缺失数据传感器网络中压缩感知的测量界
Measurement Bounds for Compressed Sensing in Sensor Networks with Missing Data
摘要：
在本文中，我们研究的问题，稀疏向量恢复在传感器网络的融合中心从线性传感器测量时，有丢失的数据。在存在缺失数据的情况下，已知在压缩感知中采用的随机采样方法提供优异的重构精度。然而，当有缺失数据时，与稀疏恢复相关的理论保证尚未得到很好的研究。因此，在本文中，我们推导出一个上限的最小数量的测量，以确保忠实恢复稀疏信号时，使用伯努利擦除信道建模的丢失数据的产生。我们分析了三种不同的网络拓扑，即，星型，（中继辅助）树，和串行星型拓扑。我们的分析建立了恢复所需的最小测量数量如何与网络参数，测量矩阵的属性和恢复算法相结合。最后，通过数值模拟，我们显示了不同的系统参数的最小所需的测量数的变化，并验证了我们的理论结果。
英文摘要：
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in compressed sensing is known to provide excellent reconstruction accuracy. However, when there is missing data, the theoretical guarantees associated with sparse recovery have not been well studied. Therefore, in this paper, we derive an upper bound on the minimum number of measurements required to ensure faithful recovery of a sparse signal when the generation of missing data is modeled using a Bernoulli erasure channel. We analyze three different network topologies, namely, star, (relay aided-)tree, and serial-star topologies. Our analysis establishes how the minimum required number of measurements for recovery scales with the network parameters, the properties of the measurement matrix, and the recovery algorithm. Finally, through numerical simulations, we show the variation of the minimum required number of measurements with different system parameters and validate our theoretical results.
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