中文摘要：

受到硬阈值追踪算法（HTP）的启发,提出了用于求解压缩感知问题的A硬阈值追踪算法（A graded hard thresholding pursuit algorithm,APGHTP）,并在约束等距条件下给出了该算法的理论保证。在数值实验中,不论测量值是否包含误差,APGHTP都表现较好,证明了该算法的稀疏恢复能力。在恢复稀疏向量时,APGHTP所需的迭代数与稀疏向量的稀疏度相同。

英文摘要：

Inspired by hard thresholding pursuit algorithm （HTP）. A＊ graded hard thresholding pursuit algorithm （APGHTP） was proposed for solving compressive sensing problems. The theoretical guarantees of the new algorithm were given under restricted isometry property （RIP） condition. In the numerical experiment, regardless of whether the measured value contains error, APGHTP performance is better, which proves the sparse recovery ability of the algo- rithm. When recovering sparse vectors, the number of iterations required for APGHTP is the same as that of sparse vec- tors.