Praveen Pankajakshan and Rangavittal Narayanan
Physiological signals, Inverse problems, Total Variation, Regularization, Optimization
Sensors that are attached to a patient for monitoring the various vital physiological parameters, under ambulatory conditions, often acquire signals with very low signal-to-noise ratio. One characteristic that is observed is that the acquired data has the signal and the noise exhibiting overlapping spectral characteristics. Drawing a meaningful analysis, from these signals, can be quite a challenge when the classical linear filtering techniques are unable to separate the signal from the noise. In addition, the signals are nonstationary in nature. So, any method that enhances these signals should safeguard the salient points within the series and avoid smoothening of the feature rich segments. In this work, we propose a method to recover the vital physiological signals from the observation. As the problem is not well posed, it is redefined by introducing some smoothness constraints on the solution. We introduce different ways of modeling the problem, and show how the physiological signal can be recovered with minimal loss in information. A numerical case example is taken from Electrocardiogram signals to demonstrate the proposed approach, while comparison is made with some popular techniques from the literature.
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