Graphs and networks are ubiquitous in science and technology, including imagine processing, research in Internet of Things and analysis of social network data. Since its emergence, graph signal processing (GSP) has become an important tool in such areas.

a. Generalized GSP. We develop a broad framework that not only encompasses traditional GSP as a special case, but also includes a hybrid framework of graph and classical signal processing over a continuous domain. Our framework generalizes traditional GSP to graph signals in a separable Hilbert space with infinite dimensions.

b. Folded graph signal recovery. The signals observed in many applications can be modeled as graph signals. Examples include photographs, CMOS sensor images, and readings from sensor networks. Self-reset analog-to-digital converters (ADCs) are used to sample high dynamic range signals resulting in modulo-operation based folded signal samples. In this work, we develop a theory to characterize when a folded graph signal can be recovered and propose algorithms to achieve this.

c. Signal processing over a high order graph structures. For signals on a point cloud, we want to develop signal processing framework without knowing explicit connections between points; and instead, only prior knowledge of the distribution of all possible connections is required. We also aim to develop advanced geometric signal processing framework in dealing with signals living on more complicated geometric objects (than graphs) such as simplicial complexes, manifolds, etc. Applications of these new frameworks include anomaly detection, denoising, new graph neural network architecture, etc.

For more information, you may contact our professor Tay Wee Peng.