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Cellular Neural Networks - Analysis, Design and Optimization (Hardcover, 2000 ed.)
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Cellular Neural Networks - Analysis, Design and Optimization (Hardcover, 2000 ed.)
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Cellular Neural Networks (CNNs) constitute a class of nonlinear,
recurrent and locally coupled arrays of identical dynamical cells
that operate in parallel. ANALOG chips are being developed for use
in applications where sophisticated signal processing at low power
consumption is required. Signal processing via CNNs only becomes
efficient if the network is implemented in analog hardware. In view
of the physical limitations that analog implementations entail,
robust operation of a CNN chip with respect to parameter variations
has to be insured. By far not all mathematically possible CNN tasks
can be carried out reliably on an analog chip; some of them are
inherently too sensitive. This book defines a robustness measure to
quantify the degree of robustness and proposes an exact and direct
analytical design method for the synthesis of optimally robust
network parameters. The method is based on a design centering
technique which is generally applicable where linear constraints
have to be satisfied in an optimum way. Processing speed is always
crucial when discussing signal-processing devices. In the case of
the CNN, it is shown that the setting time can be specified in
closed analytical expressions, which permits, on the one hand,
parameter optimization with respect to speed and, on the other
hand, efficient numerical integration of CNNs. Interdependence
between robustness and speed issues are also addressed. Another
goal pursued is the unification of the theory of continuous-time
and discrete-time systems. By means of a delta-operator approach,
it is proven that the same network parameters can be used for both
of these classes, even if their nonlinear output functions differ.
More complex CNN optimization problems that cannot be solved
analytically necessitate resorting to numerical methods. Among
these, stochastic optimization techniques such as genetic
algorithms prove their usefulness, for example in image
classification problems. Since the inception of the CNN, the
problem of finding the network parameters for a desired task has
been regarded as a learning or training problem, and
computationally expensive methods derived from standard neural
networks have been applied. Furthermore, numerous useful parameter
sets have been derived by intuition. In this book, a direct and
exact analytical design method for the network parameters is
presented. The approach yields solutions which are optimum with
respect to robustness, an aspect which is crucial for successful
implementation of the analog CNN hardware that has often been
neglected. This beautifully rounded work provides many interesting
and useful results, for both CNN theorists and circuit designers.'
Leon O. Chua
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