  While convolutional neural nets (CNNs) have achieved remarkable performance
for a wide range of inverse imaging applications, the filter coefficients are
computed in a purely data-driven manner and are not explainable. Inspired by an
analytically derived CNN by Hadji et al., in this paper we construct a new
layered graph neural net (GNN) using GraphBio as our graph filter. Unlike
convolutional filters in previous GNNs, our employed GraphBio is analytically
defined and requires no training, and we optimize the end-to-end system only
via learning of appropriate graph topology at each layer. In signal filtering
terms, it means that our linear graph filter at each layer is always
intrepretable as low-pass with known biorthogonal conditions, while the graph
spectrum itself is optimized via data training. As an example application, we
show that our analytical GNN achieves image denoising performance comparable to
a state-of-the-art CNN-based scheme when the training and testing data share
the same statistics, and when they differ, our analytical GNN outperforms it by
more than 1dB in PSNR.
