Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

An algorithm for image reconstruction based on lp norm

Ning Fang-Li He Bi-Jing Wei Juan

An algorithm for image reconstruction based on lp norm

Ning Fang-Li, He Bi-Jing, Wei Juan
PDF
Get Citation
  • Image reconstruction is one of the key technologies in the fields of physical imaging, which include optical imaging, photoacoustic imaging, sonar imaging, magnetic resonance imaging, and celestial imaging etc. Compressive sensing theory, the new research spot in recent years, describes that a small group of non-adaptive linear projections of a sparse or compressible signal contains enough information for signal reconstruction. Compressive sensing has been applied in many physical imaging systems. In this paper, we propose a new image reconstruction algorithm based on lp norm compressive sensing by combining the penalty function and revised Hesse sequence quadratic programming, and using block compressive sensing. Several images, such as “cameraman”, “barbara” and “mandrill”, are chosen as the images for image reconstruction. First, we take different sampling rates for image reconstruction to verify the algorithm. When the sampling rate is as low as 0.3, the signal-to-noise ratio of the reconstructed image can reach up to 32.23 dB. Then, when the sampling rate is above 0.5, by comparing with OMP algorithm, reconstructed images can be obtained with a higher signal-to-noise ratio and a shorter imaging time. Especially, when the sampling rate is 0.7, the imaging time is reduced by 88%. Finally compared with the existing algorithm based on lp norm compressive sensing, simulation results show that the new algorithm can improve the signal-to-noise ratio of reconstructed images, and greatly reduce the imaging time.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51075329), the Shaanxi Science and Technology Research and Development Project, China (Grant No. 2012GY2-41), NPU Foundation for Fundamental Research, China (Grant No. NPU-FFR-JCY20130117), and the Graduate Starting Fund of Northwestern Polytechnical University, China (Grant No. Z2013029).
    [1]

    Zhang Q S, Lv X X, Yu Q T, Liu G Y 2009 Chin. Phys. B 18 2764

    [2]

    Huang L M, Ding Z H, Hong W, Wang C 2012 Acta Phys. Sin. 61 023401 (in Chinese) [黄良敏, 丁志华, 洪威, 王川 2012 物理学报 61 023401]

    [3]

    Yang S H, Yin G Z, Xing D 2010 Chin. Phys. Lett. 27 094302

    [4]

    Zhang C H, Liu J Y 2006 Physics 35 408

    [5]

    Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289

    [6]

    Candes E J, Romberg J 2006 IEEE Trans.Inform.Theory 52 489

    [7]

    Duarte M F, Davenport M A, Takhar D, Laska J N, Sun T, Kelly K F, Baraniuk R G 2008 IEEE Sig. Proc. Mag. 25 83

    [8]

    Filiipe M, Francisco M A, Miguel V C 2011 Appl. Optics. 50 405

    [9]

    Chen T, Li Z W, Wang J L, Wang B, Guo S 2012 Optics and Precision Engineering 20 2523 (in Chinese) [陈涛, 李正炜, 王建立, 王斌, 郭爽 2012 光学精密工程 20 2523]

    [10]

    Lustig M, Donoho D, Pauly J M 2007 Magn. Reson. Med. 58 1182

    [11]

    Lingala S G, Hu Y, Dibella E, Jacob M 2011 IEEE Trans. Med. Imaging 30 1042

    [12]

    Motefusco L B, Lazzaro D, Papi S, Guerini C 2011 IEEE Trans. Med. imaging 30 1064

    [13]

    Bobin J, Starck J L, Ottensamer R 2008 IEEE Sel. Top. Sig. Proc. 2 718

    [14]

    Lu M H, Shen X, Han S S 2011 Acta Opt. Sin. 31 0711002 (in Chinese) [陆明海, 沈夏, 韩申生 2011 光学学报 31 0711002]

    [15]

    Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]

    [16]

    Mallat S, Zhang Z F 1993 IEEE Trans. Sig. Proc. 41 3397

    [17]

    Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655

    [18]

    Needell D, Vershynin R 2009 Found. Comput. Math. 9 317

    [19]

    Chen S, Saunders M A, Donoho D L 2001 SIMA Review 43 129

    [20]

    Figueiredo M, Nowak R D, Wright S J 2007 IEEE Sel. Top. Sig. Proc. 1 586

    [21]

