应用于非负稀疏信号重构的交替方向乘子法  

Nonnegative Sparse Signal Recovery via Alternating Direction Method of Multipliers

作　　者：闵刚[1,2] 张雄伟[1] 杨吉斌[1] 胡永刚[1] 潘竟峰[3] 

机构地区：[1]解放军理工大学指挥信息系统学院,南京210007 [2]西安通信学院,西安710106 [3]空军预警学院,武汉430019

出　　处：《信号处理》2015年第11期1411-1417,共7页Journal of Signal Processing

基　　金：国家自然科学基金(61471349;61402519);江苏省自然科学基金(BK2012510;BK20140071;BK20140074)

摘　　要：非负稀疏信号在欠定线性观测条件下的重构效果不理想,仍有进一步提高的余地。文中将非负稀疏信号重构建模为线性规划问题,在交替方向乘子法的框架下得到了具有闭合解形式的优化算法,且算法复杂度较低。为了进一步增强重构信号的稀疏性,提出了迭代加权线性规划算法,通过对权值向量和重构信号交替优化提高了重构准确率。实验仿真验证了算法的有效性,针对随机生成信号和实际语音能量谱这两类非负稀疏信号均取得了较好的重构效果,重构性能优于目前一些流行的稀疏信号重构算法。The recovery of nonnegative sparse signals is not perfect given their underdetermined linear measurements at present,which can be improved further. This paper models this problem as linear programming and presents an optimization method with closed-form solution updated using the alternating direction method of multipliers. Moreover,the computational complexity is low. To enhance the sparsity of the recovered signal,this paper proposes the algorithm of iteratively reweighted linear programming,then the rate of successful recovery is increased by alternately optimizing the solution vector and the weighting vector. The effectiveness of the proposed algorithms and the recovering performance are verified by experiments on randomly generated signals and the actual power spectrum of speech signals,which outperform some state of the art sparse recovery algorithms.

关 键 词：非负 稀疏 交替方向乘子法 信号重构 

分 类 号：TN912.3[电子电信—通信与信息系统]