  While deep learning (DL) architectures like convolutional neural networks
(CNNs) have enabled effective solutions in image denoising, in general their
implementations overly rely on training data, lack interpretability, and
require tuning of a large parameter set. In this paper, we combine classical
graph signal filtering with deep feature learning into a competitive hybrid
design -- one that utilizes interpretable analytical low-pass graph filters and
employs 80% fewer network parameters than state-of-the-art DL denoising scheme
DnCNN. Specifically, to construct a suitable similarity graph for graph
spectral filtering, we first adopt a CNN to learn feature representations per
pixel, and then compute feature distances to establish edge weights. Given a
constructed graph, we next formulate a convex optimization problem for
denoising using a graph total variation (GTV) prior. Via a $l_1$ graph
Laplacian reformulation, we interpret its solution in an iterative procedure as
a graph low-pass filter and derive its frequency response. For fast filter
implementation, we realize this response using a Lanczos approximation.
Experimental results show that in the case of statistical mistmatch, our
algorithm outperformed DnCNN by up to 3dB in PSNR.
