基于修正的拟牛顿法的基追踪去噪研究

为提高一维信号去除噪声的稀疏分解基追踪算法的效率，提出了采用修正的拟牛顿法来解决基追踪去噪过程中的无约束优化问题。该算法在传统拟牛顿法的基础上，对BFGS(Broyden-Fletcher-Goldfarb-Shanno)公式进行修正，有效地减少了最优化过程中所需的迭代次数。实验结果表明，修正的拟牛顿法与传统算法相比，能够明显提高目标函数的收敛速率。

Basic pursuit denoising research based on the modified quasi-Newton method

To improve the efficiency of using basic pursuit algorithm which belongs to the sparse decomposition for one dimensional signal de-noising, in this paper modified quasi-Newton method was proposed to solve the unconstrained optimization problem in the process of basic pursuit de-noising. On the basis of traditional quasi Newton method, in this algorithm the Broyden-Fletcher-Goldfarb-Shanno(BFGS)-type formula was modified, the number of iterations was reduced effectively in the optimization process. Experimental results show that the modified quasi Newton method compared to the traditional one can obviously improve the convergence rate of the objective function.