满足重构概率约束的更少贝努利观测

宋晓霞; 石光明

doi:10.3724/SP.J.1004.2013.00053

满足重构概率约束的更少贝努利观测

doi: 10.3724/SP.J.1004.2013.00053

1.
西安电子科技大学智能感知与图像理解教育部重点实验室西安 710071

详细信息

通讯作者:
宋晓霞

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- 被引次数: 0
出版历程
- 收稿日期: 2011-07-21
- 修回日期: 2012-04-09
- 刊出日期: 2013-01-20

Fewer Bernoulli Measurements Satisfying the Constraint of Reconstruction Probability

1.
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi'an 710071

摘要

摘要: 在压缩感知(Compressed sensing, CS)中,一些方法统计地提供了给定观测数量下的信号重构概率. 然而,在重构概率有约束的情况下,现有方法不能找到满足约束的观测. 本文以压缩感知中常用的贝努利观测集为研究对象, 基于贝努利观测的特征和序列压缩感知理论获得了满足重构概率约束的观测. 另外,由于所提方法能从获取的过多观测中移除部分冗余观测, 观测结果包含更少的观测数据. 所提方法有三个优点:满足重构概率约束、包含更少的观测数据以及具有全局收敛的属性. 理论分析和实验结果验证了所提方法的有效性.
- 压缩感知 /
- 贝努利观测 /
- 信号重构 /
- 序列压缩感知
Abstract: In the compressed sensing (CS) framework, the previous methods statistically provide the probability of signal reconstruction when the number of measurements is given. However, when the reconstruction probability of the signal is constrained, these existing methods do not provide an effective mechanism to find the measurements satisfying the constraint. To handle the problem, we focus on Bernoulli measurements and utilize the reconstruction feature of Bernoulli measurements and sequential CS to determine the measurements such that they can satisfy the constraint of reconstruction probability. Moreover, the measurements obtained by the proposed method are fewer than those by the classical methods because some redundant measurements are removed from the obtained measurement sequence. In summary, the proposed method has three unique features: satisfying the constraint of reconstruction probability, containing fewer measurements, and having the property of global convergence. Both theoretical analysis and experimental results suggest that the proposed method can obtain fewer measurements which satisfy the required reconstruction probability for different sparse signals and different initial measurements.
- Compressed sensing (CS) /
- Bernoulli measurements /
- signal reconstruction /
- sequential compressed sensing

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参考文献(1)

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