Heart Sound Background Noise Removal

Haim AppleboimBiomedical Seminar

February 2007

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

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)

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

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

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.

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

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

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

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

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

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

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

Experimental Setup and Methodology

FilterReorgenize

Data

Set ICAParameters

RunAlgorithmic

Analysis

MeasuredHS

Noise FreeHS

AlgorithmQuality

AssesmentAlgorithm Quality

Recorded Noise

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

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’

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

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

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’

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

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

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’

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’

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

Thank You

Principles of ICA Estimation (Measures of nongaussianity)

Measures of nongaussianityKurtosis

Negentropy

Minimization of mutual information

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.

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.

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.

Negentropy

Practically the estimation of NEGENTROPY is rather difficult. Therefore we usually us some approximations for this purpose

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)

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.