EAGER: Exploring Compressive Sampling for Extreme-Scale Data Visualization

AbstractThis EAGER的目的是提供一个更大的项目称为实例最佳抽样的可行性的实际证据。实例最优采样是极端规模（分散的，非结构化的和结构化的）数据集的最优表示的基础框架。使用稠密多面体包装算法，实例最优采样框架开发了以最优最小采样率对给定数据集进行采样的策略。基于奈奎斯特频率的多维概念推导了实例最优表示;因此，在本发明中，这种方法最好与压缩采样（CS）方法互补，压缩采样（CS）方法利用数据集的稀疏性将采样率显著降低到奈奎斯特速率以下而不丢失信息。最佳采样将潜在地允许将极端尺度数据集减小到与该数据集中的样本数量成几何比例并且与其稀疏性成线性比例的大小。该研究解决了体数据和时变数据集稀疏重建的计算效率问题，为CS在计算机图形学中的应用奠定了基础。主要的挑战是三维或时变数据重建算法的计算成本。本研究探讨了采用张量积方法进行压缩采样的可行性。

AbstractThis EAGER aims to provide practical evidence of feasibility for a larger project called instance-optimal sampling. The instance-optimal sampling is a foundational framework for optimal representation of extreme-scale (scattered, unstructured, and structured) datasets. Using the dense polytope packing algorithms, the instance-optimal sampling framework develops strategies for sampling a given dataset at the optimally minimal sampling rate. The instance-optimal representation is derived based on the multidimensional notion of Nyquist frequencies; therefore, this approach is best complemented with the compressive sampling (CS) methods that exploit the sparsity of a dataset to reduce the sampling rate significantly below the Nyquist rate with no loss of information.The main motivation in this research is that the synergy of compressive sampling and instance-optimal sampling would potentially allow the reduction of an extreme-scale dataset to sizes that are logarithmically proportional to number of samples in that dataset and linearly proportional to its sparsity. The research addresses the computational efficiency issue of sparse reconstruction for volumetric and time-varying datasets, which can lay the basis for applying CS to computer graphics problems. The main challenge is the computational cost of the reconstruction algorithm for 3-D or time-varying data. This research examines the feasibility of adopting a tensor-product approach to compressive sampling.