S complexes cause high

rotations of ui's iiiuch like high amplitude noise does. Good results were obta.ined with a

=

1

-

2-13.

T h e algorithm is sensitive t o DC levels. DC compo- nents behave like independent signal sources. 'The rank

of M increases t o accomplish this. This means inore

QRS containing cliannels are seen a t tlie output. 'They do not c o n h i n signals with different morphologies but

the same signals with different I)C levels. 'l'he only information they add t o the decomposed signal set, is the DC value. A first order Butterworth high pass fil-

ter with a cut-off frequency of' 0.7 Hz is applied t o the input si& t o assure a zero DC level. Since the order of tlie filter is low, it do" not affect the morphology of

ECG.

T h e third signal chainnel, when exists, i s a low a n -

plitude channel. It is not immune to noise as much as

other output channels. To overcome this problem, a limit is enforced on the speed of the rotat,ion of 113.

It can he observed t h a t the algorithm is capable of sepera.ting EMG noise and BW, rpovided that the for- getting €actor is chosen properly. 'rhe decomposed sig- nal sets ca.n be seen in Figure 2.

5 .

ST Aiialysis

ST segment's potential level measurements were done both on the origiiial aiicl reconstructed d a t a sets a t two points, BO and SO m s after QRS. ECG records in Fig-

ures 3 and 4, which are 14:40 min. and 21:40 inin. long respectively, are sampled a t 500 sainples/sec. ST iiieasiireinents were take11 on average heat>s of succes- sive 20 sec. episodes. D a t a in Figure 3 is taken from

ECG with ST level variation and has 44 d a t a points.

Data. i n Fignre 4 is t,al.:en horn ECG without S T level

variat,ion and has 65 data points. T h e measureinent>s were c,oinpaied iisiiig linea,r regression analysis for each

500 0 -500 -2500 -

2z-y-j

-t u 0 1 2 3 4 5 6 7 8 9 10 Time ( sec ) SVD of ECG slor~als 0 -500 -1000 -1500 2000 -2500 0 I 2 3 4 5 6 7 a 9 10 Time ( s e c )

Figure 2: ( a ) SVD Of ECG With U W

(b) SVD Of ECG With EMG

channel. ?'he model used is y j = U x "ui

+

b , where

yi's and xi's are

ST

measureinelits of original and re- constructed d a t a , respectively. I n the d a t a with ST

level shifts, a line with a slope close t o 1 is fitted by

MINITAB.

S'r

iiieasurements on channel DIT, which is the hardest t o reconstruct are compared in Figures 2 and

1.

T h e regression lines in Figure 3 aiitl 4 are

yi = 0.991 x xi -

0.028

and yi =: 0.913 x zi-

0.018).

In the d a t a from normal ECG, which has d m o s t constant

S'r

levels, no line is fitted, however, ,the ST measure- ments in both dat,a sets are almost equal (see Figure 4). T h e enhancement in ECG is clear w h m the iiuinber of

QRS complexes included in the iiieasurements are com-

pared. For the d a t a in Figure 3 the number of QRS

complexes accepted in DII are 1625 and 1765 for orig- inal and reconstructed signals respectively. They are 1004 and 1058 for the dat,a in Figure 4 . Ally disconti- nuity in the ST measureiiiciits iii the original data. due I,O high noise are removed in tlie reconstructed data.

Comparison 01 STBO measurements 0 1 5 - 0 1

-

> 0 0 5 - 0 - p 0 -

-

_{-0 0 5} - t -0 1 ~ - 0 1 5 - -0 2 - 0 2 - 0 1 5 - 0 1 -005 0 0 0 5 0 1 0 1 5 0 2

ST shill in reconstructed DII (mV)

Figurc 3:

ST

~iiea~urements from abnormal ECG

Comparison of ST60 measurements 0 1

-

> - 0 0 5 - 0 - p 0 -

-

;

-0 05 b -0 1 - x *.x x x 1 -0 151

-I

-0 2 -02 -075 - 0 1 - 0 0 5 0 0 0 5 0 1 0 1 5 0 2 ST shift in reconstructed DII (mV)

Figure

4:

S7’ measurenlents from normal

ECG

7.

References

A new approach for online noise elimination in ex-

ercise ECG sigiials is described. It is based on t h e redundaacy iii standard 12 lead ECG signals. I t is observed tjliatl signal c.omponents can be represented in 2 diineiisioiial space with preserving arryhthniic n-ior- phologies. Original signals can be reconstructed with- out noise and totally lost cliaiiiiels can be constructed providing a non-stop exercise t,est.

This algorithm improves data. compression by pro-

viding noise-free ECG signals which can be compressed

more eflic,iently. T h e most, important improvement, is the inforniation compression. If t h e analysis of ECG

is done 011 t,lie decomposed signal set, which is guaran-

teed to contain all the informatioii, then keeping this redmed dimensional signal set would be enough, which provides a compression of 1 to 4. As a first step, QRS

detection on decomposed signals was done by Caglar

[5].

Further research is needed on arrylltllmia detect,ioil and classification on t,liese low dimensional orthogonal

ECG signals.

Afoiiso

V.X.,

Toiiipkins W . J . , Nguyeii T.Q., Michler li., Lilo S . , “Comparing stress ECG eiiliaiicement al- gorit,hnis,” IEEE EMB M a g a z i n e , vol. 15, No. 3,pp. 37-44

,

M a y / J u i i e 1 9 9 6 .

Acar

B.

~ “Singu1a.r value decomposition based online

ECG signal orthogorialization,” To lie s u b m i t t e d as an

M.S. T h e s i s t o B i l k e n t U n i v e r s i t y ! i l n k a r a , Turkey,

Sept,ember l99G.

Vsnderschoot, J., e t al. “Two nietlrods Tor opt.imal

MECG elimination a n d FECG det,ectioii from skin elctrode signals,” IEEE Trun,s. O n Uiornedical Eny.,

vol. BME-34, No. 3 , pp. 233-242, March 1987. Goliib G.H., Va.n Loan C.F., “Matrix Computations,”,

Jolm IIopkins University Press, Baltimore, 1989. <!.@Jar I<., .‘QRS dctec1,ioii 011 01 t8hogoiialized signals,”

To be strbmitted a s r i n Al.S. T h e s i s t o Bilkent 1Jniver-

s i t y , A n k a r a , Tuvkey, Sept.emher 1996. Address for correspondence:

Bilkent University

Eng. E‘ac. EE Dept,. 06533 Ankara Turkey

tel/fax: ++90-312-2664307 e-mail: b u r a k a ~ e e . h i 1 k e n t . e d u . t ~

240

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