分段正则化正交匹配追踪算法  

Stagewise regularized orthogonal matching pursuit algorithm

作　　者：吴迪 王奎民[2] 赵玉新[1] 王巍[3] 陈立娟 

机构地区：[1]哈尔滨工程大学自动化学院,黑龙江哈尔滨150001 [2]中国人民解放军海军驻锦州地区军事代表室,辽宁锦州121000 [3]中国船舶重工集团公司第七〇三研究所,黑龙江哈尔滨150078

出　　处：《光学精密工程》2014年第5期1395-1402,共8页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.51109045);中央高校基本科研业务费专项资金资助项目(No.HEUCFX41302)

摘　　要：为了使压缩感知重构算法在实际重构信号时不需要稀疏度先验信息,本文提出了分段正则化正交匹配追踪算法。该算法根据信号重构残差量设计阈值,构建候选集。通过正则化候选集提取出用于表示信号的原子,并将其存入支撑集;当候选集为空集时,选择相关系数最大的原子加入支撑集。最后,针对支撑集中的原子求解最小二乘问题实现信号的逼近和残差量的更新。实验结果表明:针对长度为256的高斯信号和二值信号,提出的算法在稀疏度分别达到50和40时,精确重构率可达90%以上;在信号稀疏度相同的条件下,重构效果和速度整体优于现有的同类算法,具有速度快、稳定性好的特点。A novel reconstruction algorithm（stagewise regularized orthogonal matching pursuit）was proposed to reconstruct signals without prior sparsity information.The method constructed the candidate set by designing threshold based on the residual from signal reconstruction.The extracted signal atoms from the candidate set were merged with the previous support set.When the candidate set was a null set,the atom with the greatest correlation was directly added to the support set.Finally,the refinement of signal approximation and residual updating were achieved by solving a least-square algorithm on the support set.The experimental results for Gaussian signal and binary signal with a length of 256show that the probability of exact reconstruction can be reached above 90%on the conditions of signal sparsity of 50and 40,and the reconstructing effects and reconstructing speeds are better thanthose of similar algorithms under the same condition of signal sparsity.This algorithm is proved to be higher processing speeds and more stabile.

关 键 词：压缩感知 重构算法 分段正则化 匹配追踪 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术] TN911.7[自动化与计算机技术—计算机科学与技术]