一种改进的OMP算法及其在图像重构上的应用

摘要

为了提高正交匹配追踪(orthogonal matching pursuit,OMP)算法的重构精度,缩短重构时间,以此改善算法的重构性能,提出一种改进的双阈值分段迭代匹配追踪(dual threshold stage-wise iteration matching pursuit,DTSIMP)算法.该算法首先利用OMP算法迭代若干次,当残差小于第一阈值时引入回溯思想,利用压缩采样匹配追踪(compressed sampling matching pursuit,CoSaMP)算法继续迭代,并且将OMP算法迭代所得的残差和原子作为CoSaMP算法的初始输入值,当残差小于第二阈值时停止迭代.双阈值中,第一阈值控制OMP算法迭代次数,得到CoSaMP算法的最优初始输入;第二阈值控制信号的重构精度,以此实现精确快速地重构出稀疏信号.实验结果表明,对于一维的随机高斯信号,该算法重构误差小,重构时间少,并且在不同稀疏度和观测值下,算法重构成功率均高于原算法;对于二维图像信号,该算法重构时间少,重构效果好.%In order to improve the reconstruction accuracy and performance of orthogonal matching pursuit (OMP) and shorten its recon-struction time,we propose an improved dual threshold stage-wise iteration matching pursuit (DTSIMP).It first uses the OMP for iteration until residual error is less than the first threshold value,then the idea of backtrack is added into the algorithm,which we take the compressed sampling matching pursuit(CoSaMP) for iteration again.The residual and atoms obtained from the OMP iterated are used as the input of the second step.Iteration stops when residual error is also less than the second preset threshold value.The first threshold controls the number of iterations of the OMP to get the optimal initial input of the CoSaMP,and the second threshold determines reconstruction accuracy of signal, so as to reconstruct sparse signals quickly and accurately.The experiment shows that the proposed algorithm is of little reconstruction error and reconstruction time with better reconstruction success rate for one-dimensional Gauss random signal when compared with OMP and Co-SaMP.For two-dimensional image signal,it has the advantages of fast reconstruction time and excellent reconstruction effects.