A sparse signal reconstruction perspective for source localization with sensor arrays
A sparse signal reconstruction perspective for source localization with sensor arrays
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DOI：
10.1109/tsp.2005.850882
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发表时间：
2005-08-01
影响因子：
5.4
通讯作者：
Willsky, AS
中科院分区：
文献类型：
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作者：
Malioutov, D;Çetin, M;Willsky, AS
我们提出了一种基于传感器测量的稀疏表示的源定位方法，该方法由来自阵列流形的样本组成过完备基。我们通过施加基于l(1)-范数的惩罚来加强稀疏性。最近关于l(1)惩罚的稀疏化性质的一些理论结果证明了这种选择是正确的。明确地执行表示的稀疏性是出于获得显示超分辨率的空间谱的精确估计的愿望。我们建议使用数据矩阵的奇异值分解（SVD）来汇总多个时间或频率样本。我们的公式导致了一个优化问题，我们通过内点实现在二阶锥（SOC）规划框架中有效地解决了这个问题。我们提出了一种网格细化方法来减轻限制估计对空间位置网格的影响，并为我们的方法中涉及的正则化参数引入了一个自动选择标准。我们通过空间光谱图和比较估计方差与Cramar-Rao界（CRB）证明了该方法在模拟数据上的有效性。我们观察到，与其他源定位技术相比，我们的方法具有许多优点，包括提高分辨率、提高对噪声的鲁棒性、数据量的限制和源的相关性，以及不需要精确的初始化。
We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the l(1)-norm. A number of recent theoretical results on sparsifying properties of l(1) penalties justify this choice. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the spatial spectrum that exhibits super-resolution. We propose to use the singular value decomposition (SVD) of the data matrix to summarize multiple time or frequency samples. Our formulation leads to an optimization problem, which we solve efficiently in a second-order cone (SOC) programming framework by an interior point implementation. We propose a grid refinement method to mitigate the effects of limiting estimates to a grid of spatial locations and introduce an automatic selection criterion for the regularization parameter involved in our approach. We demonstrate the effectiveness of the method on simulated data by plots of spatial spectra and by comparing the estimator variance to the Cramar-Rao bound (CRB). We observe that our approach has a number of advantages over other source localization techniques, including increased resolution, improved robustness to noise, limitations in data quantity, and correlation of the sources, as well as not requiring an accurate initialization.