Compressed Sensing With Combinatorial Designs: Theory and Simulations

Darryn Bryant; Charles J. Colbourn; Daniel Horsley; Padraig Ó Catháin

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Compressed Sensing With Combinatorial Designs: Theory and Simulations

机译：组合设计的压缩感知：理论与仿真

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We use deterministic and probabilistic methods to analyze the performance of compressed sensing matrices constructed from Hadamard matrices and pairwise balanced designs, previously introduced by a subset of the authors. In this paper, we obtain upper and lower bounds on the sparsity of signals for which our matrices guarantee recovery. These bounds are tight to within a multiplicative factor of at most 4sqrt {2}42√ . We provide new theoretical results and detailed simulations, which indicate that the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. A new recovery algorithm tailored to the construction is also given.

机译：我们使用确定性和概率方法来分析由Hadamard矩阵和成对平衡设计构造的压缩感测矩阵的性能，该模型先前由一组作者引入。在本文中，我们获得了信号稀疏性的上限和下限，矩阵保证了这些稀疏性的恢复。这些界限严格限制在最多4sqrt {2}42√的乘法因子内。我们提供了新的理论结果和详细的仿真结果，表明该结构与高斯随机矩阵具有竞争性，并且恢复能力对噪声具有容忍性。还给出了针对该构造的新的恢复算法。

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来源
《IEEE Transactions on Information Theory》 |2017年第8期|4850-4859|共10页
作者
Darryn Bryant; Charles J. Colbourn; Daniel Horsley; Padraig Ó Catháin;
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作者单位

School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, Australia;

School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA;

School of Mathematical Sciences, Monash University, Melbourne, VIC, Australia;

School of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA;

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正文语种 eng
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关键词
Compressed sensing; Error correction; Error correction codes; Matrices; Sparse matrices; Standards; Electronic mail;

机译：压缩感知;纠错;纠错码;矩阵;稀疏矩阵;标准;电子邮件;

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6. Nonconvex prior image constrained compressed sensing (NCPICCS): Theory and simulations on perfusion CT [O] . J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, -1

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机译：具有组合设计的压缩感知：理论和模拟

Compressed Sensing With Combinatorial Designs: Theory and Simulations

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