Compressive MUSIC: Revisiting the Link Between Compressive Sensing and Array Signal Processing
Compressive MUSIC: Revisiting the Link Between Compressive Sensing and Array Signal Processing
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DOI：
10.1109/tit.2013.2262311
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发表时间：
2012-01
影响因子：
2.5
通讯作者：
Jongmin Kim;J. C. Ye
中科院分区：
文献类型：
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作者：
Jongmin Kim;J. C. Ye
多测量向量（MMV）问题解决了共享公共稀疏支持的未知输入向量的识别。尽管MMV问题传统上已经在传感器阵列信号处理的上下文中得到解决，但最近的趋势是应用压缩感知（CS），这是由于其即使在快照数量不足的情况下也能估计稀疏支持的能力，在这种情况下，经典的阵列信号处理失败。然而，CS以概率的方式保证了准确的恢复，这往往表现出较差的性能，在传统的阵列信号处理方法成功的制度。概率CS和确定性传感器阵列信号处理之间的明显二分法尚未完全理解。本文的主要贡献是一个统一的方法，重新访问CS和阵列信号处理之间的联系首次在20世纪90年代中期由冯和Bresler。新算法，我们称之为压缩MUSIC，确定支持使用CS的部分，然后使用一种新的广义MUSIC准则估计剩余的支持。使用一个大的系统MMV模型，我们表明，我们的压缩MUSIC需要一个更少的传感器元件的准确支持恢复比现有的CS方法，它可以接近最佳的约束与有限数量的快照，即使在信号是线性相关的情况下。
The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems have been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS) due to its capability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees the accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the probabilistic CS and deterministic sensor array signal processing has not been fully understood. The main contribution of the present article is a unified approach that revisits the link between CS and array signal processing first unveiled in the mid 1990s by Feng and Bresler. The new algorithm, which we call compressive MUSIC, identifies the parts of support using CS, after which the remaining supports are estimated using a novel generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and that it can approach the optimal -bound with finite number of snapshots even in cases where the signals are linearly dependent.