结合字典稀疏表示和非局部相似性的自适应压缩成像算法

doi:10.3969/j.issn.0372-2112.2012.07.021

电子学报

结合字典稀疏表示和非局部相似性的自适应压缩成像算法

练秋生, 周婷

燕山大学信息科学与工程学院, 河北秦皇岛 066004

收稿日期:2011-07-22 修回日期:2011-12-27 出版日期:2012-07-25
- 作者简介:
- 练秋生男,1969年8月生于江西遂川.博士,现为燕山大学信息科学与工程学院教授/博士生导师.获省科技进步二等奖二项,发表论文三十余篇.主要研究方向为图像处理,压缩感知及多尺度几何分析等. E-mail:lianqs@ysu.edu.cn 周婷女,1986年8月生于河北衡水.现为燕山大学信息科学与工程学院硕士研究生.主要研究方向为图像处理,压缩感知等. E-mail:zhouting1986.ok@163.com
- 基金资助:
- 国家自然科学基金 (No.61071200,No.60772079); 河北省自然科学基金 (No.F2010001294)

Adaptive Compressed Imaging Algorithm Combined the Sparse Representation in the Dictionaries with Non-Local Similarity

LIAN Qiu-sheng, ZHOU Ting

Institute of Information Science and Technology, Yanshan University, Qinhuangdao, Hebei 066004, China

Received:2011-07-22 Revised:2011-12-27 Online:2012-07-25 Published:2012-07-25
- Supported by:
- National Natural Science Foundation of China (No.61071200, No.60772079); Natural Science Foundation of Hebei Province, China (No.F2010001294)

摘要/Abstract

摘要： 如何以较少的观测值重构出高质量的图像是压缩成像系统的一个关键问题.本文根据图像块随机投影能量大小分布特点,提出了一种新的自适应采样方式以及针对自适应采样的有效重构算法.重构时利用了图像在字典下的稀疏表示原理和图像的非局部相似性先验知识.为实现图像的稀疏表示,文中构造了由多个方向字典和一个正交DCT字典组成的冗余字典,并用l₁范数作为约束条件求解稀疏优化问题.由于充分利用了图像块的局部特性和图像的非局部特性,本文的压缩成像算法在低采样率下能重构出较高质量的图像.

关键词: 压缩成像, 自适应采样, 冗余字典, 稀疏表示, 非局部相似性

Abstract: How to reconstruct the original image from fewer observations is still a crucial question in compressed imaging.According to the probability distribution characteristics of the random projection energy,a novel adaptive sampling method and the corresponding reconstruction algorithm are proposed.The algorithm makes full use of the priors of the sparse representation based on the dictionary and the non-local properties.In order to achieve the sparse image representation,we construct the redundant dictionary that contains several directional dictionaries and one orthogonal DCT dictionary,and solve the sparse optimization problem with constraint of l₁ norm.The proposed compressed imaging algorithm which combines the local traits of the image patches and the non-local properties of the image can reconstruct the high quality image in low sampling rate.

Key words: compressed imaging, adaptive sampling, redundant dictionary, sparse representation, non-local similarity

中图分类号:

TN911.73

练秋生, 周婷. 结合字典稀疏表示和非局部相似性的自适应压缩成像算法[J]. 电子学报, DOI: 10.3969/j.issn.0372-2112.2012.07.021.

LIAN Qiu-sheng, ZHOU Ting . Adaptive Compressed Imaging Algorithm Combined the Sparse Representation in the Dictionaries with Non-Local Similarity[J]. Acta Electronica Sinica, DOI: 10.3969/j.issn.0372-2112.2012.07.021.

参考文献

[1] E J Candes,M B Wakin.An introduction to compressive sampling[J].IEEE Signal Processing Magazine,2008,25(2):21-30.

[2] D L Donoho.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.

