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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.
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Keywords:
- image reconstruction /
- compressive sensing /
- penalty function /
- revised Hesse sequence quadratic programming
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[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]
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[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 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
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[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 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 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
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