Biomedical Engineering Reference
In-Depth Information
dimensional velocity can be reconstructed from the neuron spiking events by Monte Carlo sequen-
tial estimation algorithm. This algorithm can provide a probabilistic approach to infer the most
probable velocity as one of the components of the state. This decoding simulation updates the state
estimation simultaneously and applies this estimation to reconstruct the signal, which assumes the
interdependence between the encoding and decoding so that the accuracy of the receptive field es-
timation and the accuracy of the signal reconstruction are reliable. Notice that dealing with a point
process is a more complex problem than when firing rates (continuous observations) are used as
traditionally considered in particle filtering [
20
].
Let us first explain how the simulated data was generated. The tuning function of the recep-
tive field that models the relation between the velocity and the firing rate is assumed exponential
and given by (
6.17
)
l
(
t
)
=
exp(
m b
+
v
)
(6.17)
k
k
k
where
m
exp( )
is the background firing rate without any movement and
b
k
is the modulation in
firing rate due to the velocity
v
. In practice in the electrophysiology laboratory, this function is
unknown. Therefore, an educated guess needs to be made about the functional form, but the expo-
nential function is widely utilized [
21
].
The desired velocity was generated as a random walk with a noise variance
2.5
´
10
-
5
at each
1-msec time step, as shown in Figure
6.1
.
The background-firing rate exp(
μ
) and the modulation parameter
b
k
are set as 1 and 3, re-
spectively, for the whole simulation time, 200 sec. A neuron spike is drawn as a Bernoulli random
variable with probability
λ
within each 1-msec time window [
22
]. The neuron spike train is
t
k
)
t
shown in Figure
6.2
.
1.5
1
0.5
0
-0.5
-1
-1.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
time (ms)
x 10
5
FIgURE 6.1:
The desired velocity generated by random walk.
