02-02-2013, 04:08 PM
Cellular Neural Networks
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INTRODUCTION
A cellular neural network (CNN) is an artificial neural network which features a multi-dimensional array of neurons and local interconnections among the cells.
The original CNN paradigm was first proposed by Chua and Yang in 1988. The two most fundamental ingredients of the CNN paradigm are: the use of analog processing cells with continuous signal values, and local interaction within a finite radius. A CNN is a nonlinear analog circuit which processes signals in real time. It is made of a massive aggregate of regularly spaced cloned circuit, called cells, which communicate with each other directly only through their nearest neighbors.
Architecture of Cellular Neural Networks
Any cell in a CNN is connected only to its neighbor cells. The adjacent cells can interact directly with each other. Cells not directly connected together may affect each other indirectly because of the propagation effects of the dynamics of CNNs. An example of a two-dimensional CNN is shown below.
Every cell is influenced by a limited number of cells in its environment. This locality of connections between the units is the main difference between CNNs and other neural networks. Large CNN chips can be implemented using VLSI techniques.
The figure above shows the emphasized cell (black) connected to the nearest neighbors (gray). The cells marked in gray represent the neighborhood cells of the black cell. The neighborhood includes the black cell itself. This is called a "3*3-neighborhood".
Similarly, we could define a "5*5-neighborhood", a "7*7-neigborhood" and so on.
The basic circuit unit of CNNs is called a cell. It contains linear and nonlinear circuit elements, which typically are linear capacitors, linear resistors, linear and nonlinear controlled sources, and independent sources. All the cells of a CNN have the same circuit structure and element values. A typical circuit of a single cell is shown in the figure below.
Global behavior of Cellular Neural Networks
In image processing, n-by-m rectangular grid arrays are often used. n and m are the numbers of rows and columns, respectively. Each cell in a CNN corresponds to an element of the array.
Assuming that each cell is connected to its nearest neighbors only ("3*3-neighborhood") and that the local connections of a cell do not depend on the cell's position, the Template set contains 19 coefficients (A-Template: a1 .. a9, B-Template: b1 .. b9, Bias I). The behavior of the CNN is completely determined by this Template set.
New CNN-Templates for arbitrary tasks may be found using a training algorithm, or by defining local rules for a given global task. The local rules describe a cell's equilibrium state depending on the inputs and outputs of the neighbor cells. The inputs and the outputs of the neighbor cells are assumed the be constant. The dynamics of the cell is not specified.
If Template values for the local rules are found, simulations are very helpful to test the dynamic global behavior of the entire clone of cells.