Graph Spectral Imaging: Sampling, Representation and Restoration

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My research focuses on the harmonic analysis and processing of signals that reside on irregular sampling kernels best described by graphs, in an emerging and fast-growing field called Graph Signal Processing (GSP). A graph is a very general abstract data structure containing nodes and edges. A node represents a sample-collecting sensor, and an edge connects two nodes with a weight that reflects pairwise similarity or correlation. Data that are modeled as signals on graphs include: (i) color attributes of a 3D point cloud representing a human body, (ii) temperature readings on a distributed network of wireless sensors in a forest, and (iii) presidential voting patterns of users on a social network like Facebook. I focus on three fundamental aspects of GSP-representation, restoration and sampling-for imaging applications and beyond. 1. Representation: Compact signal representation is critical for compression applications. We will address the fundamental problem of designing a graph spectrum that optimally decorrelates input data given a limited observable dataset via transforms and wavelets. We also investigate fast implementation using the lifting technique. Practical applications include compression of dynamic 3D point cloud, light field images and 360 virtual reality video. 2. Restoration: Given only partially observed noisy samples, we study restoration methods to recover the original signal with the help of signal priors. We investigate combining our previous graph-model-based approach with data-driven methods such as convolution neural networks (CNN) to optimize average-case performance while guaranteeing a worst-case quality via spectral graph theory. We study this hybrid mode-based / data-driven approach for a range of restoration problems, including point cloud denoising & super-resolution, 3D shape reconstruction, and graph-based classifier learning.  3. Sampling: We investigate new sampling and reconstruction strategies for bandlimited signals on graphs, generalizing the known Nyquist sampling theorem to the graph-signal domain. We study practical scenarios including sampling with noise, active sampling, and sampling with time-varying graph topologies. Sampling plays an important role in applications where obtaining a sample is either expensive or time-consuming, such as energy-efficient depth image sensing, MRI imaging, and social network survey. The research will be conducted by a capable and efficient team at York University, with well-established international partners in Japan, Taiwan, China, US and UK. Industrial collaborations with Cisco (Canada), NTT (Japan) and Kandao (China) are expected. The program provides excellent professional training opportunities for graduate students and post-docs in the fields of theoretical signal processing and machine learning to support a fast growing job market in 3D imaging and intelligent sensing in Canada.