Empirical Mode Decomposition based Technique applied in experimental biosignals

1. Empirical Mode Decomposition based Technique applied in experimental biosignals Alexandros Karagiannis Mobile Radio Communications Laboratory School of Electrical and Computer Engineering National Technical University of Athens

2. Outline Respiration Signal Monitoring Empirical Mode Decomposition (EMD) EMD based technique proposed in this presentation Experimental procedure - Sensor Network Processing procedure Experimental Results Conclusions Standard Hospital Equipment Miniaturized sensors Biosignal - Respiration Signal

3. Respiration monitoring Acceleration Vector Respiration Mechanism is comprised of changes in some physical quantities such as : Muscular motion Volume Pressure Flow Muscular contraction is composed of Low frequency movement related to the whole contraction (0 - 5 Hz) High frequency component due to vibrations (2 – 40Hz) Acceleration X,Y,Z components of acceleration vector

4. Empiricalmode decomposition Method for processing nonstationary signals and signals produced by nonlinear processes Decomposition of the signal into a set of Intrinsic Mode Functions (IMF) which are defined as • Functions with equal number of extrema and zero crossings (or at most differed by one) • Signal must have a zero-mean Why Empirical Mode Decomposition? To determine characteristic time/frequency scales for the energy Method that is adaptive Nonlinear decomposition method for time series which are generated by an underlying dynamical system obeying nonlinear equations Basic Parts of the Empirical Mode Decomposition • Interpolation technique (cubic spline) • Sifting process to extract and identify intrinsic modes • Numerical convergence criteria (mainly to stop the iterative process of identifying every IMF as well as the whole set of IMFs)

5. Empirical mode decomposition algorithm 1. Local maxima and minima of d0(t) = x(t). 2. Interpolate between the maxima and connect them by a cubic spline curve. The same applies for the minima in order to obtain the upper and lower envelopes eu(t) and el(t), respectively. 3. Compute the mean of the envelopes m(t): 4. Extract the detail d1 (t) = d0(t)-m(t) (sifting process) 5. Iterate steps 1-4 on the residual until the detail signal dk(t) can be considered an IMF: c1(t)= dk(t) 6. Iterate steps 1-5 on the residual rn(t)=x(t) - cn(t) in order to obtain all the IMFs c1(t),.., cN(t) of the signal. The procedure terminates when the residual signal is either a constant, a monotonic slope, or a function with only one extrema.

6. Empirical mode decomposition Mathematical Expression of EMD processed signal Lower order IMFs capture fast oscillation modes while higher order IMFs capture slow oscillation modes Criteria used for Numerical Convergence The sifting process ends (IMF extraction) when the range of the mean of the envelopes m(t) is lower than 1‰ (0.001) of Ci (Candidate IMF) Iteration process ends when the residue r(t) is 10% or lower of the d(t) IMF set residual

7. Empirical mode decomposition based technique applied on biosignals Basic Idea • Partial Signal Reconstruction by appropriate selection of IMFs and exclusion of those IMFs that contribute to the noise contamination and feature distortion of the signal. • Some IMFs of the produced IMF set may have a physical meaning while other IMFs don’t have a physical meaning. How can we select the appropriate IMFs? Application of criteria on each IMF based on the spectral characteristics (frequency ,power) of each IMF corresponding to the spectral characteristics of the signal that we wish to delineate. Decision stage for IMF selection or exclusion. Determination of spectral characteristics of experimental signals • Literature documentation • Statistically identify the spectral content of the experimental signals

8. Empiricalmode decomposition based technique algorithm applied on biosignals EMD processed Experimental Respiratory Signal Apply spectral criteria on i-th IMF

9. Empirical mode decomposition based technique algorithm applied on biosignals Experimental Procedure Respiration imported for processing Respiration signal sampled from the mote

10. Empirical mode decomposition based technique algorithm applied on biosignals ExperimentalSetup Analog 2-axis Accelerometer Multichannel Sampling of X, Y axes.Dataare packed in one Radio message and transmitted 00 FF FFFFFF 10 00 03 00 00 05 07 07 EB 06 0B 05 1F 07 E7 05 FF AC 4B ADC0 ADC1 ADC2 ADC10 ADC11 ADC12 Timestamp Destination Address Source Address GroupID handler moteID Channel 1 Code developed in TinyOS-NesC oriented for event driven applications. Channel 3 (Y axis) Channel 2 (X axis)

11. Empirical mode decomposition based technique algorithm applied onbiosignal Processing Procedure • Respiration signals were monitored in X,Y axes by measuring the acceleration • Application of the EMD on each axis signal • Application of the spectral criteria on each IMF of 2-axes respiratory signal • Evaluation of the EMD based technique was aided by metrics computation (Cross Correlation Coefficients) data Metric for overall performance EMD Set of IMF Apply Spectral Criteria on the IMF set Partial Signal Reconstruction Select IMF

12. Empirical mode decomposition based technique algorithm applied on biosignal Application of EMD based technique in both X,Y axes signal from the 2-axis accelerometer. Original Y axis signal Lower order IMFs Higher order IMFs Residual signal

13. Empirical mode decomposition based technique algorithm applied on biosignals Experimental Results • Decision Stage for the selection of appropriate IMFs computes the mean power of the N max power peaks in order to have a smoother estimate and more precise view of the power spectral density of each IMF • Axis components (X,Y,Z) magnitude is closely related to the measurement point selection • Y axis component is significantly higher compared to X axis component in measurement point 1 and the opposite stands for measurement point 2 X,Y axes components.

14. Empirical mode decomposition based technique algorithm applied on biosignals Experimental Results Adaptive power threshold criterion (based on the max mean power and minimum mean power of each IMF) produces a smaller number of IMFs suitable for partial signal reconstruction. Rigid power thresholds (based on the minimum of mean power of all IMFs) produce greater IMF set. Different frequency ranges and power thresholds result in different IMF sets. IMF sets produced by the adaptive power threshold stage suitable for partial signal reconstruction have smaller correlation with the original axis signal without compromising the characteristics of the signal. (Trade Off)

15. Empirical mode decomposition based technique algorithm applied on biosignals Experimental Results High frequency denoising due to removal from the IMF set of the lower order IMFs is accomplished without altering the characteristic attributes of the signal Adaptive power threshold stage is more effective in filtering after the partial signal reconstruction rather than rigid power thresholds. This is due to the smaller IMF sets. Measurement point 2 X axis Measurement point 2 Y axis

16. Empirical mode decomposition based technique algorithm applied on biosignals Conclusions Empirical Mode Decomposition based technique that utilize the decomposition of the signal to IMFs in order to apply a Partial Signal Reconstruction process The proposed technique tries to identify and use at the partial signal reconstruction stage those IMFs that may have a physical meaning. Two stage process of the technique – Decision based on the spectral characteristics of the IMFs (frequency, power) IMFs that satisfy conditions (frequency criterion, power criterion) are considered for Partial Signal Reconstruction. The others are excluded. Different conditions set by the criteria produce different IMF sets for the Partial Signal Reconstruction Mode mixing problem does not affect significantly the decision stage because of the disparate scales of the IMFs of the EMD processed respiratory signals. EMD demands high computational and memory resources. A preprocessing stage prior to the application of the technique reduce time and resource demands without compromising signal quality Future work : MIT-BIH records to apply the technique, lung sounds, Weighed Partial Signal Reconstruction, Implementation on sensor network node level .

17. Thank you Metamorphosis by M.S. Escher