Compressed sensing and redundant dictionaries
Compressed sensing and redundant dictionaries
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DOI：
10.1109/tit.2008.920190
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发表时间：
2008-05-01
影响因子：
2.5
通讯作者：
Vandergheynst, Pierre
中科院分区：
文献类型：
--
作者：
Rauhut, Holger;Schnass, Karin;Vandergheynst, Pierre
本文将压缩感知的概念扩展到在标准正交基中不稀疏但在冗余字典中稀疏的信号。证明了由某种类型的随机矩阵和确定性字典组成的矩阵具有小的限制等距常数。因此，相对于字典稀疏的信号可以通过基追踪（BP）从少量随机测量中恢复。此外，阈值压缩感知的恢复算法进行了研究，并提供了条件，保证重建的概率高。通过数值实验对不同格式进行了比较。
This paper extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants. Thus, signals that are sparse with respect to the dictionary can be recovered via basis pursuit (BP) from a small number of random measurements. Further, thresholding is investigated as recovery algorithm for compressed sensing, and conditions are provided that guarantee reconstruction with high probability. The different schemes are compared by numerical experiments.