CIF: Small: Dictionary Learning for Compressed Sensing

数字信息革命依赖于对语音、音乐、图像和电影等现实信号的感知和转换，以使其成为计算机可以处理的数字。压缩感知是数学上的一项新突破，它使这种感知和转换比以往任何时候都更有效、更可靠。关键是有效的字典的可用性，使自然信号的非常紧凑的表示。虽然字典是从数学原理中发展出来的，但最近的一个发现是，如果字典本身是从数据的例子中学习的，那么它们的效率可以大大提高。由于压缩感知关键取决于字典与感知机制的相互作用，因此从数据本身对两者进行联合学习有望提供最大的好处。然而，到目前为止，在这个方向上只有少数启发式的尝试。研究者正在开发第一个系统的理论，用于词典学习，以及词典和感知机制的联合学习。他将展示真实的传感应用的理论和算法，特别是在具有挑战性的医疗诊断应用中。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）压缩传感稀疏信号表示的字典学习;（ii）字典和压缩传感最佳传感算子的联合学习;（iii）压缩传感最佳传感算子的联合学习。并展示具有挑战性的磁共振成像（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，用于在更短的时间内从更少的数据中改善跳动的心脏或大脑功能的成像，改善医疗保健并降低其成本。

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.