一种稀疏度自适应广义正交匹配追踪算法

A Sparsity Adaptive Generalized Orthogonal Matching Pursuit Algorithm

针对压缩感知(Compressive Sensing,CS)在信号重构时稀疏度往往未知,导致过估计及重构误差变大、复杂度高等问题,通过分析重构残差与支撑集原子数目之间的变化关系,提出一种稀疏度自适应广义正交匹配追踪算法,该算法无需原始信号稀疏度的先验知识。首先,算法采用分阶段变步长的方式扩充支撑集原子数,然后在迭代后期重构残差变化缓慢时改变原子搜索策略精确估计稀疏度,完成原始信号的重构。仿真实验将完成重构所需迭代的次数作为算法复杂度衡量标准,将重构精度、准确重构率及重构运行时间作为评判算法性能的指标。结果表明,该算法重构概率远高于传统的OMP、gOMP算法,重构图像视觉效果更佳,且运算时间低于同类盲稀疏度算法。

A novel sparsity adaptive generalized orthogonal matching pursuit algorithm which based on the relationship between the residuals and the number of atoms in the support set is proposed to reconstruct the sparse signals with unknown sparsity which resulting in overestimation and reconstruction errors and high complexity in compressive sensing. First, the fixed step is used to quickly expand the number of atoms in the support set. Then, the sparsity is accurately estimated according to the slow change of signal rebuilding residual error in the later stage of iteration, and the algorithm exactly rebuild the original signal. The number of iterations needed to complete the reconstruction is used as a measure of the complexity of the algorithm, and the reconstruction accuracy, accurate reconstruction rate, and reconstruction runtime are used as indicators of the performance of the evaluation algorithm. Simulation results show that the proposed algorithm is competitive in recovering accuracy and visual effect, compared to other unknown sparsity algorithms, the running speed is better.