Abstract:
Recently there has been a lot of interest in health tele-monitoring. Some vital heath indicators
like EEC, ECG, MEG, Pulse Plethysmograph etc. are collected by sensor nodes; the acquired
signal is transmitted to a remote healthcare facility for monitoring and analysis. In e ect, this
comprises a Wireless Body Area Network (WBAN). Such a system allows for health monitoring
of the elderly in western countries without the intruding presence of a paramedic. In India, such
systems would bene t healthcare penetration into remote rural areas.
In a WBAN, the main challenge is to preserve energy. There are three main energy sinks
namely : sensing, processing and transmission. The transmission energy is the highest, therefore
the priority is to reduce it. This requires signal compression; however since the computational
capacity at the sensor nodes is limited; this precludes application of sophisticated transform
coding techniques. Recent studies proposed an alternate Compressed Sensing (CS) based ap-
proach wherein the sampled signal is projected onto a lower dimension by a random matrix,
thereby e ecting compression. The compressed signal is transmitted to the base station, where
it is recovered by sophisticated CS recovery algorithms. Since computational power at the base
station is not at a premium, this is a plausible model.
In this work, we are particularly interested in EEG. However the contribution of this work
extends to any biomedical signal in general. EEG signals are acquired via multiple probes.
All the probes monitor the same brain activity; therefore the EEG signals from the multiple
probes/channels are correlated. We reviewed prior studies in this area and observed that all
these studies concentrated on piecemeal recovery of the compressed EEG signal - they did not
exploit the inter-channel correlations. For the rst time, we exploited inter-channel correlations
for EEG reconstructions. We proposed three methods - group-sparse recovery; Kronecker CS
recovery and low-rank matrix recovery. The fundamental idea in all of the three remain the
same, these are three di erent approaches to model the inter-channel correlations. We were
able to show that the recovery results improved considerably compared to previous CS based
methods.
The second contribution of this work is even more signi cant. We showed that by exploiting
the inter-channel correlations we can actually reduce sensing energy and eliminate the require-
ment for processing / compression altogether. This simply requires randomly under-sampling
the EEG signals. Such an operation reduces sensing cost and as the signal is compressed during
acquisition, it eliminates processing costs. We found that our recovery techniques works well in
this framework and yields good recovery, i.e. accuracy from random under-sampling is the same
as accuracy from full sampling followed by compression.
The nal contribution of this work is towards the signal processing community. We have
derived algorithms for solving group-sparse recovery problems, low-rank matrix recovery prob-
lems and rank-aware sparse / group-sparse recovery problems. These algorithms are derived on
the Split Bregman approach. These general purpose algorithms will nd other areas of signal
processing like multi-spectral imaging, X-Ray CT imaging and Magnetic Resonance Imaging to
name a few.