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 Systems Drexel University, Philadelphia PA 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  S ( k ) : samples of input signal n ( k ) : additive noise, Cost function CF = C 00 P(accept H 0, H 0 true) + C 01 P(accept H 0, H 1 true) + C 10 P(accept H 1, H 0 true) + C 11 P(accept H 1, H 1 true)

School of Biomedical Engineering, Science and Health Systems Likelihood Ratio Test and Minimal Error Criterion Likelihood Ratio Test Minimum error criterion C 00 = C 11 = 0 C 10 = C 01 = 1 , 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 orthogonality W : details or wavelet coefficients = DWT A : Approximation  Sampling Frequency = 1000 Hz Time-Frequency (time-scale) Description  - j time Scale  j j = 1 j = 2 j = 3 j = 4

School of Biomedical Engineering, Science and Health Systems Wavelet Combined Fusion System Source (H 0,H 1 )  DWT Data Fusion Center (DFC) Transient Features Local Decisions (LD) LD Global Decisions (GD) Fusion Criterion Optimal operating points

School of Biomedical Engineering, Science and Health Systems Probability density function for Chi-square and Gamma distribution Degree of Freedom Variance 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 Receiver Operating Characteristics (ROC) Smooting in Scale Log Likelihood Ratio  Probability of detection and false alarm DOF increases

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 Local and Global Decisions 

School of Biomedical Engineering, Science and Health Systems Receiver Operating Characteristics (ROC) Analysis  Respiration Blood Pressure EEG Respiration Blood Pressure EEG max(P F ) when P D =1 min(P F ) when P D =1

School of Biomedical Engineering, Science and Health Systems Results : Numerical False Alarm (FA) at Local Sensors and Data Fusion Center (DFC)  (SE : Standard Error, All units are in %) False Alarm Reduction : % during ROR/GOR Profiles % during Flight Run % 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 

School of Biomedical Engineering, Science and Health Systems 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 