Bayesian signal reconstruction for 1-bit compressed sensing
Bayesian signal reconstruction for 1-bit compressed sensing
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DOI：
10.1088/1742-5468/2014/11/p11015
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发表时间：
2014-06
期刊：
影响因子：
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通讯作者：
Y. Xu;Y. Kabashima;L. Zdeborová
中科院分区：
文献类型：
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作者：
Y. Xu;Y. Kabashima;L. Zdeborová
1比特压缩感测框架使得能够从其线性变换的每个条目的符号信息恢复稀疏向量x。丢弃幅度信息可以显著减少数据量，这在实际应用中是非常有利的。在本文中，我们提出了一种贝叶斯方法来重建1比特压缩感知信号，并分析其典型性能使用统计力学。作为基本设置，我们考虑测量矩阵Φ具有i.i.d项并且测量y无噪声的情况。利用副本的方法，我们表明，贝叶斯方法可以更好地重建比l1-范数最小化方法，渐近饱和的性能时，信号的非零条目的位置是已知的，其非零条目遵循零均值高斯分布的信号。我们还测试了一个消息传递算法的信号重建的基础上的信念传播。数值实验结果与理论分析结果一致。
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly beneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing and analyze its typical performance using statistical mechanics. As a basic setup, we consider the case that the measuring matrix Φ has i.i.d entries and the measurements y are noiseless. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the l1-norm minimization approach, asymptotically saturating the performance obtained when the non-zero entry positions of the signal are known, for signals whose non-zero entries follow zero mean Gaussian distributions. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis.