Abstract: Traditionally, compressed sensing has large problems in applying to 2D signal, such as image, leading to poor quality and block effect of output image with wasted flowchart. Based on a few recovery programs designed after 2D Measurement Model（2DMM）, a new algorithm is proposed named 2D Stagewise Orthogonal Matching Pursuit（2D-StOMP）. Learned from the ideas of 2D-OMP, the new algorithm matches atoms with the same weight in one step, so it can cluster larger and more precise dictionary within the same iteration. Theoretical calculation, as well as simulation result, approves that, the new algorithm deals better than state-of-art methods in PSNR without running more time.

Key words: compressed sensing, 2D reconstruction algorithm, 2D Stagewise Orthogonal Matching Pursuit（2D-StOMP）

摘要： 在图像等二维信号的应用与处理上，常规压缩感知理论框架存在重构算法效果差、图像块效应明显、对噪声敏感等问题。针对这些问题，根据现有二维观测模型和二维重构算法设计思想，可以设计一种新的重构算法：二维逐步正交匹配追踪算法。该算法借鉴了相关一维重构算法的设计思想，通过每次迭代选取符合阈值条件的多列原子进而正交化处理的步骤，提升了重构效率，改善了恢复图像质量。理论分析和实验结果表明，提出的算法在重构时间得到控制的情况下，得到的图像信噪比有较大提升，超越了现有典型的二维重构算法。

关键词: 压缩感知, 二维重构算法, 二维逐步正交匹配追踪重构算法（2D-StOMP）