正交匹配追踪算法的迭代残差重建方法

An iterative residual reconstruction method of the orthogonal matching pursuit algorithm

正交匹配追踪(OrthogonalMatchingPursuit,OMP)算法是一种重要的压缩感知重构算法.OMP算法在每次迭代中选择与当前残差最相关的原子.针对每次迭代需要重新计算残差的问题,本文考虑偶数次迭代下残差未知的情况.首先,研究了奇数次迭代的残差与下一次迭代的残差之间的关系,得到了一种偶数次迭代时选择原子的标准.然后,引入一种回溯机制来处理前面所得的迭代结果,这种机制通过剔除其中多余的原子来实现精确重建.据此,提出了可减少计算残差的改进型正交匹配追踪算法.

Orthogonal Matching Pursuit(OMP)is an important compressed sensing reconstruction algorithm.The OMP algorithm selects the atoms which are most associated to the current residual in each iteration.For the problem of recalculating the residual in each iteration,we consider the case where the residual of even number iterations is unknown.First,we study the relationship between the residuals of odd number iterations and the residuals of the next iteration followed by obtaining a benchmark for selecting atoms in even number iterations.Then we introduce a backtracking mechanism to process the results of previous iterations.The mechanism achieves the precise reconstruction by removing the extra atoms.An improved orthogonal matching pursuit algorithm is thus presented in this study.