Robust one-bit compressive sensing with weighted ℓ1-norm minimization
Robust one-bit compressive sensing with weighted ℓ1-norm minimization
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DOI：
10.1016/j.sigpro.2019.06.027
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发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
Peng Xiao;B. Liao
中科院分区：
文献类型：
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作者：
Peng Xiao;B. Liao
近年来，1比特压缩感知（1-bit CS）因其系统复杂度低、环境鲁棒性强等优点而受到广泛关注。然而，如何从1比特测量值中恢复信号仍然需要更深入的研究。受传统压缩编码技术中加权最小范数算法的优良性能的启发，本文提出了一种基于加权最小范数的1比特压缩编码鲁棒算法。具体地说，它首先表明，被动模型的解析解可以直接扩展到加权的情况下，权重不一定是积极的。在此基础上，介绍了两种有代表性的权重计算方法。在加权范数极小化框架下，提出的加权范数极小化算法易于实现。数值模拟表明，加权的最小化方法可以有效地提高恢复保真度。
In recent years, one-bit compressive sensing (1-bit CS) has been attracting much attentions owing to its advantages of low system complexity and outstanding environmental robustness. Nevertheless, how to recover the signal from 1-bit measurements still needs deeper investigation. Inspired by the excellent performance of weighted ℓ1-norm minimization in conventional CS techniques, this paper presents robust algorithms with weighted ℓ1-norm minimization for 1-bit CS. Specifically, it is first shown that the analytical solution for Passive model can be straightforwardly extended to the weighted case, and the weights are not necessarily positive. On this basis, two representative ways are introduced to calculate the weights. Under the weighted ℓ1-norm minimization framework, the proposed weighted ℓ1-norm algorithms can be easily implemented. Numerical simulations show that the recovery fidelity can be effectively improved with the weighted ℓ1-norm minimization techniques.