CIF: Small: Dictionary Learning for Compressed Sensing

CIF：小：压缩感知的字典学习

• 批准号: 1018660
• 负责人: Yoram Bresler
• 金额: $ 47.11万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018660&HistoricalAwards=false
• 关键词: CIF; Small; Dictionary; Learning; Compressed

The digital information revolution relies on the sensing and conversion of real-life signals such as speech, music, images and movies to numbers that can be manipulated by computers. Compressed sensing is a recent breakthrough in mathematics that enables to do this sensing and conversion more efficiently and reliably than ever thought possible. Key to this, is the availability of efficient dictionaries that enable very compact representation of natural signals. While dictionaries have been developed from mathematical principles, a recent discovery is that their efficiency can be greatly enhanced, if the dictionary itself is learned from examples of the data. Because compressive sensing depends critically on the interaction of the dictionary with the sensing mechanism, joint learning of the two from the data itself is expected to provide the greatest benefits. However, to date there have been only a handful of heuristic attempts in this direction. The investigator is developing the first systematic theory for dictionary learning, and for joint learning of dictionaries and sensing mechanism. He will demonstrate the theory and algorithms on real sensing applications, and in particular on challenging medical diagnostic applications.The specific goals of this project are to develop theory and algorithms with performance guarantees for (i) learning dictionaries for sparse signal representation for compressive sensing; (ii) joint learning of dictionary and the sensing operators optimum for compressive sensing; and to demonstrate the theory and algorithms on challenging magnetic resonance imaging (MRI) and computerized tomography (CT) applications. Ultimately, this research may lead to MRI and CT techniques for improved imaging of the beating heart or brain function from less data in less time, improving health care and reducing its cost.

数字信息革命依赖于语音，音乐，图像和电影等现实信号的传感和转换，这些数字可以通过计算机操纵。压缩传感是最近在数学方面的突破，它使得能够比以往任何时候都更有效，可靠地进行这种感应和转换。这样做的关键是有效词典的可用性，可以使自然信号非常紧凑。尽管词典是根据数学原则开发的，但最近的发现是，如果词典本身是从数据示例中学到的，则可以大大提高其效率。由于压缩感应取决于词典与传感机制的相互作用，因此从数据本身中对两者进行联合学习有望提供最大的好处。但是，迄今为止，朝这个方向只有少数启发式尝试。研究者正在开发第一个用于字典学习的系统理论，以及词典和感应机制的联合学习。他将展示有关实际感应应用的理论和算法，尤其是在挑战性的医学诊断应用方面。该项目的具体目标是开发理论和算法，并具有（i）学习稀疏信号表示词典的性能保证； （ii）词典和传感操作员的联合学习最佳的压缩感；并展示有关挑战磁共振成像（MRI）和计算机断层扫描（CT）应用的理论和算法。最终，这项研究可能会导致MRI和CT技术，以改善较少的数据，从而改善较少的数据，改善医疗保健并降低其成本。