KDI: Towards Ideal Data Representations

9872890Ron在通信、传感和计算能力方面的进步导致了数据的爆炸性增长。这些数据集的大小和不同的格式对现有的传输、存储、查询、显示和数字处理技术提出了挑战，以至于对它们的可访问性和便携性的限制可能会严重限制它们对人类知识的有用性。这往往会导致一种矛盾的情况，即实验或数值计算产生丰富的、精细的详细信息，而在这一点上，没有足够的分析工具。为了应对这一挑战，这位研究人员和他的同事们开发了一种新的数据表示技术，它基于多尺度分解和冗余表示这两个基本原则。多尺度分解将数据排列成反映其相对重要性的层。这允许快速访问数据的良好粗略解决方案，同时保留日益精细的表示的灵活性。冗余表示法适用于大量数据分解。从表面上看，这似乎与提高效率的需要背道而驰，但缺乏灵活性，可以从一个统一的代表人家族中选择“最佳代表”，从而提供效率和稳健性。这项研究有望在以下方面取得重要成果：(I)图像和声学数据的精确表示，(Ii)高维数据的简约表示，(Iii)沿曲线和曲面具有奇异性的图像和体积对象的简约表示，(Iv)科学/工程计算的加速。KDI的倡议发生在知识分子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，以及互联网连接。在商业、工程和科学努力的所有领域，一个明确的优先事项必须是识别和利用这个新时代可用的机会。这项工作的中心应该是加紧开发新的方案，以表示以数字方式获得的数据，并快速处理这些表示。事实上，这一核心领域的进展产生了巨大的影响，加速了其他所有领域的进展。对于努力探测来自宇宙最远端的微弱引力信号的天文学家，或者追溯到创世后最早的时刻，寻找温度波动的线索，以提供关于物理学核心理论的线索；对于寻找地球内部结构中的细微变形以寻找关于我们地震未来的线索的地球物理学家；对于开发新的医学成像设备的工程师；甚至对于想要更逼真的计算机图形模拟来进行大规模娱乐的好莱坞企业家来说，数据呈现发挥了关键作用。为此，该项目召集了一个专家团队，以解决开发新的数据表示和新的分析和操作方法的问题。这一冒险的前提是，数据表示方面的重大进步需要跨学科的力量，将来自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在一起。因此，拟议的研究小组由数学家、统计学家、计算机科学家和工程师组成，他们在数据集表示法的开发和使用方面拥有广泛的技能和经验。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一系列应用领域。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成果，也以用于科学和商业部门的算法和软件的形式产生具体的成果。该项目作为一个国家数据表示中心。该项目与其他处理数据集的国家和国际中心之间的互动得到了培养。该项目还为理论进步、实现技术和软件开发提供了全国性的资源。

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.