基于非局部相似块低秩的压缩感知图像重建算法

doi:10.3969/j.issn.0372-2112.2017.03.029

电子学报 ›› 2017, Vol. 45 ›› Issue (3): 695-703.DOI: 10.3969/j.issn.0372-2112.2017.03.029

基于非局部相似块低秩的压缩感知图像重建算法

宋云^1,2,3, 李雪玉^1,2,4, 沈燕飞⁴, 杨高波³

1. 长沙理工大学综合交通运输大数据智能处理湖南省重点实验室, 湖南长沙 410114;
2. 长沙理工大学计算机与通信工程学院, 湖南长沙 410114;
3. 湖南大学信息科学与工程学院, 湖南长沙 410012;
4. 中国科学院计算技术研究所, 北京 100190

收稿日期:2015-08-05 修回日期:2015-11-10 出版日期:2017-03-25
- 作者简介:
- 宋云男,1974年9月出生于湖南省汨罗市.长沙理工大学计算机与通信工程学院副教授,硕士研究生导师,现于湖南大学信息科学与工程学院攻读博士学位.主要研究方向包括数字图像处理、视频编解码、压缩感知和计算机视觉等.E-mail:sonie@126.com;李雪玉 女,1991年1月出生于河南省信阳市,长沙理工大学硕士研究生,中国科学院计算技术研究所客座学生.主要研究方向为数字图像处理、视频编解码和计算机视觉等.E-mail:lixueyu_17@163.com;沈燕飞 男,1976年4月出生于江苏省靖江市,中国科学院计算技术研究所副研究员,博士.主要从事数字图像处理、多媒体通信和计算机视觉等方面的研究工作.E-mail:syf@ict.ac.cn;杨高波 男,1974年7月出生于湖南省岳阳市,湖南大学信息科学与工程学院教授,博士研究生导师,主要研究方向为数字图像处理、视频编解码、数字图像安全等.E-mail:yanggaobo@hnu.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61471343，No.61572183，No.61402053）; 湖南省教育厅科学研究重点项目 (No.13A107，No.15A007）; 湖南省自然科学基金 (No.2016JJ2005）; 湖南省科技计划项目 (No.2014FJ6047，No.2014GK3030）

Compressed Sensing Image Reconstruction Based on Low Rank of Non-local Similar Patches

SONG Yun^1,2,3, LI Xue-yu^1,2,4, SHEN Yan-fei⁴, YANG Gao-bo³

1. Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, Changsha University of Science and Technology, Changsha, Hunan 410114 China;
2. School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114 China;
3. College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan 410012 China;
4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China

Received:2015-08-05 Revised:2015-11-10 Online:2017-03-25 Published:2017-03-25
- Supported by:
- National Natural Science Foundation of China (No.61471343, No.61572183, No.61402053); Key Program of Science Research of Education Department of Hunan Province (No.13A107, No.15A007); Natural Science Foundation of Hunan Province, China (No.2016JJ2005); Science and Technology Project of Hunan Province (No.2014FJ6047, No.2014GK3030)

摘要/Abstract

摘要：

传统的压缩感知重建算法利用信号在某个特征空间下的稀疏性构建目标优化函数，但没有充分考虑信号的局部特性和结构化属性，影响了算法的重建性能和算法的适应性.本文考虑图像的非局部自相似性（Nonlocal Self-Similarity，NLSS），提出一种基于图像相似块低秩的压缩感知图像重建算法，将图像恢复问题转化为聚合的相似块矩阵秩最小问题.算法以最小压缩感知重建误差为约束构建优化模型，并采用加权核范数最小化算法（Weighed Nuclear Norm Minimization，WNNM）求解低秩优化问题，很好地挖掘了图像自身的信息和结构化稀疏特征，保护了图像的结构和纹理细节.多个测试图像、不同采样率下的实验证明了算法的有效性，特别是在低采率下对于纹理较为丰富的图像，提出的算法图像重建质量较明显的优于最新的同类算法.

关键词: 压缩感知, 图像重建, 非局部自相似, 低秩优化

Abstract:

Generally,traditional compressed sensing (CS) image recovery methods build the objective optimization function by using the signal sparsity in some specific feature spaces.They do not fully take the local features and structural properties of signal into account,which leads to constraints of the recovery performance and flexibility.In this paper,considering the non-local self-similarity (NLSS) in images,we propose an image CS reconstruction method based on the image low-rank property by converting the CS recovery problem into a matrix rank minimization problem of aggregating similar image patches.The proposed algorithm builds optimization model under the constraint of minimal recovery errors and employs the weighed nuclear norm minimization (WNNM) method to solve the low-rank optimization problem.By taking advantage of them,the proposed method exploits the self-information and structured sparse characteristics of the image very well,and therefore provides a better protection of image structures and textures.Experiments on different test images under various sampling rates have shown the effectiveness of the proposed algorithm.Especially,for richly-textured images,our method outperforms the art-of-the-state algorithms significantly under low sampling rates.

Key words: compressive sensing, image recovery, non-local self-similarity, low-rank optimization

中图分类号:

TP391

宋云, 李雪玉, 沈燕飞, 等. 基于非局部相似块低秩的压缩感知图像重建算法[J]. 电子学报, 2017, 45(3): 695-703.

SONG Yun, LI Xue-yu, SHEN Yan-fei, et al. Compressed Sensing Image Reconstruction Based on Low Rank of Non-local Similar Patches[J]. Acta Electronica Sinica, 2017, 45(3): 695-703.

