鲁棒稀疏重构问题的凝聚同伦算法  

Aggregate Homotopy Algorithm for Robust Sparse Reconstruction Problem

作　　者：张洲 盛强 熊慧娟[1] 石峰[1] ZHANG Zhou;SHENG Qiang;XIONG Huijuan;SHI Feng(College of Science,Huazhong Agricultural University,Wuhan 430070,China)

机构地区：[1]华中农业大学理学院,湖北武汉430070

出　　处：《应用数学》2019年第1期206-211,共6页Mathematica Applicata

基　　金：湖北省教改项目"农林院校数据分析类课程的改革与实践"(2016167);国家自然科学基金青年基金项目(11601174);中央高校基本科研业务费专项资金(2662016PY019);华中农业大学科技创新资金(2016304)

摘　　要：鲁棒稀疏重构问题是信号处理领域的重要问题,该问题的数学本质是一个NP难的数学优化问题.同伦算法是一类典型的路径跟踪算法,该算法是解非线性问题的一类成熟算法,具有全局收敛性,且易于并行实现.本文考虑同伦算法在鲁棒稀疏重构问题中的数值求解.基于l_∞范数及罚函数策略,我们首先将原始的基于l_0范数的最优化模型,转化为含参数的无约束极大极小值问题,进而构造凝聚函数光滑化模型中的极大值函数,并构造凝聚同伦算法数值求解.数值仿真实验验证了新方法的有效性,为大规模鲁棒重构问题的并行化数值求解奠定基础.Robust sparse reconstruction problem is an important problem in the field of signal processing. The mathematical nature of the problem is an NP difficult mathematical problem. The homotopy algorithm is a kind of typical path tracking algorithm, which is a kind of mature algorithm for solving nonlinear problems with global convergence and is easy to be parallel implemented. In this paper,we consider the numerical solution of homotopy algorithm in robust sparse reconstruction. Based on the l∞ norm and the penalty function strategy, we firstly transform the original optimization model based on the l0 norm into the unconstrained minima problem with parameters. And then, in conjunction aggregate smoothing technique with homotopy method, we introduce an aggregate smoothing homotopy method for solving the problem. The numerical simulation experiments verify the effectiveness of the new method.Moreover, it can be seen as an early-stage preparation of numerical numerical solution of the large-scale robust reconstruction problem in parallel circumstance.

关 键 词：稀疏重构问题 凝聚函数 同伦算法 

分 类 号：TN911.72[电子电信—通信与信息系统] O221[电子电信—信息与通信工程]