KDI: Towards Ideal Data Representations

9872890Ron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各种格式挑战了现有的传输、存储、查询、显示和数值操作技术，以至于它们的可访问性和可移植性的限制可能严重限制它们对人类知识的有用性。这常常导致这样一种矛盾的情况，即实验或数值计算产生丰富而细致的信息，而此时却没有足够的分析工具。为了应对这一挑战，研究者和他的同事基于多尺度分解和冗余表示两个基本原则开发了一种新的数据表示技术。多尺度分解将数据按层排列，以反映其相对重要性。这允许快速访问数据的良好粗分辨率，同时保留越来越精细表示的灵活性。冗余表示允许大量的数据分解。虽然从表面上看，这似乎与效率的需求背道而驰，但冗余提供了从统一的代表家族中选择“最佳代表”的灵活性，从而提供了效率和健壮性。拟议的研究预计将提供主要成果：(i)图像和声学数据的准确表示，（ii）高维数据的简洁表示，（iii）沿曲线和表面具有奇点的图像和体积物体的简洁表示，（iv）科学/工程计算的加速。KDI的倡议发生在知识和商业生活开始感受到革命性结合的影响的时候：传感器无处不在，计算无处不在，互联网连接。在商业、工程和科学努力的所有领域，明确的优先事项必须是识别和利用这个新时代的机会。努力的中心应该是集中开发新的方案来表示数字获取的数据，并快速处理这些表示。事实上，这个中心领域的进步产生了巨大的影响，加速了其他领域的进步。对于天文学家来说，他们努力探测来自宇宙最远处的微弱引力信号，或者回顾宇宙诞生后最早的时刻，寻找温度波动，从而为物理学的核心理论提供线索；对于寻找地球内部结构细微变形的地球物理学家来说，这是关于我们未来地震的线索；为工程师开发新的医疗成像设备；甚至对于想要为大众娱乐提供更逼真的计算机图形模拟的好莱坞企业家来说，数据表示也起着关键作用。为此，该项目组建了一个专家团队来解决开发新的数据表示和新的分析和操作方法的问题。该项目的前提是，数据表示的重大进步需要跨学科的努力，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，提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，他们在数据集表示的开发和使用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图像和信号处理，大规模计算和计算机图形学的应用领域。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可交付成果。它还以算法和软件的形式为科学和商业部门提供具体的可交付成果。该项目作为国家数据表示中心。培养项目与其他处理数据集的国家和国际中心之间的互动。该项目还为理论进步、实现技术和软件开发提供了国家资源。

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.