Graph Spectral Imaging: Sampling, Representation and Restoration

我的研究重点是对驻留在不规则采样核上的信号进行谐波分析和处理，这是一个新兴且快速增长的领域，称为图信号处理(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采集传感器，一个边用反映成对相似性或相关性的权重连接两个节点。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)森林中无线传感器的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。我将重点放在GPS表示、恢复和采样的三个基本方面，以用于成像应用和其他方面。 1.表示：紧凑的信号表示对于压缩应用至关重要。我们将解决一个基本问题，即通过变换和小波，在给定有限的可观测数据集的情况下，设计一种最佳地去相关输入数据的图谱。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虚拟现实视频的压缩。 2.恢复：在只有部分观测到的噪声样本的情况下，我们研究了利用信号先验恢复原始信号的方法。我们研究结合我们以前的基于图模型的方法和数据驱动的方法，例如卷积神经网络(CNN)来优化平均情况的性能，同时通过谱图理论来保证最坏情况的质量。我们研究了这种基于模式/数据驱动的混合方法来解决一系列恢复问题，包括点云去噪 3.采样：研究了图上带限信号的采样和重构策略，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、有源采样和具有时变图拓扑的采样。在获取样本既昂贵又耗时的应用中，采样扮演着重要的角色，例如节能的深度图像传感、核磁共振成像和社交网络调查。 这项研究将由约克大学一个有能力、有效率的团队进行，合作伙伴包括日本、台湾、中国、美国和英国。预计将与思科(加拿大)、NTT(日本)和Kandao(中国)进行行业合作。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绝佳的专业培训机会，以支持加拿大快速增长的3D成像和智能传感就业市场。

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.