记忆梯度追踪压缩感知图像重构

目的：重构算法是压缩感知理论的关键问题之一，为了减少压缩感知方向追踪算法重建时间，并确保相对较高的重建精度，提出了一种非单调记忆梯度追踪（memory gradient pursuit,MGP）重构信号处理算法。方法：该算法建立在方向追踪框架下，采用正则化正交匹配策略实现了原子集的快速有效选择，对所选原子集利用非单调线性搜索准则确定步长，用记忆梯度算法计算更新方向，从而得到稀疏信号估计值。结果：该算法充分利用记忆梯度算法在Armijo线搜索下全局收敛性快速稳定的优点避免收敛到局部最优解，提升收敛效率。提出的MGP算法运行时间上比近似共轭梯度追踪算法缩短30%，可以精确重构一维信号和二维图像信号。结论：实验结果表明，该算法兼顾了效率和重建精度，有效提高信号重建性能，在相同测试条件下优于其他同类的重构算法。

Image reconstruction of compressed sensing based on memory gradient pursuit

Objective Reconstruction algorithms are critical for the successful use of the compressive sensing theory. To reduce the signal reconstruction time and ensure the relatively high reconstruction accuracy of the directional pursuit algorithm,an algorithm for compressive sensing signal reconstruction is studied. In this paper,a nonmonotone memory gradient pursuit algorithm(MGP)for reconstructed signals is proposed. Method Under the framework of direction pursuit based on optimization theory,the algorithm first adopts a regularization orthogonal matching strategy to select atom sets fast and efficiently. However,both the least square method part for residual minimization and the direction update part of regularization orthogonal matching are abandoned. Instead,the search step size is determined by a non-monotonic linear search strategy, Furthermore the update direction is fixed with the memory gradient algorithm which increases the degree of freedom of parameter selection. After that,estimated values of sparse coefficients are established. Result The proposed algorithm takes full advantage of globally fast and stable convergence of the memory gradient algorithm with Armijo line search to avoid local optimal solution under some mild condition. By choosing a larger accepted step size at each iteration, Therefore the evaluation of optimization function can be effectively reduced. Besides that,by formula derivation and clever manipulation, the parameter of the direction search can be calculated more rapidly. In this way,the efficiency of convergence is improved. Derivation of direction parameter formula in the original memory gradient method is achieved,and it is more efficiently. The computational cost for memory gradient algorithm is 30% less than that of approximate conjugate gradient pursuit algorithm. Moreover, the MGP algorithm is less insensitive to Gaussian noise than other greedy iteration algorithms. Finally,the one dimension signal and image signal is reconstructed accurately.The reconstruction quality is better when sample rate exceeds 0.2. Conclusion The experiment results of one-dimensional signal and two-dimensional image signal demonstrate that the algorithm is striking a balance between efficiency and reconstruction accuracy and that it has an improved signal reconstruction performance. Additionally,under the same test conditions the proposed algorithm outperforms other similar reconstruction algorithm in time and quality.