CIF: Small: Dictionary Learning for Compressed Sensing

数字信息革命依赖于将语音、音乐、图像和电影等现实生活中的信号感知并转换为计算机可以处理的数字。压缩传感是最近在数学上的一项突破，它使这种传感和转换比人们想象的更高效、更可靠。关键是要有高效的词典，能够非常紧凑地表示自然信号。虽然词典是从数学原理发展而来的，但最近的一个发现是，如果词典本身是从数据的例子中学习的，那么词典的效率可以大大提高。由于压缩感知在很大程度上依赖于词典与感知机制的相互作用，因此从数据本身联合学习两者可望提供最大的益处。然而，到目前为止，在这个方向上只有几次启发式的尝试。研究人员正在开发第一个系统的词典学习理论，以及词典和感知机制的联合学习理论。他将演示实际传感应用的理论和算法，特别是具有挑战性的医疗诊断应用。该项目的具体目标是开发具有性能保证的理论和算法，用于(I)学习用于压缩传感的稀疏信号表示的字典；(Ii)联合学习字典和用于压缩传感的最佳传感算子；以及演示关于挑战磁共振成像(MRI)和计算机层析成像(CT)应用的理论和算法。最终，这项研究可能会带来MRI和CT技术，以便在更短的时间内从更少的数据中改进心脏或大脑跳动功能的成像，改善医疗保健并降低成本。

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.