school of biomedical engineering, science and health systems application of wavelet based fusion...

School of Biomedical Engineering, Science and Health Systems

APPLICATION OF WAVELET BASED FUSION TECHNIQUES TO PHYSIOLOGICAL MONITORING

Han C. Ryoo,

Leonid Hrebien

Hun H. Sun

School of Biomedical Engineering, Science and Health SystemsDrexel University, Philadelphia PA. 19104

February 10, 2001


Motivation

1. High rates of false alarm in current monitoring systems

2. Very little research on physiological state monitoring by signal-level data fusion

3. Difficulties to realize fusion system due to observations often dependent from sensor to sensor in practical cases

4. No research about which fusion criterion is optimal under various input statistics - why or when ?

5. Lack of unifying rule to find optimal combination of local thresholds


Binary Decision Problems

0H : f (k) =n(k)

1H : f (k) = s(k) +n(k)

S (k) : samples of input signaln (k) : additive noise, N (0, 0

2σ )

Source(H0, H1)Decide

H1

DecideH0

DecisionRule(R )

zProbabilisticTransitionMechanism

ObservationSpace

R(z) = H1R(z) = H0

τAccept H0Accept H1P(H0/H1)H1 : P(α/H1)ThresholdMiss ProbabilityFalse AlarmP(H1/H0)H0 : P(α/H0)

Cost function

CF = C00 P(accept H0, H0 true) + C01P(accept H0, H1 true) + C10P(accept H1, H0 true) + C11P(accept H1, H1 true)


Likelihood Ratio Test and Minimal Error CriterionLikelihood Ratio Test

Minimum error criterion

C00 = C11 = 0C10 = C01 = 1

p(z / 1H )

p(z / 0H )

1H

><

0H

( 10C − 00C )P( 0H )

( 01C − 11C )P( 1H )

p(z / 1H )

p(z / 0H )

1H

><

0H

P( 0H )

P( 1H )

D = f ( 1D , 2D ,..., KD )

f ( 1D , 2D ,..., KD / 1H )

f ( 1D , 2D ,..., KD / 0H )

1H><

0H

T T =

P( 0H )( 10C − 00C )

P( 1H )( 01C − 11C )

P( 1D , 2D ,..., KD / 1H )

P ( 1D , 2D ,..., KD / 0H )=

P( iD = +1/ 1H )

P( iD = +1/ 0H )+1U∏

P( iD = −1/ 1H )

P ( iD = −1/ 0H )−1U∏ =

idP

ifP+1U∏

(1−idP )

(1−ifP )−1U

∏

,

Multi-Sensor (distributed) Fusion Systems

1. Fixed fusion rule --> optimal local threshold ? 2. Fixed local threshold --> Optimal fusion rule ? 3. Varying fusion rule --> varying local threshold ?

Applying various fusion rules to all subjects- not possible

We fix fusion rule and operate it optimally

Typical issues in fusion systems


Problems of General Fusion Theory applied to Biological Signals

• Heavy constraints : the same volume of observations and identical statistics

• Little work on nonstationary (biological) signals

• No comparative data from real biological phenomena

• Analytical work and numerical simulations

• nonidentical statistics and individual differences in human physiology

• Which fusion rule and why optimal ?


Wavelet Transform Method f (t) : input signal, j, k : dilation (Scale) and translation index : orthonormal scaling and wavelet filter coefficients related by orthogonalityW : details or wavelet coefficients = DWTA : Approximation

f (t) = j,kAk∑ j,kφ

j∑ (t) + j,kW

k∑ j,kϕ

j∑ (t)

j,kW = f (t), j,kϕ

j,kA = f (t), j,kφ

SamplingFrequency = 1000 Hz

ScalesFrequency (Hz)123250 ~ 500125 ~ 25062.25 ~ 125

Time-Frequency (time-scale) Description

τ- j time

Sca

le

j

j = 1j = 2j = 3

j = 4


Wavelet Combined Fusion System

Source(H0,H1)

DWT

DataFusionCenter(DFC)

TransientFeatures

LocalDecisions

(LD)

LD

GlobalDecisions

(GD)

Fusion CriterionOptimal operating points


Probability density function for Chi-square and Gamma distribution

Degree of Freedom

1248

16

Variance

1248

With different degrees of freedom (DOF) Different variances with DOF=3


Indices of System performance at local detectors and Fusion center

jSP

1H><

0H

2 2δ {logT +N log(δ)}2δ −1

FP = LiD − iD

2− iFP

⎛

⎝ ⎜ ⎞

⎠ ⎟

i=1

K∏

KD =−1

+1∑

2D =−1

+1∑

1D =−1

+1∑ U

iD + iD

2iDP

iFP

⎛ ⎝ ⎜ ⎞

⎠ ⎟

i=1

K∏

iD − iD

2iF1 −P

1− iDP

⎛ ⎝ ⎜ ⎞

⎠ ⎟ −T

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

DP = LiD − iD

2− iDP

⎛

⎝ ⎜ ⎞

⎠ ⎟

i=1

K∏

KD =−1

+1∑

2D =−1

+1∑

1D =−1

+1∑ U

iD + iD

2iDP

iFP

⎛ ⎝ ⎜ ⎞

⎠ ⎟

i=1

K∏

iD − iD

2iF1 −P

1− iDP

⎛ ⎝ ⎜ ⎞

⎠ ⎟ −T

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

ReceiverOperating

Characteristics(ROC)

