正则化正交匹配追踪算法由于重构效率高在信号重构中得到广泛应用, 然而该算法需要以信号稀疏度为先验条件, 若稀疏度水平估计不合适会造成重构结果不稳定.针对该问题, 提出了一种基于弱选择正则化的正交匹配追踪算法.该算法可以实现在信号稀疏度未知的条件下, 根据弱选择标准对算法中每次迭代产生的余量与观测矩阵之间的相关性进行判定, 并且自适应地确定表示原信号的原子数目和原子候选集, 进而通过正则化原则从候选集中快速有效地挑选出完成信号重构的最优原子组.数值实验表明, 所提出算法和其它贪婪算法相比较, 峰值信噪比提高0.5~1.5 dB, 最小均方差也明显降低, 图像信号重构效果优于其它同类算法.

Regularized Orthogonal Match Pursuit(ROMP) is widely applied as a signal reconstruction algorithm. Despite its high efficiency, ROMP requires the prior knowledge of signal sparsity, and would be unstable if the sparsity level is improperly estimated. To overcome this drawback, a weak selection strategy was introduced to adaptively determine the number of atoms and the candidate atoms by estimating the relevance between iterative residue and measurement matrix of the original ROMP algorithm. Thus, an optimal atom set for the signal reconstruction procedure could be selected from the candidate atoms according to the regularization principle. Numerical results demonstrate that the proposed method outperforms other greedy algorithms with 0.5~1.5 dB higher PSNR and much lower MSE.