稀疏相位恢复的加权L_(1)-正则Huber回归方法

Weighted L_(1)-regularized Huber Method for Sparse Phase Retrieval

相位恢复是指从傅里叶变换或线性变换的幅值中恢复信号,广泛应用于物理科学、机器学习和工程等领域.由于相位信息的丢失导致该问题是病态的,而恢复原始信号一般需要信号的先验知识.本文已知信号稀疏性,提出了一种将Huber损失函数与加权L_(1)正则项相结合的相位恢复方法.该方法运用Majorization-Minimization(MM)优化技术对目标函数进行优化,将原始非凸相位恢复问题转化为容易求解的替代优化问题,接着利用软阈值算子求解给出不动点方程,构造算法框架并进行收敛性分析.数值实验结果表明了加权L_(1)-Huber方法的有效性和稳健性.

Phase retrieval is the problem of recovering a signal from the magnitude of its Fourier transform,or of linear transform.It is widely used in physical science,machine learning and engineering.The problem is ill-posed due to the loss of phase information.Recovering the original signal generally requires prior knowledge of the signal.In this paper,we consider the signal sparsity is known.We proposed a novel method which consists of Huber loss function and an L_(1)regularization.This method used Majorization-Minimization(MM)optimization technique to optimize the objective function.The original non-convex phase retrival problem is transformed into an easy alternative optimization problem.Then the fixed point equation is solved by using the soft threshold operator,the algorithm framework is constructed and the convergence analysis is carried out.The results of numerical experiments show the validity and robustness of the weighted L_(1)Huber method.