基于稀疏表示的数据分离
Data Separation by Sparse Representations
AI总结：
本文介绍并综述了利用稀疏表示通过ℓ1最小化或阈值化方法分离由多个形态不同成分组成的数据的研究领域。
摘要：
近年来，稀疏性已成为应用数学、计算机科学和电气工程等多个领域的关键概念。这一新方法论的一个应用是分离由两个（或更多）形态不同的成分组成的数据。其核心思想是精心选择表示系统，每个系统能对其中一个分量提供稀疏逼近。然后，通过ℓ1最小化或阈值化方法，计算在组合的（因此高度冗余的）表示系统中表示数据的最稀疏系数向量，从而自动实现分离。本文旨在作为这一激动人心的研究领域的介绍和综述，以及该领域最新进展的参考。它将作为一章出现在由Yonina Eldar和Gitta Kutyniok编辑的《压缩感知：理论与应用》一书中。
英文摘要：
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more) morphologically distinct constituents. The key idea is to carefully select representation systems each providing sparse approximations of one of the components. Then the sparsest coefficient vector representing the data within the composed - and therefore highly redundant - representation system is computed by $\ell_1$ minimization or thresholding. This automatically enforces separation. This paper shall serve as an introduction to and a survey about this exciting area of research as well as a reference for the state-of-the-art of this research field. It will appear as a chapter in a book on "Compressed Sensing: Theory and Applications" edited by Yonina Eldar and Gitta Kutyniok.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
