Interpretable Graph Signal Denoising Using Regularization by Denoising

In this paper, we propose an interpretable denoising method for graph signals using regularization by denoising (RED). RED is a technique developed for image restoration that uses an efficient (and sometimes black-box) denoiser in the regularization term of the optimization problem. By using RED, optimization problems can be designed with the explicit use of the denoiser, and the gradient of the regularization term can easily be computed under mild conditions. We adapt RED for denoising of graph signals beyond image processing. We show that many graph signal denoisers, including graph neural networks, theoretically or practically satisfy the conditions for RED. As a result, we can use various high-performance graph signal denoisers for regularization that are expected to improve restoration qualities. We further reveal the effectiveness of RED from a graph filter perspective. Denoising experiments for the synthetic and 3D point cloud datasets show that our proposed method improved the signal denoising accuracy in MSE compared to existing graph signal denoising methods.