Discreteness-Aware Approximate Message Passing for Discrete-Valued Vector Reconstruction
Discreteness-Aware Approximate Message Passing for Discrete-Valued Vector Reconstruction
复制标题
用于离散值向量重建的离散感知近似消息传递
DOI：
10.1109/tsp.2018.2877170
复制
发表时间：
2018
影响因子：
5.4
通讯作者：
R. Hayakawa and K. Hayashi
中科院分区：
文献类型：
--
作者：
BABA Yasuyuki;KUBO Teruhiro;MORI Nobuhito;WATANABE Yasunori;YAMADA Tomohito;SARUWATARI Ayumi;OTSUKA Junichi;UCHIYAMA Yusuke;NINOMIYA Junichi;R. Hayakawa and K. Hayashi
本文考虑了利用绝对值和（SOAV）优化从可能欠定的线性测量值重构离散值随机向量。所提出的算法，称为离散性感知近似消息传递（DAMP），是基于近似消息传递（AMP），这是最初提出的压缩感知的想法。DAMP算法具有较低的计算复杂度，其性能在大的系统限制，可以通过状态演化框架，其中我们提供了一个条件，在无噪声的情况下与DAMP的准确重建分析预测。通过分析，我们还提出了一种确定SOAV优化参数的方法。此外，基于状态演化，我们提供贝叶斯最优DAMP，它具有最小的均方误差在算法的每次迭代。仿真结果表明，DAMP算法可以从欠定线性测量重构离散值向量，并且在大系统中的经验性能与我们的理论结果一致。当问题规模不够大时，在高信噪比条件下，采用所提参数的SOAV优化算法可以获得比DAMP算法更好的性能。
This paper considers the reconstruction of a discrete-valued random vector from possibly underdetermined linear measurements using sum-of-absolute-value (SOAV) optimization. The proposed algorithm, referred to as discreteness-aware approximate message passing (DAMP), is based on the idea of approximate message passing (AMP), which has been originally proposed for compressed sensing. The DAMP algorithm has low computational complexity and its performance in the large system limit can be predicted analytically via state evolution framework, where we provide a condition for the exact reconstruction with DAMP in the noise-free case. From the analysis, we also propose a method to determine the parameters of the SOAV optimization. Moreover, based on the state evolution, we provide Bayes optimal DAMP, which has the minimum mean-square-error at each iteration of the algorithm. Simulation results show that the DAMP algorithms can reconstruct the discrete-valued vector from underdetermined linear measurements and the empirical performance agrees with our theoretical results in large-scale systems. When the problem size is not large enough, the SOAV optimization with the proposed parameters can achieve better performance than the DAMP algorithms for high signal-to-noise ratio.