电子学报 ›› 2018, Vol. 46 ›› Issue (10): 2347-2350.DOI: 10.3969/j.issn.0372-2112.2018.10.006

• 学术论文 • 上一篇    下一篇

基于高斯混合模型的衍射成像算法

练秋生, 侯亚伟, 苏月明, 石保顺   

  1. 燕山大学信息科学与工程学院, 河北秦皇岛 066004
  • 收稿日期:2017-06-16 修回日期:2017-11-17 出版日期:2018-10-25
    • 作者简介:
    • 练秋生,男,1969年8月出生于江西遂川,现为燕山大学信息科学与工程学院教授、博士生导师,主要研究方向为图像处理、稀疏表示、压缩感知及相位恢复等.E-mail:lianqs@ysu.edu.cn;侯亚伟,女,1993年6月出生于山东莱芜,现为燕山大学信息科学与工程学院硕士研究生,主要研究方向为非线性压缩感知、相位恢复.E-mail:hyw8269@163.com
    • 基金资助:
    • 国家自然科学基金 (No.61471313); 河北省自然科学基金 (No.F2014203076)

A Diffraction Imaging Algorithm Based on Gaussian Mixture Model

LIAN Qiu-sheng, HOU Ya-wei, SU Yue-ming, SHI Bao-shun   

  1. School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China
  • Received:2017-06-16 Revised:2017-11-17 Online:2018-10-25 Published:2018-10-25
    • Supported by:
    • National Natural Science Foundation of China (No.61471313); Natural Science Foundation of Hebei Province (No.F2014203076)

摘要: 编码衍射成像系统中记录的测量值丢失了相位,而相位含有关于图像的大部分结构信息.如何利用无相位测量值重构原始图像是相位恢复(Phase Retrieval,PR)算法面临的一个重要问题.由期望最大(EM)算法训练高斯混合模型(GMM)的最优参数,任一图像块可以选用GMM中某一模型分量最佳表示.基于该认识,本文利用GMM的统计特性融合数据保真项构造PR优化问题,并用加速邻近梯度法求解该问题.实验结果表明,该算法在噪声强度较大、编码衍射图案较少的情况下仍能获得较高质量的图像重构.

关键词: 相位恢复, 编码衍射图案, 高斯混合模型, 加速邻近梯度

Abstract: The phase information of the recorded measurements is lost in the coded diffraction imaging system. However, the phase contains most of structural information about the image. How to reconstruct the original image from measurements without phase information is a crucial problem faced by the phase retrieval algorithms. The optimal parameters of the Gaussian mixture model (GMM) are trained by the expectation maximization (EM) algorithm. An image patch can be represented optimally by one of the components in the GMM model. Based on this fact, a PR optimization problem which fuses the statistical properties of GMM and the data fidelity term is formulated. Moreover, the accelerated proximal gradient method is utilized to solve this problem. The experimental results show that the proposed method can achieve high-quality image at the case of few coded diffraction patterns and high noise levels.

Key words: phase retrieval, coded diffraction pattern, Gaussian mixture model, accelerated proximal gradient

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