Page 202 - Glucose Monitoring Devices

Possible approaches to CGM denoising 205

additive and uncorrelated from the useful signal, the purpose of denoising is recov-
ering u(t) from y(t). Digital filtering is the most appropriate technology that can be
used to enhance the quality of the CGM signal and reduce the random noise compo-
nent [19e21]. Given the expected spectral characteristics of noise, for example,
noise is white, (causal) low-pass filtering represents the most natural candidate to
separate signal from noise in online applications [22]. One major problem in
low-pass filtering is that, as signal and noise spectra normally overlap, it is not
possible to remove the random noise v(t) from the measured signal y(t) without dis-
torting the true signal u(t). In particular, distortion results in a delay affecting the es-
timate u ˆ(t) with respect to the true u(t): the more the filtering, the larger the delay. It
is easily understood that having a consistently delayed, even if the less noisy version
of CGM data could be useless in practice, for example, for the generation of timely
hypoalerts. A clinically significant filtering issue is thus the establishment of a
compromise between the regularity of u ˆ(t) and its delay with respect to the true u(t).

Possible approaches to CGM denoising
Moving-average (MA) filtering is a first candidate approach to deal with CGM
denoising. MA filters are commonly used in denoising in many applications,
including processing in commercial CGM devices [21]. Briefly, having fixed the or-
der, k, the output of the filter relative to the nth sample is given by a weighted sum of
the last k measured samples

w 1 yðnÞþ w 2 yðn 1Þþ / þ w k yðn k þ 1Þ
b uðnÞ¼ (10.2)
P k
w
i¼1 i
where y(n) represents glucose of the nth sample. The parameters of the filter are the
order k and the weights w 1 , ., w k . The higher is k, the longer is the “memory” of
the past data. Increasing k usually produces a more significant noise reduction
and, at the same time, a larger signal distortion, for example, u ˆ(n) is significantly
delayed, thus being unable to track fast changes of the true u(n). Having fixed the
order k, the weights w 1 , ., w k can be chosen in several ways. The most common
i
strategy is an MA with exponential weights, where w i ¼ m , with m (a real between
0 and 1) acting as a “forgetting factor” (the higher m, the higher the memory of past
data). The major weakness of MA is that, once weights have been chosen, it treats all
the time series in the same way, irrespectively of possible differences of their signal-
to-noise ratio (SNR) due to sensor and individual variability (see Fig. 10.1). As a
consequence, a filter with fixed parameters is at risk of being suboptimal in denois-
ing CGM data.
A different CGM denoising procedure, proposed by Chase et al. [7], was based on
an integral-based fitting and filtering method. Even if the procedure can be used in real
time during clinical trials, its major limitation is, in fact, that some of its components
(e.g., the concentration of plasma insulin) cannot be identified if only CGM data are
available. This hinders the possibility of using the method in daily-life conditions.