Piecewise-exponential approximation for fast time-domain simulation of 2-D cellular neural networks

Cellular neural networks (CNNs) were introduced as promising image processing systems. However, since analytical design techniques are rarely available, extensive simulation is the main practical tool for developing significant applications. This paper presents a new algorithm for fast simulation of large-scale CNNs. It is based on the discretization of the sigmoid generating the output from the state of each cell. This discretization leads to a piecewise exponential approximation of the time-domain solution. Computation is only required when the output of a cell jumps to a different discrete level and involves only this cell and its neighbors. The algorithm is spatially adaptive since the computational effort is concentrated on the most rapidly evolving portions of the array.