EAGER: Exploring Compressive Sampling for Extreme-Scale Data Visualization

摘要本文旨在为更大的实例最优抽样项目提供可行性的实践证据。实例最优抽样是极端尺度（分散、非结构化和结构化）数据集最优表示的基础框架。使用密集多面体填充算法，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，这种方法最好与压缩采样（CS）方法相结合，压缩采样方法利用数据集的稀疏性，在不丢失信息的情况下将采样率显著降低到奈奎斯特率以下。本研究的主要动机是压缩采样和实例优化采样的协同作用可能允许将极端规模数据集减少到与该数据集中的样本数量成对数比例的大小，并与其稀疏度成线性比例。该研究解决了体积和时变数据集稀疏重建的计算效率问题，为CS在计算机图形学问题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.