Compressed Sensing and Source Separation
Compressed Sensing and Source Separation
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DOI：
10.1007/978-3-540-74494-8_43
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发表时间：
2007-09
期刊：
影响因子：
--
通讯作者：
T. Blumensath;M. Davies
中科院分区：
文献类型：
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作者：
T. Blumensath;M. Davies
欠定混合物的分离是信号处理中的一个重要问题，多年来一直受到人们的广泛关注。解决这类问题需要先验知识，而稀疏结构是最常见的结构形式之一。信号处理中的另一个中心问题是采样。最近的研究表明，只要信号有额外的结构，就有可能远低于奈奎斯特极限进行采样。这一理论被称为压缩感知或压缩采样，对于允许稀疏表示的信号已经获得了丰富的理论见解。在本文中，我们指出了压缩感知和源分离之间的几个相似之处。这里我们主要假设混合系统是已知的，即我们不研究盲源分离。从源分离的角度出发，我们将压缩感知中的一些结果推广到更一般的过完备稀疏表示，并研究了解对混合系统误差的敏感性。
Separation of underdetermined mixtures is an important problem in signal processing that has attracted a great deal of attention over the years. Prior knowledge is required to solve such problems and one of the most common forms of structure exploited is sparsity.Another central problem in signal processing is sampling. Recently, it has been shown that it is possible to sample well below the Nyquist limit whenever the signal has additional structure. This theory is known as compressed sensing or compressive sampling and a wealth of theoretical insight has been gained for signals that permit a sparse representation.In this paper we point out several similarities between compressed sensing and source separation. We here mainly assume that the mixing system is known, i.e. we do not studyblindsource separation. With a particular view towards source separation, we extend some of the results in compressed sensing to more general overcomplete sparse representations and study the sensitivity of the solution to errors in the mixing system.