Compressed Sensing Image Reconstruction Algorithm Based on Rank Minimization

doi:10.3969/j.issn.0372-2112.2016.03.012

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ACTA ELECTRONICA SINICA ›› 2016, Vol. 44 ›› Issue (3) : 572-579. DOI: 10.3969/j.issn.0372-2112.2016.03.012

Compressed Sensing Image Reconstruction Algorithm Based on Rank Minimization

SHEN Yan-fei^1,2, ZHU Zhen-min¹, ZHANG Yong-dong¹, LI Jin-tao¹

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Abstract

The problem of compressed sensing image reconstruction is imagined as a low rank matrix recovery problem for research.In order to construct this low rank matrix,the nonlocal similarity model is exploited,and every similar image block is treated as a column vector in the matrix.The matrix has the low rank property because the column vectors are strong correlation.The algorithm model is to solve the low rank matrix recovery problem subject to the compressed sensing measurement constraints.In the solution of our proposed algorithm,the constrained optimization problem is converted to unconstrained optimization problem by the augmented lagrangian method,and then the alternating direction multiplier method is employed to solve it.To reduce the computational burden,the linear technique based on Taylor series expansion is taken to accelerate the proposed algorithm.The experimental results show that the subjective and objective performance of our proposed reconstruction algorithm is superior to the state of art reconstruction algorithms.

Key words

compressed sensing / rank minimization / image recovery / non-local similarity

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SHEN Yan-fei, ZHU Zhen-min, ZHANG Yong-dong, LI Jin-tao. Compressed Sensing Image Reconstruction Algorithm Based on Rank Minimization[J]. Acta Electronica Sinica, 2016, 44(3): 572-579. https://doi.org/10.3969/j.issn.0372-2112.2016.03.012

