KDI: Towards Ideal Data Representations

小行星9872890 通信、传感和计算能力的进步导致了数据的爆炸式增长。 这些数据集的大小和不同格式对现有的传输、存储 查询、显示和数字操作，以至于它们的可访问性和可移植性的限制可能严重限制了它们对人类知识的有用性。 这常常导致一种矛盾的情况，即实验或数值计算产生了丰富的、精细的细节信息，而在这一点上，还没有足够的分析工具。 为了应对这一挑战，研究者和他的同事们开发了一种基于以下两个基本原则的数据呈现新技术： 多尺度合成和冗余表示。 多尺度合成将数据排列成反映其相对重要性的层次。 这允许快速访问数据的良好粗略分辨率，同时保留越来越精细表示的灵活性。 冗余表示法不适用于大量的数据分解. 虽然表面上看，这似乎与效率的需要相反，但它提供了选择“最佳呈现”的灵活性。 从一个统一的家庭的代表，从而提供了效率和鲁棒性。 该研究有望在以下几个方面取得重要成果：（i）图像和声学数据的精确表示，（ii）高维数据的简约表示，（iii）图像和具有沿着曲线和曲面奇点的体积对象的简约表示，（iv）科学/工程计算的加速。 KDI计划发生在知识和商业生活开始感受到一种革命性组合的影响的时候：传感器无处不在，计算无处不在，互联网连接。 在商业、工程和奋进的所有领域中，一个明确的优先事项必须是识别和利用这个新时代的机会。 努力的中心应该是密集开发新的方案来表示数字化获取的数据，并快速处理这些表示。 事实上，这一核心领域的进步产生了巨大的影响，加速了其他领域的进步。 天文学家们努力探测来自宇宙最遥远处的微弱引力信号，或者回溯宇宙创生的最初时刻，寻找温度波动，从而为物理学的中心理论提供线索;地球物理学家们寻找地球内部结构的微妙变形，以寻找我们未来地震的线索;工程师们开发新的医学成像设备;即使对于好莱坞的企业家来说，他们想要更真实的计算机图形模拟来满足大众娱乐的需要--数据呈现也扮演着关键的角色。 为此，该项目组建了一个专家团队，以解决开发新数据表示和新的分析和操作方法的问题。 这项事业的前提是，数据表示的重大进展需要跨学科的努力，将涉及大型数据集的不同研究领域的理论家和实践者的技能和知识结合起来。 因此，拟议的研究团队由数学家，统计学家，计算机科学家和工程师组成，他们在开发和使用数据集表示方面具有丰富的技能和经验。 该项目的一个主要组成部分是在图像和信号处理，大规模计算和计算机图形学的应用领域的集合。 该项目以存储、压缩、去噪和查询数据的新方法的形式产生概念性的交付成果，也以算法和软件的形式产生具体的交付成果，供科学和商业部门使用。 该项目作为一个国家中心的数据表示。该项目和其他国家和国际中心之间的互动处理数据集的培养。 该项目还提供了一个国家资源的理论进步，技术的实施，和软件开发。

9872890Ron Advances in communication, sensing, and computational powerhave led to an explosion of data. The size and varied formats forthese datasets challenge existing techniques for transmission,storage, querying, display, and numerical manipulation, tothe point where limits on their accessibility and portability mayseverely restrict their usefulness for human knowledge. Thisoften leads to the paradoxical situation where experiments ornumerical computations produce rich, exquisitely detailedinformation, for which, at this point, no adequate analysistools exist. In order to address this challenge, theinvestigator and his colleagues develop a new technology for datarepresentation based on the two basic principles of multiscaledecompositions and redundant representations. Multiscaledecompositions arrange data into strata reflecting their relativeimportance. This allows for rapid access to good coarseresolution of the data while retaining the flexibility forincreasingly fine representations. Redundant representationsallow for a multitude of data decompositions. While this on thesurface appears contrary to the need for efficiency, theredundancy gives the flexibility of choosing `bestrepresentations' from a unified family of representers andthereby provides efficiency and robustness. The proposedresearch is expected to deliver major results for: (i) accuraterepresentation of image and acoustic data, (ii) parsimoniousrepresentation of high dimensional data, (iii) parsimoniousrepresentation of images and volumetric objects withsingularities along curves and surfaces, (iv) acceleration ofscientific/engineering computations. The KDI initiative takes place at a time when intellectualand commercial life are beginning to feel the effects of arevolutionary combination: sensor ubiquity, computationalubiquity, and internet connectivity. A clear priority in allfields of commercial, engineering, and scientific endeavor mustbe to identify and exploit the opportunities available in thisnew era. The center of the effort should be the intensivedevelopment of new schemes for representing digitally acquireddata, and for rapidly manipulating those representations. Infact, advances in this central area have tremendousrepercussions, accelerating progress in every other area. Forastronomers straining to detect faint gravitational signalscoming from the farthest reaches of the universe, or looking backin time to the earliest moments after creation, searching fortemperature fluctuations that would give clues about the centraltheories of physics; for geophysicists looking for subtledeformations in the earth's inner structure for clues about ourseismic future; for engineers developing new medical imagingdevices; even for Hollywood entrepreneurs wanting more realisticcomputer graphic simulations for mass entertainment -- datarepresentation plays a key role. To this end, this projectassembles a team of experts to address issues of developing newdata representations and new methods of analysis andmanipulation. The premise of this venture is that significantadvances in data representation require an interdisciplinaryeffort, meshing the skills and knowledge of theoreticians andpractitioners from varied fields of research that involve largedatasets. Thus, the proposed research team consists ofmathematicians, statisticians, computer scientists, and engineerswith extensive skills and experience in the development and useof representations for datasets. A primary component of theproject is the set of application areas in image and signalprocessing, large scale computation, and computer graphics. Theproject produces conceptual deliverables in the form of newmethods for storing, compressing, denoising, and querying data.It also produces concrete deliverables in the form of algorithmsand software for use in the scientific and commercial sector. Theproject serves as a national center for data representation.Interaction between the project and other national andinternational centers treating datasets is cultivated. Theproject also provides a national resource for theoreticaladvances, techniques of implementation, and software development.