摘要
To improve the reconstruction performance of the greedy algorithm for sparse signals, an improved greedy algorithm, called sparsity estimation variable step-size matching pursuit, is proposed. Compared with state-of-the-art greedy algorithms, the proposed algorithm incorporates the restricted isometry property and variable step-size, which is utilized for sparsity estimation and reduces the reconstruction time, respectively. Based on the sparsity estimation, the initial value including sparsity level and support set is computed at the beginning of the reconstruction, which provides preliminary sparsity information for signal reconstruction. Then, the residual and correlation are calculated according to the initial value and the support set is refined at the next iteration associated with variable step-size and backtracking. Finally, the correct support set is obtained when the halting condition is reached and the original signal is reconstructed accurately. The simulation results demonstrate that the proposed algorithm improves the recovery performance and considerably outperforms the existing algorithm in terms of the running time in sparse signal reconstruction.
为了提高稀疏信号贪婪算法的重构性能,提出了一种改进的贪婪重构算法,即稀疏度估计变步长匹配追踪算法.与现有的贪婪算法相比,该算法用约束等距常数和变步长分别来进行稀疏度估计和减少重构所需的时间.通过稀疏度估计,在重构的开始阶段得到估计的稀疏度和支撑集作为初始值,为信号重构提供了初始的稀疏信息.然后,根据初始值计算相关值以及残差,通过回溯思想和可变步长更新上一次迭代得到的支撑集.最后,当满足算法终止条件时,得到正确的信号支撑集,从而准确地重构出原始信号.仿真结果证明,针对稀疏信号重构,所提出的算法提高了重构性能,所需要的运算时间较之前的算法大幅减少.
基金
The National Basic Research Program of China(973Program)(No.2013CB329003)
