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Support Recovery of Sparse Signals in the Presence of Multiple Measurement Vectors

机译：在多个测量向量的情况下支持稀疏信号的恢复

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摘要

This paper studies the performance limits in the support recovery of sparse signals based on multiple measurement vectors (MMV). An information-theoretic analytical framework inspired by the connection to the single-input multiple-output multiple-access channel communication is established to reveal the performance limits in the support recovery of sparse signals with fixed number of nonzero entries. Sharp sufficient and necessary conditions for asymptotically successful support recovery are derived in terms of the number of measurements per vector, the number of nonzero rows, the measurement noise level, and the number of measurement vectors. Through the interpretations of the results, the benefit of having MMV for sparse signal recovery is illustrated, thus providing a theoretical foundation to the performance improvement enabled by MMV as observed in many existing simulation results. In particular, it is shown that the structure (rank) of the matrix formed by the nonzero entries plays an important role in the performance limits of support recovery.
机译：<？Pub Dtl？>本文研究了基于多个测量向量（MMV）的稀疏信号支持恢复的性能极限。建立了一个信息理论分析框架，该框架受到与单输入多输出多访问信道通信的连接的启发，以揭示在支持恢复具有固定数量的非零条目的稀疏信号时的性能限制。根据每个矢量的测量数量，非零行的数量，测量噪声级别和测量矢量的数量，得出了渐近成功支持恢复的尖锐充分必要条件。通过对结果的解释，可以说明使用MMV进行稀疏信号恢复的好处，从而为在许多现有仿真结果中观察到的MMV实现的性能改进提供了理论基础。特别地，显示了由非零条目形成的矩阵的结构（等级）在支持恢复的性能极限中起重要作用。

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