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.
翻译:最小偏差缩缩和选择操作器(LASSO)是一种正规化技术,用于估计各种应用中出现的微弱兴趣信号,可以通过倍数的交替方向法(ADMM)来有效解决,该方法将被称为LASSO-ADMM算法。 选择身份化参数对LASSO-ADMM算法的性能有重大影响。然而,现有的LASSO-ADM算法中身份化参数的优化尚未解决。 为了优化这一正规化参数,我们建议通过反复更新LASSO-ADM算法中的正规化参数(ADMMM)来有效解决。此外,一种方法旨在反复更新身份化参数,在LASSO-ADMM算法的外推法值上增加外推法。 内部的LASSO-ADMM算法的零支持值被用于估计噪音变化, 并且使用噪音变异的阈值更新阈值的阈值阈值, 其最终的内算法值正在更新它的内程。