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A New Smoothed LO Regularization Approach for Sparse Signal Recovery

机译：稀疏信号恢复的新平滑LO正规化方法

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摘要

Sparse signal reconstruction, as the main link of compressive sensing (CS) theory, has attracted extensive attention in recent years. The essence of sparse signal reconstruction is how to recover the original signal accurately and effectively from an underdetermined linear system equation (ULSE). For this problem, we propose a new algorithm called regularization reweighted smoothed L0 norm minimization algorithm, which is simply called RRSL0 algorithm. Three innovations are made under the framework of this method: (1) a new smoothed function called compound inverse proportional function (CIPF) is proposed; (2) a new reweighted function is proposed; and (3) a mixed conjugate gradient (MCG) method is proposed. In this algorithm, the reweighted function and the new smoothed function are combined as the sparsity promoting objective, and the constraint condition parallel to y-Phi x parallel to(2)(2) is taken as a deviation term. Both of them constitute an unconstrained optimization problem under the Tikhonov regularization criterion and the MCG method constructed is used to optimize the problem and realize high-precision reconstruction of sparse signals under noise conditions. Sparse signal recovery experiments on both the simulated and real data show the proposed RRSL0 algorithm performs better than other popular approaches and achieves state-of-the-art performances in signal and image processing.
机译：稀疏信号重建，作为压缩感应（CS）理论的主要链路，近年来引起了广泛的关注。稀疏信号重建的本质是如何从未确定的线性系统方程（ULSE）精确且有效地恢复原始信号。对于此问题，我们提出了一种称为正规化重量平滑L0标准最小化算法的新算法，简称RRSL0算法。在该方法的框架下进行了三种创新：（1）提出了一种名为复合逆比例函数（CIPF）的新平滑功能; （2）提出了一种新的重新重量职能; （3）提出了一种混合共轭梯度（MCG）方法。在该算法中，将重重功能和新的平滑功能组合为稀疏性促进目标，并平行于与（2）（2）平行于（2）的Y-PHI X的约束条件作为偏差项。在Tikhonov正则化标准下构成了无约束的优化问题，并且构造的MCG方法用于优化问题，并在噪声条件下实现稀疏信号的高精度重建。模拟和实数据的稀疏信号恢复实验显示所提出的RRSL0算法比其他流行方法更好，并实现了信号处理中的最先进的性能。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第16期|1978154.1-1978154.12|共12页
  • 作者

    Xiang Jianhong; Yue Huihui; Yin Xiangjun; Wang Linyu;

  • 作者单位

    Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Heilongjiang Peoples R China;

    Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Heilongjiang Peoples R China;

    Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Heilongjiang Peoples R China;

    Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Heilongjiang Peoples R China;

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