An exact and direct analytical method for the design of optimally robust CNN templates.pdf


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304 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 46, NO. 2, FEBRUARY 1999
An Exact and Direct Analytical Method for the
Design of Optimally Robust CNN Templates
Martin Hänggi, Student Member, IEEE, and George S. Moschytz, Fellow, IEEE
Abstract— In this paper, we present an analytical design ap-
proach for the class of bipolar cellular neural networks (CNN’s)
which yields optimally robust template parameters. We give
a rigorous definition of absolute and relative robustness and
show that all well-defined CNN tasks are characterized by a
finite set of linear and homogeneous inequalities. This system
of inequalities can be analytically solved for the most robust
template by simple matrix algebra. For the relative robustness
of a task, a theoretical upper bound exists and is easily derived,
whereas the absolute robustness can be arbitrarily increased by
template scaling. A series of examples demonstrates the simplicity
and broad app


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