Exact realization of large DT-CNNs on limited-sized CNN circuits

Since their introduction, Cellular Neural Networks have been constantly developed to include a broad class of problems. Despite their theoretical success, CNN implementations still suffer size limitations. In fact while the biggest CNN chips,due to VLSI constraints, have no more than few thousands of cells distributed on a 2D array, real problems may be multi-dimensional and may require millions of cells. In this paper we introduce a theoretical result allowing the emulation of a large DTCNN on a smaller and/or lower dimensional one. The smaller DTCNN will be equipped with some additional memory with respect to a standard DTCNN. Due to the theoretical formulation of the problem the DTCNN emulation has exactly the same behavior as the original one