D2CN: Distributed Deep Convolutional Network

With the rapid growth of distributed systems, deep learning-based multi-source data processing has drawn extensive attention, especially for the multi-channel networks. However, the conventional ones lack a strong theoretical foundation and the data in each channel lack necessary interactions, giving rise to insufficient robustness. Here we derive a network termed as distributed deep convolutional network (D${}^{2}$CN) to overcome this issue, which is explained by integrating generalized singular value decomposition (GSVD) with the principles of Hankel convolution framelet. Specifically, we employ the feature extraction capability of GSVD to perform data interactions by forward/backward propagation, where numerous inputs are designed using the common bases and reliable performance is achieved by training a shared set of right bases. We go over the network's scalability to show its benefits in performance and robustness. Moreover, we show that the encoder-decoder scheme allows the network suitable for a wide range of inverse situations. Finally, we demonstrate the superiority of the D${}^{2}$CN over other fundamental networks through numerical experiments conducted on classical image denoising.