Recently, compressed sensing (CS) has aroused much attention for that sparse signals can be retrieved from a small set of linear samples. Algorithms for CS reconstruction can be roughly classified into two categories: (1) optimization-based algorithms and (2) greedy search ones. In this paper, we propose an algorithm called the preconditioned generalized orthogonal matching pursuit (Pre-gOMP) to promote the recovery performance. We provide a sufficient condition for exact recovery via the Pre-gOMP algorithm, which says that if the mutual coherence of the preconditioned sampling matrix Φ satisfies \( \mu ({\Phi }) < \frac {1}{SK -S + 1}, \) then the Pre-gOMP algorithm exactly recovers any K-sparse signals from the compressed samples, where S (>1) is the number of indices selected in each iteration of Pre-gOMP. We also apply the Pre-gOMP algorithm to the application of ghost imaging. Our experimental results demonstrate that the Pre-gOMP can largely improve the imaging quality of ghost imaging, while boosting the imaging speed.

最近，压缩感测（CS）引起了人们的极大关注，因为可以从一小组线性样本中检索稀疏信号。用于CS重建的算法大致可分为两类：（1）基于优化的算法和（2）贪婪搜索算法。在本文中，我们提出了一种称为预处理的广义正交匹配追踪（Pre-gOMP）的算法，以提高恢复性能。我们通过Pre-gOMP算法为精确恢复提供了充分的条件，该算法表示，如果预处理采样矩阵Φ的相干性满足\（\ mu（{\ Phi}）<\ frac {1} {SK -S + 1}，\），则Pre-gOMP算法从压缩样本中准确恢复所有K稀疏信号，其中S（> 1）是在Pre-gOMP的每次迭代中选择的索引数。我们还将Pre-gOMP算法应用于重影成像。我们的实验结果表明，Pre-gOMP可以大大提高重影成像的成像质量，同时提高成像速度。