Unrolling of Graph Total Variation for Image Denoising

While deep learning have enabled effective solutions in image denoising, in general their implementations overly rely on training data and require tuning of a large parameter set. In this thesis, a hybrid design that combines graph signal filtering with feature learning is proposed. It utilizes interpretable analytical low-pass graph filters and employs 80% fewer parameters than a state-of-the-art DL denoising scheme called DnCNN. Specifically, to construct a graph for graph spectral filtering, a CNN is used to learn features per pixel, then feature distances are computed to establish edge weights. Given a constructed graph, a convex optimization problem for denoising using a graph total variation prior is formulated. Its solution is interpreted in an iterative procedure as a graph low-pass filter with an analytical frequency response. For fast implementation, this response is realized by Lanczos approximation. This method outperformed DnCNN by up to 3dB in PSNR in statistical mistmatch case.