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Heart Sound Background Noise Removal
Haim AppleboimBiomedical Seminar
February 2007
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Overview
Current cardiac monitoring relies on EKG
EKG provides full information about the electrical activity but very little information about the mechanical activity
Echo provides full info about the mechanical activity
Echo can not be used for continuous monitoring
Heart Sounds may provide information about mechanical activity
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Overview
Monitoring heart sounds continuously in non clinical environment is difficult due to background sounds and noise both externally and internally
This work introduces a method for removal of internal (and external) background sound such as speech (of the patient)
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Overview
Heart Sounds are vulnerable to sounds created by the monitored person due to significant overlap in frequency with speech
Thus, filters are less effective in removing the noise
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Existing solutions
Single sensor solutions
Multi Sensor solutions
Existing Solutions - Time-Varying Wiener filtering
- Wavelet- Other filter denoising
- Spectral Subtraction
Advantages - Easy- Convenient
- Good noise removal
Disadvantages - Poor noise removal - Inconvenient
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A novel approach based on ICA
ICA: Independent component analysis is a general method for blind source separation.
It has not been used in the context of heart background sound removal
We shall demonstrate its superiority over other methods.
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ICA (Independent Component Analysis)
Sound ASound A
Sound BSound B
Sound CSound C
x = As
S1
Sm-1
Sm
Each sensor receives a linear mixture of all the signal sources
It is required to determine the source signals
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ICA definition
ICA of a random vector X consists of estimating the following generative model for the data:
The independent components are latent variables They cannot be directly observed
The independent components are assumed to have a non-Gaussian distributions
The mixing matrix is assumed to be unknown
All we observe is the general vector x and we must estimate both A and s using it
ii sasAx
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Independent Components Computation
After estimating the mixing matrix A we can de-mix by computing it’s inverse:
Then we obtain the independent components (de-mix) simply by:
1AW
xWxAS 1
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Principles of ICA Estimation
The fundamental restriction in ICA is that the fundamental components must be non-Gaussian for ICA to be possibleThe Linear combination of independent variables is more Gaussian than each of the variablesTo estimate one of the Independent components y let us write:
W is One of the rows of A-1 and should be estimated
Linear combination of independent variables is more Gaussian than each of the variables zTs is more Gaussian than each of the Si The minimal gaussianity is achieved when it equals to one of the SiWe can say that W is a vector which maximizes the nongaussianity of WTX (one of the Independent Components)
i ii
T xwXWy
WAZ T szsAWXWy TTT
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FastICA (Hyvärinen, Oja)
FastICA learning finds a direction: unit vector w, such that the projection wTx maximizes non-Gaussianity FastICA for one unit computational steps:
Choose an initial weight vector If w did not converge go back to 2
FastICA for several unitsTo estimate several independent components the one unit
algorithm must run using several units with weight vectors
To prevent different vectors converging to the samemaxima, after each iteration the outputs must be de-correlated
wxwgExwgxEw TT
www /
xwxw Tn
T ...,,.........1
nww ...,,.........1
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Spectral ICA: performing ICA on a frequency domain signal (Problem when the Spectrum is complex)
Solved using DCT (Discreet Cosine Transform)
Spectral ICA algorithmic flowPerform DCT on the input data
Run FastICA on data after DCT
Perform Inverse DCT
Spectral ICA
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Spectral ICA: Why doe’s it work better?