Smooting in Scale

Log Likelihood Ratio

jSP = jρj= 1j

2j

∑ jWP

iFP , iDP

Probability of detectionand false alarm

DOFincreases


Probability density function (PDF) of linearly combined powers

Powers

Conditional density function for Respiration, Blood Pressure and EEG


Powers and Local Thresholds under ROR and GOR runs


Powers and Local Thresholds under Flight Run


Local and Global Decisions


Receiver Operating Characteristics (ROC) Analysis

Respiration (R) Blood Pressure (BP) EEG Fusion Center

PFi PDi PFi PDi PFi PDi PF PD1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1488 1.00000.9824 1.0000 0.9366 1.0000 0.9331 1.0000 0.1388 1.00000.9261 1.0000 0.7394 1.0000 0.8063 1.0000 0.1200 1.00000.7711 1.0000 0.5282 1.0000 0.4965 1.0000 0.0739 1.00000.6092 1.0000 0.4225 1.0000 0.2746 1.0000 0.0409 1.00000.4754 1.0000 0.4225 0.9487 0.1690 1.0000 0.0251 1.00000.3521 1.0000 0.3697 0.9487 0.1690 0.9487 0.0251 0.94870.3521 0.9744 0.3697 0.9231 0.0951 0.9487 0.0141 0.94870.2887 0.9744 0.3099 0.9231 0.0775 0.9487 0.0115 0.94870.2359 0.9744 0.2711 0.9231 0.0599 0.9487 0.0089 0.94870.2359 0.9231 0.2711 0.8974 0.0599 0.9487 0.0089 0.94870.1831 0.9231 0.2465 0.8974 0.0599 0.8974 0.0089 0.89740.1514 0.9231 0.2465 0.8462 0.0563 0.8974 0.0084 0.89740.1514 0.8974 0.2359 0.8462 0.0493 0.8974 0.0073 0.89740.1232 0.8974 0.1901 0.8462 0.0493 0.8974 0.0073 0.89740.0986 0.8974 0.1901 0.8205 0.0458 0.8974 0.0068 0.8974

Respiration (R) Blood Pressure (BP) EEG Fusion Center

PFi PDi PFi PDi PFi PDi PF PD1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1693 1.00000.9930 1.0000 0.7075 1.0000 0.9877 1.0000 0.1673 1.00000.9755 1.0000 0.4694 1.0000 0.9702 1.0000 0.1643 1.00000.9545 1.0000 0.4694 0.9216 0.9317 1.0000 0.1578 1.00000.9282 1.0000 0.3257 0.9216 0.8774 1.0000 0.1486 1.00000.8651 1.0000 0.2329 0.9216 0.8284 1.0000 0.1403 1.00000.7566 1.0000 0.2329 0.7059 0.7828 1.0000 0.1326 1.00000.6165 1.0000 0.1769 0.7059 0.7548 1.0000 0.1278 1.00000.4694 1.0000 0.1331 0.7059 0.7145 1.0000 0.1210 1.00000.3608 1.0000 0.1016 0.7059 0.6795 1.0000 0.1151 1.00000.3608 0.9412 0.1016 0.6078 0.6182 1.0000 0.1047 1.00000.2732 0.9412 0.0806 0.6078 0.5464 1.0000 0.0925 1.00000.2259 0.9412 0.0718 0.6078 0.4799 1.0000 0.0813 1.00000.1926 0.9412 0.0718 0.5294 0.4799 0.9608 0.0813 0.96080.1926 0.9020 0.0613 0.5294 0.4378 0.9608 0.0741 0.96080.1646 0.9020 0.0560 0.5294 0.3975 0.9608 0.0673 0.96080.1313 0.9020 0.0473 0.5294 0.3485 0.9608 0.0590 0.96080.1313 0.8431 0.0473 0.4510 0.3485 0.9412 0.0590 0.94120.1103 0.8431 0.0473 0.4510 0.3117 0.9412 0.0528 0.94120.0963 0.8431 0.0420 0.4510 0.2785 0.9412 0.0472 0.94120.0963 0.8039 0.0420 0.3922 0.2504 0.9412 0.0424 0.94120.0823 0.8039 0.0350 0.3922 0.2504 0.9020 0.0424 0.9412

RespirationBlood PressureEEG

RespirationBlood PressureEEG

max(PF) when PD=1min(PF) when PD=1


Results : Numerical False Alarm (FA) at Local Sensors and Data Fusion Center (DFC)

Gz Profile Parameters Respiration Blood Pressure EEG DFC

ROR/GOR FA 11.96 39.72 14 1.54

SE 5.59 10.72 5.83 0.81

Flight RUN FA 39.54 42.47 32.22 7.29

SE 5.62 3.69 3.87 2.05

Overall +Gz FA 31.66 41.69 27.01 5.85

SE 5.08 3.88 3.65 1.6

(SE : Standard Error, All units are in %)

False Alarm Reduction : 10- 38 % during ROR/GOR Profiles 25-35 % during Flight Run 21-36 % During Overall Run


Conclusion

• Our fusion system, a combination of wavelet transform and general fusion system, gives significant improvement in system performance for physiological state monitoring

• Minimum error criterion

- optimal fusion rule for different variable statistics

- can be realized by a combination of AND and OR rule

- robust to sensor failure

• No harm with more number of poor local detectors

• A unifying rule to find optimal combinations of local thresholds are adaptively applied to all subjects

• Identical detectors are employed to process complex biological signals

containing various features


Recommendation for Future Works

• Other fusion criteria need to be tried– which criterion and why optimal ?

• Conditions to operate fusion system optimally

has to be found under various input statistics

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