In this paper, we propose Small-World Cellular Neural Networks (SWCNNs) featuring multiplex fault tolerant techniques. SWCNN is a Cellular Neural Networks in which cells are connected by small-world connections. SWCNN can easily process many multimedia applications such as image processing. However, SWCNN needs to be fault tolerant because it displays higher error propagations than traditional CNNs. We describe typical neural algorithms for image processing such as noise removal. Also, we propose a fault tolerant architecture for the CNN, using multiplexing. In embedded systems, this issue is important to reliability, compactness and power consumption, meaning new processor architecture is expected.