收稿日期: 2016-09-08
网络出版日期: 2018-08-31
基金资助
国家自然科学基金资助项目(61271213);国家自然科学基金资助项目(61571279);国家自然科学基金资助项目(61673253);教育部博士点基金资助项目(20133108110014)
Sparse signal recovery based on majorization-minimization with enhanced sparsity
Received date: 2016-09-08
Online published: 2018-08-31
针对稀疏信号恢复算法对稀疏性约束不强的问题, 提出了一种基于加强稀疏性非凸函数的稀疏信号恢复算法. 通过分析收缩函数和惩罚函数的关系, 提出一种新的具有加强稀疏性的非凸的惩罚函数, 利用优化最小化(majorization-minimization, MM)方法构造非凸函数的凸上界, 并对目标函数的凸部分和凸上界进行迭代求解, 实现了对稀疏信号的加强恢复. 相较于现存的基于非凸惩罚函数的稀疏信号恢复算法, 本算法具有不受参数干扰和梯度方向包含目标函数非凸部分的优势. 将提出的算法应用于稀疏无线信道的估计, 仿真结果表明, 该算法在噪声环境下可以使用更少的导频, 取得更准确的信道估计结果.
王琛, 方勇, 黄青华, 张立明 . 基于优化最小化的加强稀疏性的稀疏信号恢复算法[J]. 上海大学学报(自然科学版), 2018 , 24(4) : 572 -582 . DOI: 10.12066/j.issn.1007-2861.1839
Conventional sparse signal recovery algorithms fail to promote strong sparsity. To overcome this drawback, this paper proposes a sparse signal recovery algorithm based on a non-convex function with enhanced sparsity. Relationship between the shrinkage function and the penalty function is shown, and a new non-convex penalty function with enhanced sparsity is proposed. The majorization-minimization (MM) method is used to solve the non-convex optimization problem. The convex upper bounds are constructed to approximate the original non-convex penalty function that is hard to solve. Both the convex part and the convex upper bounds of this objective function are optimized iteratively. Compared with existing algorithms based on non-convex penalty functions, the proposed algorithm has two main advantages. First, it is free of the impact of parameter. Second, the gradient direction of the proposed algorithm includes the non-convex part of the objective function. In particular, for sparse wireless channel estimation problems, simulation shows that the proposed algorithm can achieve more accurate estimation with less pilot symbols.
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