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c-LASSO and its dual for sparse signal estimation from array data

机译：c-LASSO及其对偶用于从阵列数据估计稀疏信号

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摘要

We treat the estimation of a sparse set of sources emitting plane waves observed by a sensor array as a complex-valued LASSO (c-LASSO) problem where the usual ℓ_1-norm constraint is replaced by the ℓ_1-norm of a matrix D times the solution vector. When the sparsity order is given, algorithmically selecting a suitable value for the c-LASSO regularization parameter remains a challenging task. The corresponding dual problem is formulated and it is shown that the dual solution is useful for selecting the regularization parameter of the c-LASSO. The solution path of the c-LASSO is analyzed and this motivates an order-recursive algorithm for the selection of the regularization parameter and a faster iterative algorithm that is based on a further approximation. This greatly facilitates computation of the c-LASSO-path as we can predict the changes in the active indices as the regularization parameter is reduced. Using this regularization parameter, the directions of arrival for all sources are estimated.
机译：我们将由传感器阵列观察到的发射平面波的稀疏源估计作为复数值LASSO（c-LASSO）问题，其中通常的ℓ_1-范数约束被矩阵的ℓ_1-范数替换为D乘以解向量。当给出稀疏顺序时，从算法上为c-LASSO正则化参数选择合适的值仍然是一项艰巨的任务。提出了相应的对偶问题，证明了对偶解对于选择c-LASSO的正则化参数很有用。分析了c-LASSO的求解路径，这激发了用于选择正则化参数的阶递归算法和基于进一步逼近的更快迭代算法。由于我们可以预测正则化参数减少时活动索引的变化，因此这极大地促进了c-LASSO路径的计算。使用此正则化参数，可以估算所有源的到达方向。

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  • 来源
    《Signal processing》 |2017年第1期|204-216|共13页
  • 作者

    Christoph F. Mecklenbraeuker; Peter Gerstoft; Erich Zoechmann;

  • 作者单位

    Institute of Telecommunications, TU Wien, Gusshausstr. 25/389, A-1040 Wien, Austria,Christian Doppler Laboratory for Dependable Connectivity for the Society in Motion, Austria;

    University of California San Diego, La Jolla, USA;

    Institute of Telecommunications, TU Wien, Gusshausstr. 25/389, A-1040 Wien, Austria,Christian Doppler Laboratory for Dependable Connectivity for the Society in Motion, Austria;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    Sparsity; c-LASSO; Duality theory; Homotopy;

    机译：稀疏性c-LASSO;对偶理论;同伦;

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