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February 10, 2001. APPLICATION OF WAVELET BASED FUSION TECHNIQUES TO PHYSIOLOGICAL MONITORING. Han C. Ryoo, Leonid Hrebien Hun H. Sun School of Biomedical Engineering, Science and Health Systems Drexel University, Philadelphia PA. 19104. 1. Motivation.
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February 10, 2001 APPLICATION OF WAVELET BASED FUSION TECHNIQUES TO PHYSIOLOGICAL MONITORING Han C. Ryoo, Leonid Hrebien Hun H. Sun School of Biomedical Engineering, Science and Health Systems Drexel University, Philadelphia PA. 19104
1 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
2 Binary Decision Problems S (k) : samples of input signal n (k) : additive noise, Cost function CF = C00 P(accept H0, H0 true) + C01P(accept H0, H1 true) + C10P(accept H1, H0 true) + C11P(accept H1, H1 true)
3 Likelihood Ratio Test and Minimal Error Criterion Likelihood Ratio Test Minimum error criterion C00 = C11 = 0 C10 = C01 = 1 Multi-Sensor (distributed) Fusion Systems , Typical issues in fusion systems Applying various fusion rules to all subjects - not possible We fix fusion rule and operate it optimally 1. Fixed fusion rule --> optimal local threshold ? 2. Fixed local threshold --> Optimal fusion rule ? 3. Varying fusion rule --> varying local threshold ?
4 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 ?
5 Wavelet Transform Method f (t):input signal, j, k : dilation (Scale) and translation index f, j : orthonormal scaling and wavelet filter coefficients related by orthogonality W : details or wavelet coefficients = DWT A : Approximation Time-Frequency (time-scale) Description Dw = 2 j Scale Sampling Frequency = 1000 Hz j = 4 j = 3 j = 2 j = 1 time Dt = 2- j
6 Wavelet Combined Fusion System Local Decisions (LD) Transient Features Global Decisions (GD) DWT LD Data Fusion Center (DFC) Source (H0,H1) Fusion Criterion Optimal operating points
7 Probability density function for Chi-square and Gamma distribution With different degrees of freedom (DOF) Different variances with DOF=3 Degree of Freedom Variance 1 2 4 8 1 2 4 8 16
8 Indices of System performance at local detectors and Fusion center Smooting in Scale Receiver Operating Characteristics (ROC) DOF increases Log Likelihood Ratio Probability of detection and false alarm
9 Probability density function (PDF) of linearly combined powers Conditional density function for Respiration, Blood Pressure and EEG Powers
10 Powers and Local Thresholds under ROR and GOR runs
11 Powers and Local Thresholds under Flight Run
12 Local and Global Decisions
13 Receiver Operating Characteristics (ROC) Analysis Respiration Blood Pressure EEG max(PF) when PD=1 min(PF) when PD=1 Respiration Blood Pressure EEG
14 Results : Numerical False Alarm (FA) at Local Sensors and Data Fusion Center (DFC) (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
15 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
16 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