Distributed Deep Convolutional Network: A Generalized SVD Perspective

With the rapid advancement of distributed systems technology, deep learning-based methods have become a common scheme to implement multiple data processing. This paper presents a novel multi-channel encoder-decoder architecture (called as D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>CN), 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 the reliable performance is achieved by training shared right bases. The network intuitively shows the interactions of multiple data in propagation, which is suitable for a wide range of inverse problems. Finally, we demonstrate the superiority of D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>CN over other fundamental networks through numerical experiments conducted on inverse problem tasks.