基于拟牛顿法的梯度追踪算法研究

Investigation on Gradient Tracking Algorithm with Quasi Newton Method

为了解决传统迭代算法中需要计算正交投影的问题,将拟牛顿法与梯度追踪算法(Gradient Pursuit)相结合,提出了基于拟牛顿法的梯度追踪算法(Quasi-Newton Method based Gradient Pursuit,QNMGP)。拟牛顿法是解决无约束最优化问题的有效方法,其避免了牛顿法需要求解Hesse矩阵的问题,降低了计算量,提高了收敛速度,新提出的算法通过限域拟牛顿法来求解更新方向,并将其运用到梯度追踪算法中。为验证新提出算法的可行性与有效性,基于MATLAB仿真平台,从重构时间、均方误差和峰值信噪比三个方面对QNMGP算法与其他贪婪算法进行了仿真对比实验验证。仿真实验结果表明,在同等的测试环境下,新提出的QNMGP算法重构效果远优于其他算法,且在重构时间上也具有一定的优势。

It＇s necessary to compute the orthogonal projection in the traditional iteration algorithms. In order to solve this problem,the Quasi-Newton Method-based Gradient Pursuit （QNMGP） has been proposed, in which Quasi-Newton method is an effective one to solve unconstrained optimization problems without need of the Hesse matrix at the same time. The amount of calculation has been reduced and the convergence speed has beert raised. The proposed algorithm can change the direction for solution of Quasi-Newton method in lim- itation domain and then be applied in the gradient tracking algorithm. Based on MATLAB simulation platform,experiment tests for verifi- cation,in which the proposed QNMGP is compared with other greedy algorithms on three performances like reconstruction time, mean square error and peak signal to noise ratio. The simulation results show that the proposed QNMGP algorithm is more effective than other algorithms in the same test environment and has advantage in reconstruction time.