吉林大学学报(工学版) ›› 2013, Vol. 43 ›› Issue (增刊1): 55-59.

Previous Articles     Next Articles

Splitting method to solve Lp problem in sparse image reconstruction

ZHU Yong-gui, LIU Ping, CONG Jia   

  1. School of Science, Communication University of China, Beijing 100024, China
  • Received:2012-06-19 Published:2013-06-01

Abstract:

Lp(0<p<1) problem in sparse image reconstruction is a non-convex optimization problem.The non-convex Lp problem has been splitted into two sub-problems:X sub-problem and Y sub-problem by a half-quadratic penalty method.The closed form solution for X sub-problem could be obtained by the derivative of smooth function.And the solution of Y sub-problem was solved via shrinkage fixed point iterative formula.The splitting algorithm to solve Lp problem for sparse image reconstruction in compressive sensing was estabished by the alternating minimization method for the two sub-problems.Some different kinds of MR images was employed to test in the numerical experiment,and the results demonstrate that the non-convex splitting method is not only more accuracy but also lower sampling rate than convex splitting method in the sparse image reconstruction.

Key words: compressive sensing, non-convex optimization, sparse image, image reconstruction

CLC Number: 

  • TP391

[1] Candes E J,Romberg J,Tao T.Robust uncertainty principles:Exact signal reconstruction from highly incompletee frequency information [J].IEEE Trans Inform Theory,2006,52(2):489-509.

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

[3] Candes E J,Romberg J.Sparsity and incoherence in compressive sampling [J].Inverse Problems,2007,23(3):969-985.

[4] Natarajan B K.Sparse approximation solutions to linear systems [J].SIAM J Comput,1995,24 (2):227-234.

[5] Trzasko J,Manduca A,Borisch E.Highly undersampled magnetic resonance image reconstruction via homotopic L0-minimization [J] IEEE Transactions on Medical Imaging,2009,28(1):106-121.

[6] 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.

[7] Kim S J,Koh K,Lustig M. An interior-point method for large-scale l1-regularized least squares [J].IEEE Trans.on Selected Topics in Signal Processing,2007,1(4):606-617.

[8] Hale E,Yin W,Zhang Y.Fixed-point continuation for l1 minimization:Methodology and convergence [J].SIAM Journal on Optimization,2008,19(3):1107-1130.

[9] Hale E,Yin W,Zhang Y.Fixed-point continuation applied to compressed sensing:Implementation and numerical experiments [J].Journal of Computational Mathematics,2010,28(2):170-194.

[10] Yin W,Osher S,Goldfarb D.Bregman iterative algorithm for l1-minimization with applications to compressed sensing [J].SIAM J.Image Sciences,2008,1(1):143-168.

[11] Goldstein T,Osher S.The split bregman method for L1-regularized problems [J].SIAM J.Image Sciences,2009,2(2):323-343.

[12] He L,Chang T C,Osher S,et al.MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods [R].UCLA CAM Report,2006:6-35.

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

[14] 朱永贵,杨晓兰.稀疏MR图像重构的快速算法[J].中国图象图形学报,2011,16(9):1736-1744. Zhu Yong-gui,Yang Xiao-lan.Fast reconstruction method for sparse MR image [J].Journal of Image and Graphics,2011,16(9):1736-1744.

[15] Jung H,Ye J,Kim E.Improved k-t blask and k-t sense using focuss [J].Phys Med Biol,2007,52(11):3201-3226.

[16] Ye J C,Tak S,Han Y et al.Projection reconstruction MR imaging using FOCUSS [J].Magnetic Resonance in Medicine,2007,57(4):764-775.

[17] Chartrand R.Exact reconstruction of sparse signals via nonconvex minimization[J].IEEE signal Letters,2007,14(10):707-710.

[18] Sidky E Y,Chartrand R,Pan X.Image reconstruction from few views by non-convex optimization .IEEE transaction Medical Imaging Conference Record,2007.

[19] Chartrand R,Yin W.Iteratively reweighted algorithms for compressive sensing [C]// 33rd International Conference on Acoustics Speech,and Signal Processing,2008.

[20] Chartrand R.Fast algorithms nonconvex compressive sensing:MRI reconstruction from very few data [R].IEEE International Symposium on Biomedical Imaging,2009.

[1] YU Hua-nan, DU Yao, GUO Shu-xu. High-precision synchronous phasor measurement based on compressed sensing [J]. 吉林大学学报(工学版), 2018, 48(1): 312-318.
[2] WANG Xin-hua, OUYANG Ji-hong, ZHANG Guang, HE Yang. Super-resolution reconstruction of infrared images based on micro-scanner [J]. 吉林大学学报(工学版), 2017, 47(1): 235-241.
[3] WANG Xin-hua, OUYANG Ji-hong, PANG Wu-bin. Supper-resolution reconstruction of infrared images of compressive coded aperture [J]. 吉林大学学报(工学版), 2016, 46(4): 1239-1245.
[4] ZHU Qi-dan, XU Cong-ying, CAI Cheng-tao. Electronic image stabilization algorithm for on board catadioptric omnidirectional vision system [J]. 吉林大学学报(工学版), 2015, 45(4): 1288-1296.
[5] WANG Hong-zhi,WANG Xian-long,ZHOU Ting-ting. Image block compressive sensing reconstruction based on smooth L0 norm [J]. 吉林大学学报(工学版), 2015, 45(1): 322-327.
[6] ZHAO Chun-hui, TENG Zhi-jun, MA Shuang. Distributed compressive wideband spectrum sensing based on generalized power spectrum density [J]. , 2012, 42(04): 1015-1020.
[7] GUO Wei, CHEN He-xin. Computerized tomographic image reconstruction based on Twomey algorithm [J]. 吉林大学学报(工学版), 2011, 41(增刊1): 332-335.
[8] CHEN Mei-Mei, GUO Shu-Xu, WANG Yao, WU Bin, XU Si-Yao, SHAO Xiang-Xin. Finger vein image denoising based on compressive sensing [J]. 吉林大学学报(工学版), 2011, 41(02): 559-0562.
[9] ZHAO Wei,LI Wen-hui. Fast collision detection algorithm for space image reconstructio [J]. 吉林大学学报(工学版), 2009, 39(06): 1631-1634.
[10] LI Hong-wei, LIU Pei-jun, LIU Qing-huai . Homotopy Interior Point Method and Its Computer Realization for Non-convex & Non-smooth Optimization [J]. 吉林大学学报(工学版), 2001, (4): 49-53.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!