    Bhaskar D, Kenneth K D 1999 IEEE Trans. Sig. Proc. 47 187

    [22]

    Chartand R 2007 IEEE Sig. Proc. Let. 14 707

    [23]

    Lu G 2007 Proceedings of the 15th International Conference on Digital Signal Processing Cardiff, UK,July 1-4, 2007 p403

    [24]

    Wang X Y, Guo X, Zhang D D 2012 Chin. Phys. B 21 090507

    [25]

    Wang X Y, Wang Y X, Yun J J 2011 Chin. Phys. B 20 104202

    [26]

    Rao B D, Kreutz D K 1999 IEEE Trans. Sig. Proc. 47 187

  • [1]

    Zhang Q S, Lv X X, Yu Q T, Liu G Y 2009 Chin. Phys. B 18 2764

    [2]

    Huang L M, Ding Z H, Hong W, Wang C 2012 Acta Phys. Sin. 61 023401 (in Chinese) [黄良敏, 丁志华, 洪威, 王川 2012 物理学报 61 023401]

    [3]

    Yang S H, Yin G Z, Xing D 2010 Chin. Phys. Lett. 27 094302

    [4]

    Zhang C H, Liu J Y 2006 Physics 35 408

    [5]

    Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289

    [6]

    Candes E J, Romberg J 2006 IEEE Trans.Inform.Theory 52 489

    [7]

    Duarte M F, Davenport M A, Takhar D, Laska J N, Sun T, Kelly K F, Baraniuk R G 2008 IEEE Sig. Proc. Mag. 25 83

    [8]

    Filiipe M, Francisco M A, Miguel V C 2011 Appl. Optics. 50 405

    [9]

    Chen T, Li Z W, Wang J L, Wang B, Guo S 2012 Optics and Precision Engineering 20 2523 (in Chinese) [陈涛, 李正炜, 王建立, 王斌, 郭爽 2012 光学精密工程 20 2523]

    [10]

    Lustig M, Donoho D, Pauly J M 2007 Magn. Reson. Med. 58 1182

    [11]

    Lingala S G, Hu Y, Dibella E, Jacob M 2011 IEEE Trans. Med. Imaging 30 1042

    [12]

    Motefusco L B, Lazzaro D, Papi S, Guerini C 2011 IEEE Trans. Med. imaging 30 1064

    [13]

    Bobin J, Starck J L, Ottensamer R 2008 IEEE Sel. Top. Sig. Proc. 2 718

    [14]

    Lu M H, Shen X, Han S S 2011 Acta Opt. Sin. 31 0711002 (in Chinese) [陆明海, 沈夏, 韩申生 2011 光学学报 31 0711002]

    [15]

    Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]

    [16]

    Mallat S, Zhang Z F 1993 IEEE Trans. Sig. Proc. 41 3397

    [17]

    Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655

    [18]

    Needell D, Vershynin R 2009 Found. Comput. Math. 9 317

    [19]

    Chen S, Saunders M A, Donoho D L 2001 SIMA Review 43 129

    [20]

    Figueiredo M, Nowak R D, Wright S J 2007 IEEE Sel. Top. Sig. Proc. 1 586

    [21]

    Bhaskar D, Kenneth K D 1999 IEEE Trans. Sig. Proc. 47 187

    [22]

    Chartand R 2007 IEEE Sig. Proc. Let. 14 707

    [23]

    Lu G 2007 Proceedings of the 15th International Conference on Digital Signal Processing Cardiff, UK,July 1-4, 2007 p403

    [24]

    Wang X Y, Guo X, Zhang D D 2012 Chin. Phys. B 21 090507

    [25]

    Wang X Y, Wang Y X, Yun J J 2011 Chin. Phys. B 20 104202

    [26]

