基于高阶马尔可夫随机场及非线性压缩感知的相位恢复算法

A Phase Retrieval Algorithm Based on Higher-Order Markov Random Fields and Nonlinear Compressed Sensing

在编码衍射成像系统中,为精确重构复图像的幅值和相位,需获取大量的编码衍射图样,导致数据采集时间长.为减少编码衍射图样的数量,本文基于非线性压缩感知理论框架,利用高阶马尔可夫随机场统计先验模型,提出了一种鲁棒相位恢复算法.该方法将复图像的幅值和相位分别进行正则化,并将数据保真项与幅值和相位正则项结合作为代价函数,采用Heavy-Ball算法求解所对应的非凸优化问题.实验结果表明,本文算法在编码衍射图样较少的情况下仍能获得较高的图像重构质量,且对噪声鲁棒.

To enable prefect reconstruction of the magnitude and phase of the complex images in the coded diffraction imaging system,many coded diffraction patterns are required,which leads to time consuming of the sampling process. To reduce the number of coded diffraction patterns,a robust phase retrieval algorithm which exploits the statistical characteristic of the higher-order Markov random fields is proposed based on the nonlinear compressed sensing framework. The presented method regularizes the magnitude and phase separately,and combines the data fidelity term with the regularization terms of the magnitude and phase to formulate the cost function. Moreover,the heavy-ball algorithm is utilized for solving the corresponding non-convex optimization problem. Experimental results showthat the proposed method can achieve high image quality with fewer coded diffraction patterns,and is robust to noise.