Recovering vital physiological signals from ambulatory devices

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Recovering vital physiological signals from

ambulatory devices

Praveen Pankajakshan and Rangavittal Narayanan

Samsung Advanced Institute of Technology, India13 February 2013

Tuesday, February 26, 13

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ToolsMethodologyContext


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Motivation and challenges• Ambulatory monitoring: Record

vital signal continuously

‣ Mostly non-invasive or minimally invasive

‣ Patients asymptotic at hospital and monitor disease progression

• Challenges:

‣ SNR is low [1]

‣ Available storage, processing power and battery is low

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Image Courtesy: Cambridge Consultants

[1] G. Garner et al., EP2327360A1, Nov. 2010.


Bayesian framework

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• Data from sensor: y[n], n=0, 1, 2, … N-1 ∈ N0.

• From Bayesian theorem [2], estimate x[n] of the signal y[n] can be realized from

‣ p(y|x) is the likelihood

‣ p(x) is the knowledge on x[n].

• Likelihood is given by the normal distribution

‣ Assumption: Residual noise is asymptotically Gaussian, variance σ2.

‣ ||•||22 is the l2 norm.

[2] J. Idier, 2008.


Sparsity of gradient

6[2] J. Idier, 2008.



6[2] J. Idier, 2008.



6[2] J. Idier, 2008.

l1 norm ofthe gradient



6[2] J. Idier, 2008.


Many coefficients are small!



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• The estimated signal x[n] must respect:

‣ Bounded signal and gradient: x[n]>- ∞ and x[n]<∞

‣ Distribution: Positive skewed, long tail with small values.

• These are satisfied by:

‣ λ: trade-off parameter, E(x) is:

[2] J. Idier, 2008.





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• The estimated signal x[n] must respect:

‣ Bounded signal and gradient: x[n]>- ∞ and x[n]<∞

‣ Distribution: Positive skewed, long tail with small values.

• These are satisfied by:

‣ λ: trade-off parameter, E(x) is:

[2] J. Idier, 2008.




A holistic solution• x[n] can be realized from y[n] by

• Equivalent convex primal problem:

‣ R is a NxN Toeplitz matrix, p lies between [1, 2].

• x[n] can be estimated directly or piece-wise from y[n] by minimizing (1) using convex optimization ([2])

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(1)

[2] J. Idier, 2008.


Solution conceptualization

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l2-TV minimization

In-Phone processing

Server-levelprocessing

l2-l2 minimization


Majorization-minimization• Find a surrogate function

J(x, xk) to E(x) such that

‣ J(x, xk) must be convex

‣ J(x, xk)≥E(x)

‣ At xk, E(xk)=J(xk, xk)

• We choose J(x, xk) [3] as:

• The iterative solution is [3]:

9 [3] M. Figueiredo et al. 2006


Case: Content selection

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ECG signal from ML-II lead [4,5]). 48 hour ambulatory ECG with fs=360Hz, 200mV 11 bit resolution over 10mV amplitude range.

[4] G. B. Moody and R. G. Mark, 2001.[5] A. L. Goldberger, et al. 2000.


Progress and convergence11














Baseline correction

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Acquired Data

Estimated Baseline

Corrected signal


Baseline correction

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Acquired Data

Estimated Baseline

Corrected signal


Baseline correction

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Acquired Data

Estimated Baseline

Corrected signal

40 minutes of data processed in 0.7 seconds with 3.2GHz and 4GB memory!


Peak detection on recovered signal

A 3 second recording of a z-normalized ECG and peak detection [6] on the restored signals

13[6] J. Pan and W. J. Tompkins, March 1985.


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Summary Highlight


Summary

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• Scope: Restore vital physiological signals from ambulatory conditions.

• Processing:

‣ For handheld-devices by minimizing a l2-l2 cost function.

‣ For accuracy at servers by minimizing a l2-TV cost function.

•Performance: Outperforms classical approaches.


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Thats all folks!


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