Graph Spectral Imaging: Sampling, Representation and Restoration

我的研究重点是谐波分析和信号的处理，这些信号驻留在不规则采样核上，最好由图来描述，在一个新兴和快速发展的领域，称为图信号处理（GSP）。图是包含节点和边的非常一般的抽象数据结构。一个节点代表一个样本采集传感器，一条边用一个权重连接两个节点，这个权重反映了两两的相似性或相关性。在图形上建模为信号的数据包括：(i)代表人体的3D点云的颜色属性，（ii）森林中分布式无线传感器网络的温度读数，以及（iii） Facebook等社交网络上用户的总统投票模式。我着重于三个基本方面的gsp -表示，恢复和采样-为成像应用和超越。1. 表示：紧凑的信号表示对于压缩应用是至关重要的。我们将通过变换和小波来解决设计一个图谱的基本问题，该图谱通过有限的可观察数据集来最佳地解关联输入数据。我们还研究了使用提升技术的快速实现。实际应用包括动态三维点云、光场图像和360度虚拟现实视频的压缩。2. 复原：在部分观测到噪声样本的情况下，研究利用信号先验恢复原始信号的复原方法。我们研究将之前基于图模型的方法与数据驱动的方法（如卷积神经网络（CNN））相结合，以优化平均情况性能，同时通过谱图理论保证最坏情况的质量。我们研究了这种基于模型/数据驱动的混合方法，用于一系列恢复问题，包括点云去噪和超分辨率，3D形状重建和基于图的分类器学习。3. 采样：我们研究了图上有限带宽信号的新的采样和重构策略，将已知的奈奎斯特采样定理推广到图-信号域。我们研究了实际场景，包括带噪声采样、主动采样和时变图拓扑采样。采样在获取样本昂贵或耗时的应用中起着重要作用，例如节能深度图像传感，MRI成像和社会网络调查。这项研究将由约克大学一个有能力和高效率的团队进行，并与日本、台湾、中国、美国和英国的知名国际合作伙伴合作。预计将与Cisco（加拿大）、NTT（日本）和Kandao（中国）进行工业合作。该项目为理论信号处理和机器学习领域的研究生和博士后提供了良好的专业培训机会，以支持加拿大3D成像和智能传感领域快速增长的就业市场。

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.