References

[1] Candes E,Romberg J,Tao T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J]. Information Theory,IEEE Transactions on,2006,52(2):489-509.
[2] David L Donoho.Compressed sensing[J]. Information Theory,IEEE Transactions on,2006,52(4):1289-1306.
[3] Bioucas-Dias JM,Figueiredo MA.A new TwIST:Two-step iterative shrinkage thresholding algorithms for image restoration[J]. Image Processing,IEEE Transactions on,2007,16(12):2992-3004.
[4] Leonid I Rudin,Stanley Osher,Emad Fatemi.Nonlinear total variation based noise removal algorithms[J]. Physica D:Nonlinear Phenomena,1992,60(11),259-268.
[5] Jianhua Luo,Wanqing Li,Yuemin Zhu.Reconstruction From limited-angle projections based on δ-u spectrum analysis[J]. Image Processing,IEEE Transactions on,2010,19(1):131-140.
[6] Buades A,Coll B,Morel J-M.A non-local algorithm for image denoising[A]. IEEE Computer Society Conference on Computer Vision and Pattern Recognition[C]. Washington,DC:IEEE Press,2005.60-65.
[7] T Chan,S Esedoglu,F Park,A Yip.In Mathematical Models of Computer Vision[M]. Berlin Germany:springer verlag,2005.
[8] A Chambolle,P L Lions.Image recovery via total variation minimization and related problems[J]. Numerische Mathematik,1997,76(3):167-188.
[9] D Goldfarb,W Yin.Second-order cone programming methods for total variation based image restoration[J]. SIAM Journal on Scientific Computing,2005,27(2):622-645.
[10] Candes E J,Tao T.Near-optimal signal recovery from random projections:Universal encoding strategies?[J]. Information Theory,IEEE Transactions on,2006,52(12):5406-5425.
[11] Bioucas-Dias J M,Figueiredo M A T.Two-step algorithms for linear inverse problems with non-quadratic regularization[A]. IEEE International Conference on Image Processing[C]. Washington,DC:IEEE Press,2007.105-108.
[12] Stephen Becker,Jerome Bobin,Emmanuel J Candes.NESTA:A fast and accurate first-order method for sparse recovery[J]. SIAM Journal on Imaging Sciences,2011,4(1):1-39.
[13] Junfeng Yang,Yin Zhang,Wotao Yin.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.
[14] C Li,W Yin,Y Zhang.TVAL3:TV minimization by augmented Lagrangian and alternating direction algorithms[EB/OL]. http://www.caam.rice.edu/optimization/L1/TVAL3/,2009.
[15] Y Xiao,J Yang,X Yuan,Alternating algorithms for total variation image reconstruction from random projections[J]. Inverse Problems and Imaging,2012,6(3):547-563.
[16] K Dabov,A Foi,V Katkovnik,K Egiazarian.Image denoising by sparse 3D transform-domain collaborative filtering[J]. IEEE Trans Image Process,2007,16(8):2080-2095.
[17] M Maggioni,V Katkovnik,et al.A nonlocal transform-domain filter for volumetric data denoising and reconstruction[J]. IEEE Trans Image Process,2013,22(1):119-133.
[18] Hui Ji,Chaoqiang Liu,et al.Robust video denoising using low rank matrix completion[A]. IEEE Conference on Computer Vision and Pattern Recognition (CVPR)[C]. Washington,DC:IEEE Press,2010.1791-1798.
[19] Hui Ji,Sibin Huang,et al.Robust video restoration by joint sparse and low rank matrix approximation[J]. SIAM Journal on Imaging Sciences,2011,4(4):1122-1142.
[20] Emmanuel J Candes,Xiaodong Li,Yi Ma,John Wright.Robust principal component analysis?[J]. Journal of the ACM,2011,58(3):1-37.
[21] Yigang Peng,Ganesh A,Wright J,Wenli Xu,Yi Ma.RASL:Robust alignment by sparse and low-rank decomposition for linearly correlated images[A]. IEEE Conference on Computer Vision and Pattern Recognition[C]. Washington,DC:IEEE Press,2010.763-770.
[22] Yigang Peng,Ganesh A,et al.RASL:Robust alignment by sparse and low-rank decomposition for linearly correlated images[J]. Pattern Analysis and Machine Intelligence,IEEE Transactions on,2012,34(11):2233-2246.
[23] Jianchao Yang,Wright J,Huang T S,Yi Ma.Image super-resolution via sparse representation[J]. Image Processing,IEEE Transactions on,2010,19(11):2861-2873.
[24] Wright J,Yang A Y,Ganesh A,Sastry S S,Yi Ma.Robust face recognition via sparse representation[J]. Pattern Analysis and Machine Intelligence,IEEE Transactions on,2009,31(2):210-227.
[25] Weisheng Dong,Guangming Shi,Xin Li.Nonlocal image restoration with bilateral variance estimation:A low-rank approach[J]. Image Processing,IEEE Transactions on,2013,22(2):700-711.
[26] Wright J,Ganesh A,Rao S,Ma Y.Robust principal component analysis:exact recovery of corrupted low-rank matrices by convex optimization[A]. Proceedings of Advances in Neural Information Processing Systems (NIPS)[C]. San Francisco:Morgan Kaufmann,2009.2080-2088.
[27] Ganesh A,Zhouchen Lin,Wright J,Leqin Wu,Minming Chen,Yi Ma.Fast algorithms for recovering a corrupted low-rank matrix[A]. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)[C]. Washington,DC:IEEE Press,2009.213-216.
[28] Jian-Feng Cai,E J Candès,Zuowei Shen.A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization,2010,20(4):1956-1982.
[29] Amir Beck,Marc Teboulle.A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences,2009,2(1):183-202.
[30] Zhouchen Lin,Minming Chen,Leqin Wu,Yi Ma.The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices[EB/OL]. http://arxiv.org/abs/1009.5055,2009.
[31] J F Yang,Yin Zhang.Alternating direction algorithms for L1-problems in compressive sensing[J]. SIAM Journal on Scientific Computing,2011,33(1):250-278.
[32] S Mun,Fowler J E.Residual reconstruction for block-based compressed sensing of video[A]. Data Compression Conference (DCC)[C]. Washington,DC:IEEE Press,2011.183-192.
[33] K Egiazarian,A Foi,V Katkovnik.Compressed sensing image reconstruction via recursive spatially adaptive filtering[A]. IEEE International Conference on Image Processing[C]. Washington,DC:IEEE Press,2007.549-552.

Funding

National Natural Science Foundation of China (No.61001123, No.61327013, No.61471343); Industry-university-research Integration Program of Department of Education of Guangdong Province (No.2012B091000106); Scientific Research Instrument and Equipment Development Project of the Chinese Academy of Sciences (No.YZ201321)