Spectral ICA attempts to separate each frequency component from different sources (ignoring the delays)
Since the background sound has overlapping spectrum with the HS but with different magnitudes in each channel, it should be easier to separate and remove
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Experimental Setup and Methodology
FilterReorgenize
Data
Set ICAParameters
RunAlgorithmic
Analysis
MeasuredHS
Noise FreeHS
AlgorithmQuality
AssesmentAlgorithm Quality
Recorded Noise
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Quality assessment methods“Human eye” assessment
Algorithmic assessmentFFT plots
Spectrogram plots
Diastole Analysis (Noise Removal Quality)
Diastole Analysis calculation steps:A = ICA Diastole Peaks average
B = NoisySig Diastole Peaks average
Noise Removal Quality = B / A
Algorithm Quality assessment
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Result with Spectral ICA (1)
Time DomainHS file name used in this example is ‘GA_Halt_1’, ICA type is ‘Gauss’, Noise file is ‘count_time’
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Result with Spectral ICA (2)
Time DomainHS file name used in this example is ‘GA_Halt_1’, ICA type is ‘Gauss’, Noise file is ‘television’ Spectral Domain
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Result with Spectral ICA (3)
Diastole (Quite period) analysis resultsHS file name used in this example is ‘GA_Halt_1’, Noise file name used is ‘snor_with_pre’ and FastICA type is ‘Gauss’
Wiener Filter
FastICA
FastICA
Wiener Filter
FastICA
Wiener Filter
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Cases when ICA doesn't work well
Unsuccessful noise removal attempt for a HS with a peak noise caused by microphone movementHS file name used in this example is ‘GA_Halt_1’, FastICA type is ‘Gauss’, Noise file is ‘count_time’
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Time vs. Spectral ICA (1)
HS file name used in this example is ‘Halt_Supine_1’, Noise file is ‘count_time, FastICA type is ‘Gauss’
SpectralICA
TimeICA
SpectralICA
TimeICA
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Time vs. Spectral ICA (2)
Spectral ICA
Time ICA
HS file name used in this example is ‘GA_Halt_1’, Noise file name used is ‘snor_with_pre’ and FastICA type is ‘Gauss’
SpectralICA
TimeFastICA
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Results vs. Nonlinearity
ICA nonlinearity = pow3
ICA nonlinearity = tanh
ICA nonlinearity = Gauss
ICA nonlinearity = skew
HS file name used in this example is ‘GA_Normal_1’, Noise file is ‘count_time’
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Real Noisy Environment Results
1 2
3
Aortic - 2nd ICS RSB
Pulmonic - 2nd ICS LSB
Apex - 5th ICS MSL
HS file name used in this example is ‘HAIM_COUNT_1’, FastICA type is ‘Gauss’
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Summery
we have introduced a practical method for background noise removal in heart sounds for the purpose of continues heart sounds monitoring
The superiority of the proposed method over conventional ones makes it into a practical way of providing high quality heart sound in a noisy environment
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Thank You
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Principles of ICA Estimation (Measures of nongaussianity)
Measures of nongaussianityKurtosis
Negentropy
Minimization of mutual information
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Kurtosis
Kurt (y) = E{y4} – 3(E{y2})2
E{y2} = 1 Kurt (y) = E{y4} – 3
Y Gaussian E{y4} = 3(E{y2})2 Kurt (y) = 0
↓
Therefore kurtosis is 0 for a Gaussian random variable.
For most Nongaussian random variables kurtosis ≠ 0
kurtosis can be both positive or negative.
Typically nongaussianity is measured by the absolute value of kurtosis.
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Negentropy
The entropy of a random variable is the degree of information that an observation of the variable gives. Entropy is related to the coding length of the random variable.The more random the variable is, the larger is it’s entropy.For a discrete random variable entropy is defined as:
H(Y) = -Σ P(Y=ai) · log P(Y=ai)Gaussian variable has the largest entropy among all random variables of equal variance therefore , entropy can be used as a measure of nongaussianity.
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Negentropy
For a continues random variable differential entropy is defined as:
H(y) = -∫f(y)·log(f(y))·dy
Negentropy (modified version of differential entropy) is defined as:
J(y) = H(ygauss) – H(y)
According to the above definition Negentropy is always non-negative and is zero if and only if y has Gaussian distribution.
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Negentropy
Practically the estimation of NEGENTROPY is rather difficult. Therefore we usually us some approximations for this purpose
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Principles of ICA Estimation(Minimization of mutual information)
Definition of mutual information I between m random variables:
I(y1,y2, …,ym) = Σ H(yi)-H(y)
Mutual Information is a measure of dependence between random variables.
It is always non negative and zero if and only if the variables are statistically independent.
For an invertible linear transformation y=Wx we can write: I(y1,y2,…) = Σ H(yi)-H(x)-log|det(w)|
I(y1,y2,…) = Σ C-J(yi)
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Principles of ICA Estimation(Minimization of mutual information)
Finding the invertible transformation W that minimizes the mutual information is equivalent to fining the direction in which the negentropy J is maximized.