基于全变差正则化的相位恢复算法

相位恢复问题是指仅通过信号傅立叶变换（或其它线性变换）的幅值恢复原始信号.由于相位信息的缺失，该问题是一个不适定问题，因此需利用先验知识确保精确重建.本文基于非线性压缩感知框架，提出利用自然图像在梯度算子下的稀疏性进行相位恢复的算法.该算法将全变差正则项融合到基于支撑约束和幅值约束的相位恢复问题中，并利用交替方向乘子法（ADMM）对所对应的非凸优化问题进行求解.实验结果表明，该算法明显优于HIO，RAAR等经典的相位恢复算法，并对噪声具有鲁棒性.

A Phase Retrieval Algorithm Based on Total Variation Regularization

The problem of phase retrieval,namely,recovery of a signal only from the magnitude of its Fourier transform,or of any other linear transform.Due to the loss of phase information,this problem is ill-posed.Therefore,the prior knowledge is required to enable its accurate reconstruction.In this work,based on the framework of nonlinear compressive sensing,a novel phase retrieval algorithm which exploits the sparsity of the natural images under the image gradient operator is proposed.The algorithm incorporates the total variation regularization into the phase retrieval problem,which based on support constraints and amplitude constraints.Moreover,alternating direction method of multipliers (ADMM) is utilized for solving the corresponding non-convex optimization problem.Experimental results indicate that the performance of the proposed algorithm outperforms the classical algorithms,such as HIO,RAAR,moreover,it is robust to noise.