一种新的贪婪回溯子空间追踪算法研究

Novel greedy backtracking subspace pursuit algorithm

针对目前的贪婪类算法在实际应用中出现的重构遮挡和虚假等问题,在分析该问题产生的原因基础上,提出了一种新的贪婪回溯子空间追踪(greedy backtracking subspace pursuit,GBSP)算法。该算法的基本思想是在每次的迭代过程中,采用回溯反馈和贪婪精选的思路进行支撑集选择。具体而言,在原子识别阶段,从残差投影中挑选出绝对值最大的K(K是信号稀疏度)个投影值位置,添加到候选支撑集中,为降低在此步骤中产生的错误概率,每次只将候选支撑集中的前s(s<K)个最大值对应的位置添加到真实支撑集中进行更新;此后再进行投影计算和残差更新,直到完成支撑集的选择。新算法结合了正交匹配追踪算法和子空间追踪算法两者的优势,所以可较好地解决重构遮挡与虚假问题,使得压缩感知重构算法更具实用性。

The existing greedy algorithms have occurred fake reconstruction points and occlusions in the practical applica- tions. This paper proposed a novel greedy backtracking subspace pursuit （GBSP） algorithm, based on the analysis of the reason of the problems. The basic idea of the GBSP algorithm was to select the support in each iteration by using the backtracking and greedy reselection methods. Specifically, in the atomic recognition stage,it selected the positions corresponding to the K largest absolute projection values of the residual. Then it added the positions to candidate support. To reduce the error probability of selecting the wrong support in this step, it added s largest absolute projection values of the candidate support to the final estimated support set. The projection calculation and residual updating were done using the final estimated support set. The GBSP combined the advantages of the orthogonal matching pursuit algorithm and subspace pursuit algorithm. It can effectively avoid the fake reconstruction and occlusions phenomenon, and makes the compressed sensing reconstruction algorithm more practical.