CIF: Small: Structured Signal Recovery from Noisy Measurements via Convex Programming: A Framework for Analyzing Performance

CIF：小：通过凸编程从噪声测量中恢复结构化信号：性能分析框架

• 批准号: 1423663
• 负责人: Babak Hassibi
• 金额: $ 40万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1423663&HistoricalAwards=false
• 关键词: CIF; Small; Structured; Signal; Recovery

With the advent of ubiquitous sensing (multi-modal sensors, imaging systems and cameras, etc.), various complex social networks, and the deluge of health-care data (DNA sequences, micro-arrays, etc.), society is now officially in the era of Big Data. In such a setting, the ability to systematically and efficiently derive structured models, and recover reliable and actionable information, from barrages of high dimensional data will have far-reaching impact on engineering challenges and on everyday life. Unfortunately, the data is often noisy, inaccurate, or partially missing. This research will develop a comprehensive theory to assess the performance of a very wide class of algorithms designed for this purpose which are based on convex programming techniques. Such performance guarantees will assist practitioners in a wide array of applications in signal processing, machine learning, statistics and data analysis.Recent years has witnessed some spectacular theoretical and algorithmic advances in convex optimization and compressed sensing that have changed how large noisy data sets are handled. Despite these successes, key challenges remain, including the need for a comprehensive theory that accurately predicts the performance of the algorithms and goes beyond the customary ?order-wise? performance guarantees. The investigators will pursue an ambitious research program to give exact performance evaluations for a wide variety of convex-optimization-based signal recovery methods, including the classical LASSO and its variants. The framework can deal with a wide array of signal-to-noise ratios, different measurement matrix ensembles, and a variety of cost functions and signal structures. The techniques draw upon a host of ideas in high-dimensional geometry, statistics, and signal processing and are the culmination of a flurry of activity by several different research communities.

随着无处不在的传感（多模态传感器、成像系统和相机等）、各种复杂的社交网络以及大量的医疗数据（DNA 序列、微阵列等）的出现，社会现在正式在大数据时代。在这样的环境中，从大量高维数据中系统地、高效地导出结构化模型并恢复可靠且可操作的信息的能力将对工程挑战和日常生活产生深远的影响。不幸的是，数据常常充满噪音、不准确或部分缺失。这项研究将开发一种全面的理论来评估为此目的而设计的基于凸规划技术的一类非常广泛的算法的性能。 这种性能保证将有助于从业者在信号处理、机器学习、统计和数据分析等领域的广泛应用。近年来，凸优化和压缩感知方面取得了一些惊人的理论和算法进步，这些进步改变了处理大型噪声数据集的方式。尽管取得了这些成功，但关键挑战仍然存在，包括需要一种全面的理论来准确预测算法的性能并超越惯用的“按顺序”的理论。性能保证。研究人员将开展一项雄心勃勃的研究计划，为各种基于凸优化的信号恢复方法（包括经典的 LASSO 及其变体）提供准确的性能评估。 该框架可以处理各种信噪比、不同的测量矩阵集合以及各种成本函数和信号结构。这些技术借鉴了高维几何、统计学和信号处理方面的大量思想，是几个不同研究团体一系列活动的结晶。