Geometry of Convolutional Neural Networks for Computational Imaging
Wednesday, October 16, 2019 - 11:20am - 12:05pm
Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning approaches for inverse problems thanks to its excellent performance. However, it is still difficult to obtain coherent geometric view why such an architecture gives the desired performance. Inspired by recent theoretical understanding on generalizability, expressivity and optimization landscape of neural networks, as well as the theory of deep convolutional framelets, here we provide a unified theoretical framework that leads to a better understanding of geometry of encoder-decoder CNNs. Our unified framework shows that encoder-decoder CNN architecture is closely related to nonlinear frame basis representation using combinatorial convolution frames, whose expressivity increases exponentially with the network depth and channels. We also demonstrate the importance of skipped connection in terms of expressivity and optimization landscape. We provide extensive experimental results from various biomedical imaging reconstruction problems to verify the performance encoder-decoder CNNs.