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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
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health Systems
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)
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health 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 ?
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health Systems
Wavelet Combined Fusion System
Source(H0,H1)
DWT
DataFusionCenter(DFC)
TransientFeatures
LocalDecisions
(LD)
LD
GlobalDecisions
(GD)
Fusion CriterionOptimal operating points
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health Systems
Probability density function (PDF) of linearly combined powers
Powers
Conditional density function for Respiration, Blood Pressure and EEG
School of Biomedical Engineering, Science and Health Systems
Powers and Local Thresholds under ROR and GOR runs
School of Biomedical Engineering, Science and Health Systems
Powers and Local Thresholds under Flight Run
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health Systems
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
School of Biomedical Engineering, Science and Health Systems
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