5.2.2
Principles of Cellular Neural Network
The Cellular Neural Network (CNN) concept was introduced by Leon O. Chua and Ling
Yang in 1988. It is a massive parallel processing paradigm which combines some of the
features of Cellular Automata (Discrete states, concept of neighborhood) [103] and
Artificial Neural Networks (simple processing elements, continuous states and parallel
computation) [92]. CNN is an n-dimensional array of mainly identical systems, called cells
[83]. What distinguishes CNN from traditional Artificial Neural Networks is the locality of
connections. Unlike artificial neural networks, every cell in cellular neural network
communicates directly to its nearest neighbors only. The locality of couplings contributes
44
to the amazingly enhanced processing speed in cellular neural networks. Each cell is made
up of a linear capacitor, a non-linear Voltage-controlled current source and a few resistive
linear circuit elements, as shown in Figure 5-2 [104].
Figure
5-2: Basic architecture of CNN cell: the equivalent electrical circuit
In Figure 5-2,
C
is a linear capacitor;
R
and
R
are linear resistors;
I
is an independent
voltage source;
I
and
I
are linear voltage controlled current sources with the
characteristics
I (i, j; k, l) = A(i, j; k, l)u
and
I (i, j; k, l) = B(i, j; k, l)u
for all
C(i, j)ЄN(i, j);
I
is a piecewise-linear voltage-controlled current source. Applying
Kirchhoff’s Current Law
(KCL) and
Kirchhoff’s Voltage Law
(KVL), the following state
equation of CNN can be derived.
(5-1)
𝑥̇
,
= −𝑥
,
+
𝐴(𝑖, 𝑗; 𝑘, 𝑙)𝑦
,
+
( , )∈ ( , )
𝐵(𝑖, 𝑗; 𝑘, 𝑙)𝑢
,
+
( , )∈ ( , )
𝐼
Where
x
is the state of the cell C (i,j); A(i,j;k,l) and B(i,j;k,l) are the feedback and control
templates respectively for all cells C(k,l) in the neighborhood N(i,j) of cell C(i,j).
The output equation is given as:
45
(5-2)
y =
1
2
( 𝑥 + 1 − 𝑥 − 1 )
The feedback template (A), the control template (B) and the Bias (I) are all core parts of a
CNN processor concept and contribute to the determination its output for a given input.
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