    Rao B D, Kreutz D K 1999 IEEE Trans. Sig. Proc. 47 187

  • [1] Shi Jie, Yang De-Sen, Shi Sheng-Guo, Hu Bo, Zhu Zhong-Rui. Compressive focused beamforming based on vector sensor array. Acta Physica Sinica, 2016, 65(2): 024302. doi: 10.7498/aps.65.024302
    [2] Shi Hang, Wang Li-Dan. Multi-process image encryption scheme based on compressed sensing and multi-dimensional chaotic system. Acta Physica Sinica, 2019, 68(20): 200501. doi: 10.7498/aps.68.20190553
    [3] Hu Yao-Hua, Liu Yan, Mu Ge, Qin Qi, Tan Zhong-Wei, Wang Mu-Guang, Yan Feng-Ping. Application of compressive sensing based on multimode fiber specklegram in optical image encryption. Acta Physica Sinica, 2020, 69(3): 034203. doi: 10.7498/aps.69.20191143
    [4] Chai Shui-Rong, Guo Li-Xin. A new fast algorithm based on compressive sensing for composite electromagnetic back scattering from a 2D ship located on a 1D rough sea surface. Acta Physica Sinica, 2015, 64(6): 060301. doi: 10.7498/aps.64.060301
    [5] Guo Jing-Bo, Li Jia-Wen. Chaotic compressive measurement and reconstruction of binary signals. Acta Physica Sinica, 2015, 64(19): 198401. doi: 10.7498/aps.64.198401
    [6] Guo Jing-Bo, Wang Ren. Construction of a circulant compressive measurement matrix based on chaotic sequence and RIPless theory. Acta Physica Sinica, 2014, 63(19): 198402. doi: 10.7498/aps.63.198402
    [7] Yang Kun, Liu Xin-Xin, Li Xiao-Wei. Influence of data interpolation on positron emission tomography image tomography reconstruction. Acta Physica Sinica, 2013, 62(14): 147802. doi: 10.7498/aps.62.147802
    [8] He Lin-Yang, Liu Jing-Hong, Li Gang. Super resolution of aerial image by means of polyphase components reconstruction. Acta Physica Sinica, 2015, 64(11): 114208. doi: 10.7498/aps.64.114208
    [9] Qiao Zhi-Wei. The total variation constrained data divergence minimization model for image reconstruction and its Chambolle-Pock solving algorithm. Acta Physica Sinica, 2018, 67(19): 198701. doi: 10.7498/aps.67.20180839
    [10] Li Long-Zhen, Yao Xu-Ri, Liu Xue-Feng, Yu Wen-Kai, Zhai Guang-Jie. Super-resolution ghost imaging via compressed sensing. Acta Physica Sinica, 2014, 63(22): 224201. doi: 10.7498/aps.63.224201
  • Citation:
Metrics
  • Abstract views:  849
  • PDF Downloads:  1500
  • Cited By: 0
Publishing process
  • Received Date:  06 May 2013
  • Accepted Date:  02 June 2013
  • Published Online:  05 September 2013

An algorithm for image reconstruction based on lp norm

  • 1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China;
  • 2. State Key Laboratory of Integrated Services Networks, School of Telecommunication Engineering, Xidian University, Xi’an 710071, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 51075329), the Shaanxi Science and Technology Research and Development Project, China (Grant No. 2012GY2-41), NPU Foundation for Fundamental Research, China (Grant No. NPU-FFR-JCY20130117), and the Graduate Starting Fund of Northwestern Polytechnical University, China (Grant No. Z2013029).

Abstract: Image reconstruction is one of the key technologies in the fields of physical imaging, which include optical imaging, photoacoustic imaging, sonar imaging, magnetic resonance imaging, and celestial imaging etc. Compressive sensing theory, the new research spot in recent years, describes that a small group of non-adaptive linear projections of a sparse or compressible signal contains enough information for signal reconstruction. Compressive sensing has been applied in many physical imaging systems. In this paper, we propose a new image reconstruction algorithm based on lp norm compressive sensing by combining the penalty function and revised Hesse sequence quadratic programming, and using block compressive sensing. Several images, such as “cameraman”, “barbara” and “mandrill”, are chosen as the images for image reconstruction. First, we take different sampling rates for image reconstruction to verify the algorithm. When the sampling rate is as low as 0.3, the signal-to-noise ratio of the reconstructed image can reach up to 32.23 dB. Then, when the sampling rate is above 0.5, by comparing with OMP algorithm, reconstructed images can be obtained with a higher signal-to-noise ratio and a shorter imaging time. Especially, when the sampling rate is 0.7, the imaging time is reduced by 88%. Finally compared with the existing algorithm based on lp norm compressive sensing, simulation results show that the new algorithm can improve the signal-to-noise ratio of reconstructed images, and greatly reduce the imaging time.

Reference (26)

Catalog

    /

    返回文章
    返回