基于分块CS的梯度追踪算法在重构中的应用

Application of Gradient Pursuit Algorithm Based on Block Compressed Sensing in Image Reconstruction

为了解决现有压缩感知图像重构算法中对大规模数据处理复杂度高且计算量大和存储量较大的问题,分别介绍了梯度追踪算法、拟牛顿法和限域拟牛顿法的核心思想并对以上算法的优缺点进行了分析。在分块压缩感知理论的基础上,对梯度追踪(Gradient Pursuit,GP)算法进行改进,通过L-BFGS算法寻找梯度追踪算法中的更新方向并不断修正,将其运用到分块压缩感知的图像重构中,形成了基于L-BFGS方法的GP算法(L-BFGS Method based on GP algorithm,LMGP)。通过对分块后的图像进行单独处理,既避免了牛顿算法中需要进行Hesse矩阵的计算,降低了计算量和复杂度,节省了重构时间,也大大提高了重构效果。该文还对提出的LMGP算法的收敛性进行了分析,并通过LMGP算法对标准图像和一般图像分别进行了重构。仿真实验表明,提出的LMGP算法在重构时间、均方误差及峰值信噪比三个方面均优于其他传统的贪婪算法,说明LMGP算法的重构性能更具有优势。

In order to solve the problem of large data processing complexity and large storage capacity in the existing compressed sensing image reconstruction algorithms,we introduce the core thought of the gradient pursuit algorithm,the quasi-Newton method and the finite domain quasi-Newton law and analyze their advantages and disadvantages.On the basis of block compressed sensing theory,the Gradient Pursuit(GP)algorithm is improved.L-BFGS algorithm is used to find the updated direction in the GP algorithm and continuously modify it,which is applied to the image reconstruction of block compressed sensing.The L-BFGS method based on GP algorithm(LMGP)is formed.By processing the segmented image separately,it not only avoids the Hesse matrix calculation in Newton’s algorithm,reduces the computation amount and complexity,saves the reconstruction time,and greatly improves the reconstruction effect.We also analyze the convergence of the proposed algorithm,and analyze the standard image and general image by LMGP.The simulation results show that the proposed algorithm is better than the other traditional greed algorithm in the reconstruction time,the average error and the peak signal ratio,and the reconstruction performance of the algorithm is more advantageous.