Sparse Signal Detection With Compressive Measurements via Partial Support Set Estimation
Sparse Signal Detection With Compressive Measurements via Partial Support Set Estimation
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DOI：
10.1109/tsipn.2016.2601025
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发表时间：
2017-03-01
影响因子：
3.2
通讯作者：
Varshney, Pramod K.
中科院分区：
文献类型：
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作者：
Wimalajeewa, Thakshila;Varshney, Pramod K.
在本文中，我们考虑分布式网络中基于部分支持集估计和压缩测量的稀疏信号检测问题。假设网络中的多个节点观察稀疏信号，这些信号共享共同但未知的支持。虽然在传统的压缩感知框架中，目标是恢复完整的稀疏信号，但在稀疏信号检测中，可能不需要完整的信号恢复来做出可靠的检测决策。具体地，可以基于部分地或不准确地估计的信号来执行检测，这需要比完全信号恢复所需的计算负担更少的计算负担。为此，我们研究了基于部分估计支持集的稀疏信号检测问题。首先，我们讨论如何确定已知支持集的最小部分，以便在集中设置中实现所需的检测性能。其次，当原始压缩观测值在中央融合中心不可用时，我们开发了两种用于稀疏信号检测的分布式算法。在这些算法中，最终的决策统计量是通过各个节点的正交匹配追踪基于局部估计的部分支持集来计算的。当估计的部分支持集的大小非常小时，所提出的具有较少通信开销的分布式算法可以提供与集中式方法相当的性能（有时更好）。
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals, which share a common but unknown support. While in the traditional compressive sensing framework, the goal is to recover the complete sparse signal, in sparse signal detection, complete signal recovery may not be necessary to make a reliable detection decision. In particular, detection can be performed based on partially or inaccurately estimated signals, which requires less computational burden than that is required for complete signal recovery. To that end, we investigate the problem of sparse signal detection based on partially estimated support set. First, we discuss how to determine the minimum fraction of the support set to be known so that a desired detection performance is achieved in a centralized setting. Second, we develop two distributed algorithms for sparse signal detection when the raw compressed observations are not available at the central fusion center. In these algorithms, the final decision statistic is computed based on locally estimated partial support sets via orthogonal matching pursuit at individual nodes. The proposed distributed algorithms with less communication overhead are shown to provide comparable performance (sometimes better) to the centralized approach when the size of the estimated partial support set is very small.