Graph Spectral Imaging: Sampling, Representation and Restoration

我的研究重点是谐波分析和信号的处理，这些信号驻留在最好由图形描述的不规则采样内核上，这是一个新兴且快速发展的领域，称为图形信号处理（GSP）。图是包含节点和边的非常通用的抽象数据结构。一个节点代表一个样本收集传感器，一条边连接两个节点，其权重反映了两两之间的相似性或相关性。被建模为图上信号的数据包括：（i）表示人体的3D点云的颜色属性，（ii）森林中无线传感器分布式网络上的温度读数，以及（iii）Facebook等社交网络上用户的总统投票模式。我专注于三个基本方面的GSPrepresentation，恢复和采样的成像应用和超越。 1.表示：紧凑的信号表示对于压缩应用至关重要。我们将解决设计一个图谱的基本问题，通过变换和小波最佳地去相关输入数据给定一个有限的可观察数据集。我们还调查使用提升技术的快速实现。实际应用包括动态3D点云、光场图像和360度虚拟现实视频的压缩。 2.复原：在只给出部分观测噪声样本的情况下，我们研究了利用信号先验知识恢复原始信号的方法。我们研究将我们以前的基于图模型的方法与卷积神经网络（CNN）等数据驱动的方法相结合，以优化平均情况下的性能，同时通过谱图理论保证最差情况下的质量。我们研究了这种基于模式/数据驱动的混合方法，用于一系列恢复问题，包括点云去噪 3.取样：我们研究新的采样和重建策略的带限信号的图，推广已知的奈奎斯特采样定理的图形信号域。我们研究的实际情况，包括采样噪声，主动采样，采样随时间变化的图形拓扑结构。采样在获取样本既昂贵又耗时的应用中起着重要作用，例如节能深度图像传感、MRI成像和社交网络调查。 这项研究将由约克大学的一个有能力和有效率的团队进行，并在日本、台湾、中国、美国和英国建立了良好的国际合作伙伴。预计将与思科（加拿大）、NTT（日本）和Kandao（中国）进行行业合作。该计划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极好的专业培训机会，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 GSPrepresentation, restoration and samplingfor 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 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.