摘要： 在图像压缩感知中，梯度投影恢复算法存在收敛速度慢、迭代次数多、对数据稀疏度过分敏感的问题。为此，提出一种基于压缩感知的图像重构算法。将拟牛顿法引入稀疏梯度投影算法中，利用拟牛顿法的估计校正机制以及其全局超线性收敛性，通过对目标函数的校正，获得更精确的搜索方向，从而减少迭代次数，构成有效收敛的图像恢复算法。实验结果表明，与传统梯度投影恢复算法相比，该算法在保证较好图像恢复效果的同时具有较好的抗噪性能，并且在减少迭代次数的基础上能有效降低重构误差，得到稳定收敛的重构结果。

关键词: 压缩感知, 梯度投影, 拟牛顿法, 重构, 稳定性, 收敛性

Abstract: There are some problems in the typical gradient projection algorithms in the application of Compressed Sensing(CS), such as the large amount of calculation, the low efficiency of convergence process and excessive dependence on the sparsity of the data matrix. In order to deal with these problems, an efficient recovery algorithm is proposed. This algorithm is based on CS which combines the Quasi-Newton method and the gradient projection method. So it can make full use of the estimating and correcting procedure and the global superlinear convergence of the Quasi-Newton method. By correcting the objective function with the Quasi-Newton method, a more accurate searching direction and fewer iteration can be got. It makes the algorithm perform efficiently with a high convergent reconstruction based on compressed sensing. Experimental results prove that this algorithm shows a good reconstruction and anti-noise performance. Compared with the traditional gradient projection recovery method, the proposed method drops the error rate to make a more stable and convergent reconstruction with fewer iteration.

Key words: Compressed Sensing(CS), gradient projection, Quasi-Newton method, reconstruction, stability, convergence

中图分类号: 

• TP391.41