Graph Spectral Image Processing - Part 1

Graph signal processing (GSP) is the study of signals that reside on irregular data kernels described by graphs. In contrast to previous graph-based studies in other computer science fields like computer vision and machine learning, GSP provides graph frequency analysis of signals on graphs, and interprets key signal operations as low-pass filtering. This graph spectral aspect of signal analysis and filtering connects very well to the long tradition of Fourier / harmonic analysis in the signal processing community. Further, the generality of the graph abstraction enables flexible encapsulation of inherent data similarity structures found in modern big data, such as wireless sensor networks, social media, and brain signals. Given its natural extension from traditional signal processing theories and general applicability to a wide range of applications, GSP has massive appeal both to signal processing theorists in academia and practitioners in industries.

Though traditional images are signals on regular 2D pixel grids, recent work in graph spectral image processing has shown that GSP tools can be designed and tailored for image processing also. Specifically, by interpreting an image as a graph signal on an appropriately chosen underlying graph that reflects pairwise pixel similarity / correlation, state-of-the-art performance can be achieved in a wide range of image applications, including image denoising, image deblurring, light field image compression, 3D point cloud denoising and super-resolution. In this tutorial, we focus on theories and applications of GSP for image processing.