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Transcript of emd reconstr
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EMPIRICAL MODE DECOMPOSITION BASED
TECHNIQUE APPLIED IN EXPERIMENTAL
BIOSIGNALS
Alexandros Karagiannis
Mobile Radio Communications Laboratory
School of Electrical and Computer EngineeringNational Technical University of Athens
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RESPIRATION MONITORING
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Acceleration Vector
Respiration Mechanism is comprised of
changes in some physical quantitiessuch as :
1. Muscular motion
2. Volume
3. Pressure
4. Flow
Muscular contraction is composed of
1. Low frequency movement related to
the whole contraction (0 - 5 Hz)
2. High frequency component due to
vibrations (2 40Hz)
X,Y,Z components of
acceleration vector
Acceleration
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EMPIRICAL MODE DECOMPOSITIONMethod 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
1. Functions with equal number of extrema and zero crossings (or at most
differed by one)
2. 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
1. Interpolation technique (cubic spline)
2. Sifting process to extract and identify intrinsic modes
3. Numerical convergence criteria (mainly to stop the iterative process of identifying
every IMF as well as the whole set of IMFs)
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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)= d
k(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.
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( ) ( )( )
2
u le t e t
m t
!
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EMPIRICAL MODE DECOMPOSITION
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Mathematical Expression of EMD processed signal
Lower order IMFs capture fast oscillation modes while higher order IMFscapture slow oscillation modes
Criteria used for Numerical Convergence
1. 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)
2. Iteration process ends when the residue r(t) is 10% or lower of the d(t)
IMF set residual
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNALS
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Apply spectral criteria on i-th IMF
EMD processed Experimental Respiratory Signal
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EMPIRICAL MODE DECOMPOSITION BASED
TECHNIQUE ALGORITHM APPLIED ON BIOSIGNALS
Experimental Procedure
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Respirationsignal sampled
from the mote
Respirationimported for
processing
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EMPIRICAL MODE DECOMPOSITION BASED
TECHNIQUE ALGORITHM APPLIED ON BIOSIGNALS
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1. Analog 2-axis Accelerometer
Experimental Setup
2. Multichannel Sampling of X, Y axes.Data are packed in one
Radio message and transmitted
Channel 1Channel 2
(X axis)
Channel 3
(Y axis)
00 FF FF FF FF 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 TimestampmoteIDDestinationAddress
Source
Address
GroupID
handler
3. Code developed in TinyOS-NesC oriented for event driven
applications.
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNAL
Processing Procedure1. Respiration signals were monitored in X,Y axes by measuring the
acceleration
2. Application of the EMD on each axis signal
3. Application of the spectral criteria on each IMF of 2-axes respiratory
signal
3. Evaluation of the EMD based technique was aided by metricscomputation (Cross Correlation Coefficients)
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data
EMD
Set of
IMF
Apply Spectral Criteria on
the IMF set
SelectIMF
Partial Signal
Reconstruction
Metric for overall
performance
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Application of EMD based technique in both X,Y axes signal from the 2-axis
accelerometer.
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNAL
Original Y axis signal
Lower order IMFs
Higher order IMFs
Residual signal
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNALS
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1. 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
2. Axis components (X,Y,Z) magnitude is closely related to the measurement
point selection
3. Y axis component is significantly higher compared to X axis component inmeasurement point 1 and the opposite stands for measurement point 2
X,Y axes components.
Experimental Results
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNALS
Experimental Results
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1. 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.
2. Different frequency ranges and power thresholds result in different IMF
sets.3. 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)
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNALS
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Experimental Results1. 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
2. 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
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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE
ALGORITHM APPLIED ON BIOSIGNALS
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Conclusions1. Empirical Mode Decomposition based technique that utilize the decomposition of
the signal to IMFs in order to apply a Partial Signal Reconstruction process
2. The proposed technique tries to identify and use at the partial signal
reconstruction stage those IMFs that may have a physical meaning.
3. Two stage process of the technique Decision based on the spectral
characteristics of the IMFs (frequency, power)
4. IMFs that satisfy conditions (frequency criterion, power criterion) are considered
for Partial Signal Reconstruction. The others are excluded.
5. Different conditions set by the criteria produce different IMF sets for the Partial
Signal Reconstruction
6. Mode mixing problem does not affect significantly the decision stage because ofthe disparate scales of the IMFs of the EMD processed respiratory signals.
7. 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
8. Future work : MIT-BIH records to apply the technique, lung sounds, Weighed
Partial Signal Reconstruction, Implementation on sensor network node level .
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Thank you
Metamorphosis by M.S.Escher