图 书 馆
突破相干屏障——压缩传感的新理论Breaking the coherence barrier - A new theory for compressed sensing |
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| 课程网址: | http://videolectures.net/sahd2014_hansen_new_theory/ |
| 主讲教师: | Anders Hansen |
| 开课单位: | 剑桥大学 |
| 开课时间: | 2014-10-29 |
| 课程语种: | 英语 |
| 中文简介: |  本文提供了压缩感知的扩展，它弥合了现有理论与其当前在现实世界应用中的应用之间的巨大差距。它引入了一个数学框架，将压缩感知的三个标准支柱即稀疏性、非相干性和均匀随机子采样概括为三个新概念：渐近稀疏性、渐近非相干性和多级随机采样。新定理表明，在这些基本放松的条件下，压缩感知也是可能的，并揭示了几个优点。这有三重重要性。首先，当前应用压缩感知的逆问题通常是相干的。新理论为压缩感知在现实世界应用中的一系列经验用法提供了第一个全面的数学解释，例如医学成像、显微镜、光谱学等。其次，在表明压缩感知不需要不连贯性，而是渐近不连贯性就足够了，新理论在传感机制的设计中提供了显着更大的灵活性。第三，通过使用渐近不相干和多级采样不仅利用稀疏性，而且利用结构，即渐进稀疏性，新理论表明可以从更少的测量中获得显着改善的重建。 |
| 课程简介: | This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard pillars of compressed sensing - namely, sparsity, incoherence and uniform random subsampling - to three new concepts: asymptotic sparsity, asymptotic incoherence and multilevel random sampling. The new theorems show that compressed sensing is also possible, and reveals several advantages, under these substantially relaxed conditions. The importance of this is threefold. First, inverse problems to which compressed sensing is currently applied are typically coherent. The new theory provides the first comprehensive mathematical explanation for a range of empirical usages of compressed sensing in real-world applications, such as medical imaging, microscopy, spectroscopy and others. Second, in showing that compressed sensing does not require incoherence, but instead that asymptotic incoherence is sufficient, the new theory offers markedly greater flexibility in the design of sensing mechanisms. Third, by using asymptotic incoherence and multi-level sampling to exploit not just sparsity, but also structure, i.e. asymptotic sparsity, the new theory shows that substantially improved reconstructions can be obtained from fewer measurements. |
| 关 键 词: | 压缩传感; 渐近稀疏性; 渐近非相干性 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-10-09：zyk |
| 最后编审: | 2021-06-25：zyk |
| 阅读次数: | 77 |