Deconvolution of non-stationary physical signals:
a smooth variance model for insulin secretion rate
Deconvolution is the process of estimating a system's input
using measurements of a causally related output
where the relationship between the input and output is known and linear.
Regularization parameters are used to balance smoothness
of the estimated input with accuracy of the measurement values.
In this paper we present a maximum marginal likelihood method
for estimating unknown regularization (and other) parameters
used during deconvolution of dynamical systems.
Our computational approach uses techniques
that were developed for Kalman filters and smoothers.
As an example application we consider estimating insulin secretion rate (ISR)
following an intravenous glucose stimulus.
This procedure is referred to in the medical literature as
an intravenous glucose tolerance test (IVGTT).
This estimation problem is difficult because ISR is a strongly non-stationary signal;
it presents a fast peak in the first minutes of the experiment,
followed by a smoother release.
We use three regularization parameters to define a smooth model for ISR variance.
This model takes into account the rapid variation of ISR
during the beginning of an IVGTT and its slower variation as time progresses.
Simulations are used to assess marginal likelihood estimation
of these regularization parameters as well as of other parameters in the system.
Simulations are also used to compare our model for ISR variance
with other stochastic ISR models.
In addition, we apply maximum marginal likelihood and our ISR variance
model to real data that have previous
ISR estimation results reported in the literature.