基于两步图像重建的鲁棒相位恢复算法  

Robust Phase Retrieval Algorithm Based on Two-Step Image Reconstruction

作　　者：陈书贞[1] 葛曼[1] 练秋生[1] 石保顺 CHEN Shu-Zhen;GE Man;LIAN Qiu-Sheng;SHI Bao-Shun(School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004)

机构地区：[1]燕山大学信息科学与工程学院,河北秦皇岛066004

出　　处：《计算机学报》2017年第11期2575-2588,共14页Chinese Journal of Computers

基　　金：国家自然科学基金(61471313);河北省自然科学基金(F2014203076)资助~~

摘　　要：相位恢复是指仅利用傅立叶变换或者其它线性变换的幅值对原始图像进行重建,文中针对相位恢复问题提出了一种对不同类型噪声及混合噪声均具有鲁棒性的相位恢复方法.该方法将相位恢复过程分为轮廓恢复和细节恢复两个步骤.首先利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解融合全变差正则项的优化问题恢复图像轮廓.由于第一步重建过程中的全变差正则项平滑了重建图像的细节成分,为保证重建结果包含丰富的细节信息,在第二步中采用第一步获得的重建图像作为原始图像的粗略估计,利用傅立叶幅值约束以及图像在双树复数小波变换下的稀疏性重建图像细节部分.同时,为了使算法能够适用于不同类型噪声,在第二步细节恢复过程中采用l_1范数与l_2范数加权和作为数据保真项.实验结果表明该方法在无需噪声类型先验的条件下仍然能够获得较高的图像重建质量,且对不同类型噪声以及混合噪声均鲁棒.Phase retrieval refers to the problem of recovering the original image from magnitude only of its Fourier transform,or of any other linear transform.A robust phase retrieval algorithm for different types of noises and mixed noise is proposed in this paper for phase retrieval problems.This method divides the phase retrieval process into two steps:contour retrieval and detail retrieval.Firstly,the alternating direction method of multipliers(ADMM)method is exploited to solve the optimization problem of incorporating the total variation regularization term,which results in retrieving the contour of the image.In the first step,the details of the reconstructed image are smoothed by the total variation regularization term.Then,in order to ensure that the reconstructed image contains rich details,the reconstructed image obtained in the first step is used as a coarse estimate of the original image for the second step.Also the Fourier magnitudes and the sparsity of the image under the dual tree complex wavelet transform are adopted to reconstruct the details of the image.Moreover,to make this method robust to different types of noises,the weighted sum of l1norm and l2norm is utilized as the fidelity term.Experimental results show that the proposed method provides high image quality without any prior knowledge of the noise distribution,meanwhile,it is robust to different types of noises and mixed noise.

关 键 词：相位恢复 轮廓恢复 细节恢复 全变差 双树复数小波变换 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]