改进的压缩采样匹配追踪算法

Modified compressed sampling pursuit matching algorithm

针对压缩采样匹配追踪(Co Sa MP)算法重构精度相对较差的问题,为了提高算法的重构性能,提出了一种基于伪逆处理改进的压缩采样匹配追踪(MCo Sa MP)算法。首先,在迭代前,对观测矩阵进行伪逆处理,以此来降低原子间的相干性,从而提高原子选择的准确性;然后,结合正交匹配追踪算法(OMP),将OMP算法迭代K次后的原子和残差作为Co Sa MP算法的输入;最后,每次迭代后,通过判断残差是否小于预设阈值来决定算法是否终止。实验结果表明,无论是对一维高斯随机信号还是二维图像信号,MCo Sa MP算法的重构效果优于Co Sa MP算法,能够在观测值相对较少的情况下,实现信号的精确重构。

Aiming at the problem that Compressed Sampling Matching Pursuit （ CoSaMP） algorithm has low accuracy in reconstruction, in order to improve the reconstruction performance of CoSaMP algorithm, , based on pseudo-inverse processing, an improved greedy algorithm—Modified Compressed Sampling Matching Pursuit （ MCoSaMP ） was proposed. Firstly, before each iteration, the proposed algorithm did pseudo-inverse processing on observation matrix, which could reduce the coherence between the atoms, thereby improving the accuracy of the selected atoms. Secondly, combined with Orthogonal Matching Pursuit （ OMP） algorithm, MCoSaMP used the atoms and residual as the input parameters of CoSaMP after OMP algorithm iterating K times. Finally, after each iteration, the residual was used to determine whether to stop algorithm by being under a preset threshold or not. The experimental results show that the proposed algorithm performs better than CoSaMP algorithm for both one-dimensional Gaussian random signal and two-dimensional image signal, which can exactly reconstruct the original signal with relatively small number of observations.