Unrolling of Deep Graph Total Variation for Image Denoising

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.