基于lp范数的压缩感知图像重建算法研究

宁方立; 何碧静; 韦娟

doi:10.7498/aps.62.174212

摘要

图像重建是光学成像、光声成像、声纳成像、核磁共振成像、天体成像等物理成像领域中的关键技术之一. 近年来提出的压缩感知理论指出: 对稀疏或者可压缩信号进行少量非自适应线性投影,投影信号含有足够的信息, 从而能对信号进行高概率重建. 压缩感知已被应用于多种物理成像系统. 将罚函数法和修正Hesse阵序列二次规划方法相结合, 并采用了分块压缩感知思想, 提出一种基于lp范数的压缩感知图像重建算法. 以cameraman, barbara和mandrill图像为例, 采用该算法进行图像重建. 首先, 在不同采样率下对图像重建. 即便采样率低至0.3时, 也能获得高达32.23dB的信噪比, 重建图像清晰可辨. 验证了该算法的正确性. 其次, 将该算法与正交匹配追踪算法进行对比, 在采样率达到0.5以上时, 能够获得高信噪比的重建图像, 成像时间也大为减少, 特别是采样率为0.7时, 成像时间减少88%. 最后, 与现有基于lp 范数的压缩感知图像重建算法进行对比, 计算结果表明在成像质量有所提高的基础上, 成像时间大为缩短.

关键词:

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.

Keywords:

image reconstruction /
compressive sensing /
penalty function /
revised Hesse sequence quadratic programming

作者及机构信息

1.
西北工业大学机电学院, 西安 710072;

2.
西安电子科技大学通信工程学院, 综合业务网理论与关键技术国家重点实验室, 西安 710071

基金项目: 国家自然科学基金(批准号: 51075329);陕西省科学技术研究发展计划项目(批准号: 2012GY2-41);西北工业大学基础研究基金(批准号: NPU-FFR-JCY20130117)和西北工业大学研究生创业种子基金(批准号: Z2013029)资助的课题.

Authors and contacts

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

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).

参考文献

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[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]
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[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

施引文献

[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

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