参考文献

[1] Candes E J,Romberg J,Tao T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information [J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[2] Donoho D L.Compressed sensing [J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[3] Hitomi Y,Gu J,Gupta M,Mitsunaga T,Nayar S K.Video from a single coded exposure photograph using a learned over-complete dictionary [A].2011 International Conference on Computer Vision (ICCV) [C].Barcelona:IEEE,2011:287-294.
[4] 刘记红,黎湘,徐少坤,庄钊文.基于改进正交匹配追踪算法的压缩感知雷达成像方法[J].电子与信息学报,2012,34(6):1844-1850 Liu J H,Li X X,Xu S K,Zhuang Z W.Compressed sensing radar imaging methods based on modified mrthogonal matching mursuit algorithms [J].Journal of Electronics and Information Technology,2012,34(6):1844-1850.(in Chinese)
[5] Chen S S,Donoho D,Saunders M A.Atomic decomposition by basis pursuit [J].SIAM Review,2001,43(1):129-159.
[6] Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit [J].IEEE Transactions Information Theory,2007,53(2):4655-4666.
[7] Dai W,Milenkovic O.Subspace Pursuit for Compressive Sensing:Closing the Gap Between Performance and Complexity [EB/OL].http://arxiv.org/abs/0803.0811,2008.
[8] Elad M,Matalon B,Shtok J,et al.A wide-angle view at iterated shrinkage algorithms [J].Optical Engineering+ Applications.International Society for Optics and Photonics,2007,6701:26-29.
[9] Osher S,Mao Y,Dong B,Yin W.Fast linearized Bregman iteration for compressive sensing and sparse denoising [J].Communications in Mathematical Sciences,2010,8(1):93-111.
[10] Trzasko J,Manduca A.Highly undersampled magnetic resonance image reconstruction via homotopic l₀-minimization [J].IEEE Transactions on Medical Imaging,2009,28(1):106-121
[11] Li C,Yin W,Zhang Y.TVAL3:TV Minimization by Augmented Lagrangian and Alternating Direction Algorithms[EB/OL].http://www.caam.rice.edu/optimization/L1/TVAL3/,2009.
[12] 李志林,陈后金,李居朋,姚畅,杨娜.一种有效的压缩感知图像重建算法[J].电子学报,2011,39(12):2796-2800. Li Z L,Chen H J,Li J P,Yao C,Yang N.An efficient algorithm for compressed sensing image reconstruction [J].Acta Electronica Sinica,2011,39(12):2796-2800.(in Chinese)
[13] 王良君,石光明,李甫,谢雪梅,林耀海.多稀疏空间下的压缩感知图像重构[J].西安电子科技大学学报(自然科学版),2013,40(3):73-80. Wang L J,Shi G M,Li F,Xie X M,Lin Y H.Compressed sensing image reconstruction in multiple sparse spaces [J].Journal of Xidian University(Natural Science),2013,40(3):73-80.(in Chinese)
[14] Dong W,Shi G,Li X,Zhang L,Wu X.Image reconstruction with locally adaptive sparsity and nonlocal robust regularization [J].Signal Processing:Image Communication,2012,27(10):1109-1122.
[15] Dong W,Shi G,Li X.Nonlocal image restoration with bilateral variance estimation:a low-rank approach [J].IEEE Transactions on Image Processing,2013,22(2):700-711.
[16] Egiazarian K,Foi A,Katkovnik V.Compressed sensing image reconstruction via recursive spatially adaptive filtering [A].2007 International Conference on Image Processing (ICIP) [C].San Antonio:IEEE,2007.I-549-I-552.
[17] Dong W,Shi G,Li X,Ma Y,Huang F.Compressive sensing via nonlocal low-rank regularization [J].IEEE Transactions on Image Processing,2014,23(8):3618-3632.
[18] Boyd S,Parikh N,Chu E,Peleato B,Eckstein J.Distributed optimization and statistical learning via the alternating direction method of multipliers [J].Foundations and Treads in Machine Learning,2010,3(1):1-122.
[19] Gu S,Zhang L,Zuo W,et al.Weighted nuclear norm minimization with application to image denoising [A].2014 Conference on Computer Vision and Pattern Recognition (CVPR) [C].Columbus:IEEE,2014.2862-2869.
[20] Plumbley M D,Bevilacqua M.Sparse reconstruction for compressive sensing using stagewise polytope faces pursuit [A].2009 International Conference on Digital Signal Processing (DSP) [C].Santorini:IEEE,2009.1-8.
[21] Buades A,Coll B,Morel J M.A non-local algorithm for image denoising [A].2005 Conference on Computer Vision and Pattern Recognition (CVPR) [C].San Diego:IEEE,2005.60-65.
[22] Dabov K,Foi A,Katkovnik V,Egiazarian K.Image denoising by sparse 3-d transform-domain collaborative filtering [J].IEEE Transactions on Image Processing,2007,16(8):2080-2095.
[23] Cai J,Candes E,Shen Z.A singular value thresholding algorithm for matrix completion [J].SIAM Journal on Optimization,2010,20(4):1956-1982.
[24] Tang S,Zheng Y T,Wang Y,Chua T S.Sparse ensemble learning for concept detection [J].IEEE Transactions on Multimedia,2012,14(1):43-54.
[25] Yang J F,Zhang Y,Yin W T.A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data [J].IEEE Journal of Selected Topics in Signal Processing,2010,4(2):288-297.
[26] Becker S,Bobin J,Candès E J.NESTA:a fast and accurate first-order method for sparse recovery [J].SIAM Journal on Imaging Sciences,2011,4(1):1-39.

基于非局部相似块低秩的压缩感知图像重建算法

Compressed Sensing Image Reconstruction Based on Low Rank of Non-local Similar Patches

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