[3] 石光明,刘丹华,高大化,刘哲,林杰,王良君.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081. Shi Guang-ming,Liu Dan-hua,Gao Da-hua,Liu Zhe,Lin Jie,Wang Liang-jun.Advances in theory and application of compressed sensing[J].Acta Electronica Sinica,2009,37(5):1070-1081.(in Chinese)

[4] 杨海蓉,张成,丁大为,韦穗.压缩传感理论与重构算法[J].电子学报,2011,39(1):142-148. Yang Hai-rong,Zhang Cheng,Ding Da-wei,Wei Sui.The theory of compressed sensing and reconstruction algorithm[J].Acta Electronica Sinica 2011,39(1):142-148.(in Chinese)

[5] R G Baraniuk.Compressive sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-121.

[6] E J Candes,J Romberg,T Tao.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.

[7] W Bajwa,J Haupt,A Sayeed,R Nowak.Compressive wireless sensing.Proceedings of the fifth International Conference on Information Processing in Sensor Networks (SN ’06).New York,USA:ACM,2006.134-142.

[8] M Lustig,D L Donoho,J M Pauly.Sparse MRI:The application of compressed sensing for rapid MR imaging[J].Magnetic Resonance in Medicine,2007,58(6):1182-1195.

[9] S S Chen,D L Donoho,M A Saunders.Atomic decomposition by basis pursuit[J].Society for Industrial and Applied Mathematics,2001,43(1):129-159.

[10] J A Tropp,A C Gilbert.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666.

[11] T T Do,L Gan,N Nguyen,T D Tran.Sparsity adaptive matching pursuit algorithm for practical compressed sensing.Proceedings of the 42nd Asilomar Conference on Signals,Systems,and Computers.Pacific Grove,California,2008.581-587.

[12] Lu Gan.Block compressed sensing of natural images.Proceedings of the 15th International Conference on Digital Signal Processing.Cardiff,UK,2007.403-406.

[13] S Mun,J E Fowler.Block compressed sensing of images using directional transforms.Proceedings of the 16th International Conference on Image Processing.Cairo,Egypt,2009.3021-3024.

[14] M F Duarte,M B Wakin,R G Baraniuk.Fast reconstruction of piecewise smooth signals from incoherent projections.In Workshop on Signal Processing with Adaptive Sparse Structured Representations.Rennes,France,2005.695-698.

[15] E Candes,J Romberg,T Tao.Stable signal recovery from incomplete and inaccurate measurements[J].Communications on Pure and Applied Mathematics,2006,59(8):1207-1223.

[16] T T Do,T D Tran,Lu Gan.Fast compressive sampling with structurally random matrices.Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing.Las Vegas,NV,2008.3369-3372.

[17] I Daubechies,M Defrise,C DeMol.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57 (11):1413-1457.

[18] 练秋生,陈书贞.基于解析轮廓波变换的图像稀疏表示及其在压缩传感中的应用[J].电子学报,2010,38(6):1293-1298. Lian Qiu-sheng,Chen Shu-zhen.Sparse image representation using the analytic Contourlet transform and its application on compressed sensing[J].Acta Electronica Sinica,2010,38(6):1293-1298.(in Chinese)

[19] R Rubinstein,A M Bruckstein,M Elad.Dictionary for sparse representation modeling[J].Proceedings of the IEEE,2010,98(6):1045-1057.

[20] M Aharon,M Elad,A Bruckstein.K-SVD:An algorithm for designing over complete dictionaries for sparse representation[J].IEEE Transaction.on Signal Processing,2006,54(11):4311-4322.

[21] Dong Wei-sheng,Zhang Lei,Shi Guang-ming,Wu Xiao-lin.Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization.IEEE Transactions on Image Processing,2011,20(7):1838-1857.

[22] B Efron,T Hastie,I Johnstone,R Tibshirani.Least angle regression[J].The Annals of Statistics,2004,32(2):407-499.

结合字典稀疏表示和非局部相似性的自适应压缩成像算法

Adaptive Compressed Imaging Algorithm Combined the Sparse Representation in the Dictionaries with Non-Local Similarity

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