On stable patterns realized by a class of one-dimensional two-layer CNNs

This paper presents some properties of stable patterns that can be realized by a certain type of one-dimensional two-layer cellular neural networks (CNNs). We first introduce a notion of admissible local pattern (ALP) set. All the stable patterns of a CNN can be completely determined by the ALP set. We next show that all of 256 possible ALP sets can be realized by two-layer CNNs, while only 59 can be realized by single-layer CNNs. This means two-layer CNNs have a much higher potential for signal processing than single-layer CNNs.