Post on 16-Jul-2015
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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
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.
Tuesday, February 26, 13
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.
Tuesday, February 26, 13
Sparsity of gradient
6[2] J. Idier, 2008.
l1 norm ofthe gradient
Many coefficients are small!
Tuesday, February 26, 13
Sparsity of gradient
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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.
l1 norm ofthe gradient
Many coefficients are small!
Tuesday, February 26, 13
Sparsity of gradient
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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.
l1 norm ofthe gradient
Many coefficients are small!
Tuesday, February 26, 13
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.
Tuesday, February 26, 13
Solution conceptualization
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l2-TV minimization
In-Phone processing
Server-levelprocessing
l2-l2 minimization
Tuesday, February 26, 13
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
Tuesday, February 26, 13
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.
Tuesday, February 26, 13
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!
Tuesday, February 26, 13
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.
Tuesday, February 26, 13
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.
Tuesday, February 26, 13