Limits on Support Recovery of Sparse Signals via Multiple-Access Communication Techniques
Limits on Support Recovery of Sparse Signals via Multiple-Access Communication Techniques
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DOI：
10.1109/tit.2011.2170116
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发表时间：
2011-12
影响因子：
2.5
通讯作者：
Yuzhe Jin;Young-Han Kim;B. Rao
中科院分区：
文献类型：
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作者：
Yuzhe Jin;Young-Han Kim;B. Rao
本文研究了基于噪声线性测量的稀疏信号的精确支持恢复问题。主要的重点是找到可靠的支撑回收的测量次数的充分必要条件。通过将支持恢复问题与高斯多址信道（MAC）上的信道编码问题进行类比，并利用为后者问题开发的数学工具，我们获得了分析支持恢复性能限制的信息论框架。具体地说，当稀疏信号的非零条目数保持固定时，表征了支持恢复所需的足够和必要的测量数的精确渐近性。此外，我们表明所提出的方法可以处理各种稀疏信号恢复模型，从而显示其作为有效分析工具的潜力。
In this paper, we consider the problem of exact support recovery of sparse signals via noisy linear measurements. The main focus is finding the sufficient and necessary condition on the number of measurements for support recovery to be reliable. By drawing an analogy between the problem of support recovery and the problem of channel coding over the Gaussian multiple-access channel (MAC), and exploiting mathematical tools developed for the latter problem, we obtain an information-theoretic framework for analyzing the performance limits of support recovery. Specifically, when the number of nonzero entries of the sparse signal is held fixed, the exact asymptotics on the number of measurements sufficient and necessary for support recovery is characterized. In addition, we show that the proposed methodology can deal with a variety of models of sparse signal recovery, hence demonstrating its potential as an effective analytical tool.