基于高斯混合模型的衍射成像算法

doi:10.3969/j.issn.0372-2112.2018.10.006

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

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

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

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/Abstract

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

中图分类号:

TN911.73

练秋生, 侯亚伟, 苏月明, 等. 基于高斯混合模型的衍射成像算法[J]. 电子学报, 2018, 46(10): 2347-2350.

LIAN Qiu-sheng, HOU Ya-wei, SU Yue-ming, et al. A Diffraction Imaging Algorithm Based on Gaussian Mixture Model[J]. Acta Electronica Sinica, 2018, 46(10): 2347-2350.

参考文献

[1] SHECHTMAN Y,ELDAR Y C,COHEN O,et al.Phase retrieval with application to optical imaging:a contemporary overview[J].IEEE Signal Processing Magazine,2015,32(3):87-109.
[2] LUSTIG M,DONOHO D L,PAULY J M.Sparse MRI:The application of compressed sensing for rapid MR imaging[J].Magnetic Resonance in Medicine,2007,58(6):1182-1195.
[3] SHECHTMAN Y,BECK A,ELDAR Y C.GESPAR:efficient phase retrieval of sparse signals[J].IEEE Transactions on Signal Processing,2014,62(4):928-938.
[4] SCHNITER P,RANGAN S.Compressive phase retrieval via generalized approximate message passing[J].IEEE Transactions on Signal Processing,2015,63(4):1043-1055.
[5] METZLER C A,MALEKI A,BARANIUK R G.BM3D-PRGAMP:Compressive phase retrieval based on BM3D denoising[A].IEEE International Conference on Image Processing[C].Phoenix,AZ,USA:ICIP,2016.2504-2508.
[6] CANDES E J,LI X,SOLTANOLKOTABI M.Phase retrieval from coded diffraction patterns[J].Applied and Computational Harmonic Analysis,2015,39(2):277-299.
[7] CANDES E J,LI X,SOLTANOLKOTABI M.Phase retrieval via wirtinger flow:theory and algorithms[J].IEEE Transactions on Information Theory,2015,61(4):1985-2007.
[8] CHEN Y,CANDES E J.Solving random quadratic systems of equations is nearly as easy as solving linear systems[A].Advances in Neural Information Processing Systems 28[C].Montreal,Canada:NIPS,2015.739-747.
[9] TILLMANN A M,ELDAR Y C,MAIRAL J M.DOLPHIn-dictionary learning for phase retrieval[J].IEEE Transactions on Signal Processing,2016,64(24):6485-6500.
[10] KATKOVNIK V.Sparse phase retrieval from noisy data:variational formulation and algorithms[A].3D Image Acquisition and Display:Technology,Perception and applications[C].Heidelberg,Germany:Optical Society of America,2016.JT3A.42.
[11] ZORAN D,WEISS Y.From learning models of natural image patches to whole image restoration[A].IEEE International Conference on Computer Vision[C].Barcelona,Spain:ICCV,2011.479-486.
[12] IKEDA S,KONO H.Phase retrieval from single biomolecule diffraction pattern[J].Optics Express,2012,20(4):3375.

[1]	李凯, 张可心. 结构α-熵的加权高斯混合模型的子空间聚类[J]. 电子学报, 2022, 50(3): 718-725.
[2]	石雪, 李玉, 赵泉华. 自适应类别的层次高斯混合模型遥感影像分割[J]. 电子学报, 2020, 48(1): 131-136.
[3]	练秋生, 宋爽, 陈书贞, 石保顺. 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[J]. 电子学报, 2017, 45(9): 2210-2217.
[4]	练秋生, 魏天姣, 陈书贞, 石保顺. 基于全变差正则化的相位恢复算法[J]. 电子学报, 2017, 45(1): 54-60.
[5]	栗雨晴, 礼欣, 韩煦, 宋丹丹, 廖乐健. 基于双语词典的微博多类情感分析方法[J]. 电子学报, 2016, 44(9): 2068-2073.
[6]	白海钏, 鲍长春, 刘鑫. 基于局部最小二乘支持向量机的音频频带扩展方法[J]. 电子学报, 2016, 44(9): 2203-2210.
[7]	车滢霞, 俞一彪. 约束条件下的结构化高斯混合模型及非平行语料语音转换[J]. 电子学报, 2016, 44(9): 2282-2288.
[8]	刘鑫, 鲍长春. 基于相似关联度神经网络的音频频带扩展[J]. 电子学报, 2015, 43(4): 816-821.
[9]	王大磊, 杨宾, 吴瑛, 王秀秀. 一种基于峰度的QAM信号盲均衡与载波相位恢复准则[J]. 电子学报, 2014, 42(7): 1403-1409.
[10]	李冬辉, 何鹏林. 基于GMM聚类的空调机组多未知模态辨识方法研究[J]. 电子学报, 2014, 42(10): 2004-2008.
[11]	何玉文, 鲍长春, 夏丙寅. 基于AR-HMM在线能量调整的语音增强方法[J]. 电子学报, 2014, 42(10): 1991-1997.
[12]	钟尚平, 徐巧芬, 陈羽中, 何凤英. 一种基于LSB序列局部特征的通用隐写检测方法[J]. 电子学报, 2013, 41(2): 239-247.
[13]	张兴涛, 鲍长春, 刘鑫, 张丽燕. 基于Volterra级数预测的音频频带扩展[J]. 电子学报, 2012, 40(12): 2501-2506.
[14]	梁岩, 鲍长春, 夏丙寅, 何玉文, 周璇, 李娜. 基于高斯混合模型的压缩域语音增强方法[J]. 电子学报, 2012, 40(10): 2031-2038.
[15]	徐宁;杨震;张玲华. 基于状态空间模型的子频带语音转换算法[J]. 电子学报, 2010, 38(3): 646-653.

基于高斯混合模型的衍射成像算法

A Diffraction Imaging Algorithm Based on Gaussian Mixture Model

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics