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压缩传感,通过L1最小化稀疏信号恢复概述

An Overview of Compressed Sensing and Sparse Signal Recovery via L1 Minimization
课程网址: http://videolectures.net/mlss09us_candes_ocsssrl1m/  
主讲教师: Emmanuel Candes
开课单位: 斯坦福大学
开课时间: 2009-07-30
课程语种: 英语
中文简介:
在许多应用中,通常具有比未知数更少的方程。虽然这似乎没有希望,但我们希望恢复的对象稀疏或几乎稀疏的前提从根本上改变了问题,使搜索解决方案变得可行。本讲座将介绍稀疏性作为一个关键的建模工具,以及涉及许多数据处理领域的一系列小奇迹。这些例子表明,找到具有最小L1范数的欠定线性方程组的*解*通常会返回''正确'的答案。此外,到目前为止,已经建立了一个以压缩感知为名的完善的工作体,它声称人们在获取普遍感兴趣的信号时可以利用稀疏性或可压缩性,并且可以设计非自适应采样技术来压缩信息。将可压缩信号转换为少量数据 - 数据点比想象的要少。我们将对这些理论进行调查,并将其一些起源追溯到50年代的早期工作。由于这些理论在本质上广泛适用,本教程将介绍可能受影响的几个应用领域,如信号处理,生物医学成像,机器学习等。最后,我们将讨论这些理论和方法如何对传感器设计和其他类型的设计产生深远的影响。
课程简介: In many applications, one often has fewer equations than unknowns. While this seems hopeless, the premise that the object we wish to recover is sparse or nearly sparse radically changes the problem, making the search for solutions feasible. This lecture will introduce sparsity as a key modeling tool together with a series of little miracles touching on many areas of data processing. These examples show that finding *that* solution to an underdetermined system of linear equations with minimum L1 norm, often returns the ''right'' answer. Further, there is by now a well-established body of work going by the name of compressed sensing, which asserts that one can exploit sparsity or compressibility when acquiring signals of general interest, and that one can design nonadaptive sampling techniques that condense the information in a compressible signal into a small amount of data - in fewer data points than were thought necessary. We will survey some of these theories and trace back some of their origins to early work done in the 50's. Because these theories are broadly applicable in nature, the tutorial will move through several applications areas that may be impacted such as signal processing, bio-medical imaging, machine learning and so on. Finally, we will discuss how these theories and methods have far reaching implications for sensor design and other types of designs.
关 键 词: 机器学习; 生物医学成像; 建模
课程来源: 视频讲座网
最后编审: 2020-06-29:zyk
阅读次数: 52