论文标题
迭代适应性的正规化套索算法，用于稀疏信号的CFAR估计：IAR-LASSO-ADMM-CFAR算法
Iterative Adaptively Regularized LASSO-ADMM Algorithm for CFAR Estimation of Sparse Signals: IAR-LASSO-ADMM-CFAR Algorithm
论文作者
论文摘要
最少吸毒的收缩和选择操作员（LASSO）是一种正则化技术，用于估计各种应用中出现的稀疏信号，并且可以通过乘数的交替方向方法有效地求解，该方法将称为Lasso-Admm算法。正则化参数的选择对套索-ADMM算法的性能有重大影响。但是，尚未解决现有的lasso-admm算法中正则化参数的优化。为了优化此正则化参数，我们提出了一种有效的迭代适应性的正规套索ADMM（IAR-LASSO-ADMM）算法，通过迭代更新Lasso-Admm算法中的正则化参数。此外，通过将外部迭代添加到lasso-admm算法中，可以迭代地更新正则化参数。具体而言，在每次外迭代中，使用内部套索ADMM算法获得的估计值的零支持用于估计噪声方差，并且使用噪声方差来根据预定义的const误报率（CFAR）来更新阈值。然后，将结果阈值用于更新估计值和正则化参数的非零支持，然后继续进行下一个内部迭代。另外，合适的停止标准旨在终止外迭代过程，以获得对稀疏测量信号估计的最终非零支持。所得算法称为IAR-LASSO-ADMM-CFAR算法。最后，已经提出了仿真结果，以表明所提出的IAR-LASSO-ADMM-CFAR算法优于传统的Lasso-Admm算法和其他现有算法的重建精度，并且其稀疏顺序估计值比现有算法更准确。
The least-absolute shrinkage and selection operator (LASSO) is a regularization technique for estimating sparse signals of interest emerging in various applications and can be efficiently solved via the alternating direction method of multipliers (ADMM), which will be termed as LASSO-ADMM algorithm. The choice of the regularization parameter has significant impact on the performance of LASSO-ADMM algorithm. However, the optimization for the regularization parameter in the existing LASSO-ADMM algorithms has not been solved yet. In order to optimize this regularization parameter, we propose an efficient iterative adaptively regularized LASSO-ADMM (IAR-LASSO-ADMM) algorithm by iteratively updating the regularization parameter in the LASSO-ADMM algorithm. Moreover, a method is designed to iteratively update the regularization parameter by adding an outer iteration to the LASSO-ADMM algorithm. Specifically, at each outer iteration the zero support of the estimate obtained by the inner LASSO-ADMM algorithm is utilized to estimate the noise variance, and the noise variance is utilized to update the threshold according to a pre-defined const false alarm rate (CFAR). Then, the resulting threshold is utilized to update both the non-zero support of the estimate and the regularization parameter, and proceed to the next inner iteration. In addition, a suitable stopping criterion is designed to terminate the outer iteration process to obtain the final non-zero support of the estimate of the sparse measurement signals. The resulting algorithm is termed as IAR-LASSO-ADMM-CFAR algorithm. Finally, simulation results have been presented to show that the proposed IAR-LASSO-ADMM-CFAR algorithm outperforms the conventional LASSO-ADMM algorithm and other existing algorithms in terms of reconstruction accuracy, and its sparsity order estimate is more accurate than the existing algorithms.
