自适应非凸稀疏正则化下自适应光学系统加性噪声的去除

张艳艳; 陈苏婷; 葛俊祥; 万发雨; 梅永; 周晓彦

doi:10.7498/aps.66.129501

摘要

自适应光学系统可以实时测量并校正波前信息，但是系统中大量的噪声严重影响了系统的探测精度.自适应光学系统中一般为加性噪声，本文提出一种全新的变分处理模型去除加性噪声，该模型采用自适应非凸正则项.非凸正则项在保持图像细节上较凸正则项具有更好的效果，能更好地保持点源目标的完整性.另外，根据不同区域的噪声水平自适应地构建正则化参数，使不同区域的像素点受到不同程度的噪声抑制，可以更好地保持目标的边缘细节.在算法实现上，为了解决非凸正则项收敛性较差的缺陷，采用分裂Bregman算法及增广拉格朗日对偶算法进行计算.实验及数值仿真结果都表明，该方法能够较好地去除系统中的加性噪声，且光斑信号保存得较为完整，处理后的质心探测精度及信噪比较高.

关键词:

Abstract

Adaptive optics (AO) system which is widely used in astronomical observations can improve the image quality by the real-time measurement and correction of the wave-front. One of the main problems in the AO system is the poor quality of the image because of the system noises. The noises in AO system are additive noises. The main sources of the noises are the background noise, the photon noise, and the readout noise of charge-coupled device. The background noise is distributed evenly and is easy to process. The photon noise is dependent on the characteristics of the spot itself. Readout noise, which is Gaussian distribution with the mean value of 0 and the variance of 2, is the main noise source in AO system. In this paper, we focus on the readout noise and propose a new regularization model to remove additive noises from the AO system. In this model, the regularization parameters can be adaptively changed. A nonconvex regularization term is used to make the homogeneous region of the image smooth efficiently, while the integrity of the spot can be well restored. The properties of the regularization proposed are shown below. 1) The proposed nonconvex regularization term can act as the L0 norm which is sparser than L1 norm. 2) The proposed model can protect the edge of the spot from over smoothing. To prevent the edges from over smoothing, the regularization parameter must be an increasing function. Moreover, it converges to a constant so that it cannot affect the strong gradient of the image. 3) The regularization term proposed is nonconvex which is more sensible to the minor change of the image. Therefore, the edges of the image can be better preserved. Though the proposed model can well preserve the edges of the spot, it is difficult to resolve by traditional methods because of the nonconvexity. Split Bregman algorithm and augmented Lagrangian duality algorithm are used to solve this problem. We can obtain a denoised spot image as well as an edge indicator by using the proposed model. The visual and quantitative evaluations are used to value the restored images. The evaluating indicators are the peak signal-to-noise ratio and centroid detecting error which includes the root mean square and the peak valley value of the centroid deviation. The simulation and experimental results show the efficiency of this model in removing the additive noises from the AO system.

Keywords:

作者及机构信息

1.
南京信息工程大学, 江苏省气象探测与信息处理重点实验室, 江苏省气象传感网技术工程中心, 江苏省大气环境与装备技术协同创新中心, 南京 210044

通信作者: 张艳艳, 002243@nuist.edu.cn

基金项目: 国家自然科学基金（批准号：61071164）、江苏省高校自然科学研究基金重大项目（批准号：12KJA510001）、江苏省气象探测与信息处理重点实验室项目（批准号：KDXS1405）、江苏省2016大学生实践创新计划（批准号：201610300254）、江苏高校优势学科II期建设工程和江苏省双创计划资助的课题.

Authors and contacts

1.
Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Jiangsu Technology and Engineering Center of Meteorological Sensor Network, Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information and Science Technology, Nanjing 210044, China

Corresponding author: Zhang Yan-Yan, 002243@nuist.edu.cn

Funds: Project supported by the National Nature Science Foundation of China (Grant No. 61071164), the Major Project of Nature Science Foundation of Higher Education Institution of Jiangsu Province, China (Grant No. 12KJA510001), the Program of Jiangsu Key Laboratory of Meteorological Observation and Information Processing, China (Grant No. KDXS1405), the Jiangsu Province College Students Practice and Innovation Training Platform, China (Grant No. 201610300254), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, and the Jiangsu Innovation and Entrepreneurship Group Talents Plan, China.

参考文献

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[2]	Law N M, Morton T, Baranec C, Riddle R, Ravichandran G, Ziegler C, Das H K 2014 Astrophys. J. 791 35
[3]	Adams E R, Dupree A K, Kulesa C, McCarthy D 2013 Astron. J. 146 71
[4]	Li C H, Xian H, Rao C H, Jiang W H 2006 Opt. Lett. 31 2821
[5]	Li C H, Xian H, Jiang W H, Rao C H 2007 Appl. Phys. B 88 367
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[7]	Ma X Y, Rao C H, Zheng H Q 2009 Opt. Express 17 8525
[8]	Arines J, Ares J 2002 Opt. Lett. 27 497
[9]	Thomas S 2004 Proc. SPIE 5490 1238
[10]	Baker K L, Moallem M M 2007 Opt. Express 15 5147
[11]	Rudin L I, Osher S, Fatemi E 1992 Physica D 60 1
[12]	Strong D M, Chan T F 1996 Spatially and Scale Adaptive Total Variation Based Regularization and Anisotropic Diffusion in Image Processing Diusion in Image Processing, UCLA Math Department CAM Report
[13]	Ramani S, Blu T, Unser M 2008 IEEE Trans. Image Process. 17 1540
[14]	Lin Y, Wohlberg B, Guo H 2010 Signal Process. 90 2546
[15]	Aubert G, Aujol J 2008 Siam. J. Appl. Math. 68 925
[16]	Han Y, Feng X C, Baciu G, Wang W W 2013 Pattern Recogn. 46 989
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施引文献

[1]	Roberto R, Enrico M, Gianpaolo V 2000 Nature 403 54
[2]	Law N M, Morton T, Baranec C, Riddle R, Ravichandran G, Ziegler C, Das H K 2014 Astrophys. J. 791 35
[3]	Adams E R, Dupree A K, Kulesa C, McCarthy D 2013 Astron. J. 146 71
[4]	Li C H, Xian H, Rao C H, Jiang W H 2006 Opt. Lett. 31 2821
[5]	Li C H, Xian H, Jiang W H, Rao C H 2007 Appl. Phys. B 88 367
[6]	Shen F, Jiang W H 2000 Acta Opt. Sin. 20 666 (in Chinese) [沈锋, 姜文汉 2000 光学学报 20 666]
[7]	Ma X Y, Rao C H, Zheng H Q 2009 Opt. Express 17 8525
[8]	Arines J, Ares J 2002 Opt. Lett. 27 497
[9]	Thomas S 2004 Proc. SPIE 5490 1238
[10]	Baker K L, Moallem M M 2007 Opt. Express 15 5147
[11]	Rudin L I, Osher S, Fatemi E 1992 Physica D 60 1
[12]	Strong D M, Chan T F 1996 Spatially and Scale Adaptive Total Variation Based Regularization and Anisotropic Diffusion in Image Processing Diusion in Image Processing, UCLA Math Department CAM Report
[13]	Ramani S, Blu T, Unser M 2008 IEEE Trans. Image Process. 17 1540
[14]	Lin Y, Wohlberg B, Guo H 2010 Signal Process. 90 2546
[15]	Aubert G, Aujol J 2008 Siam. J. Appl. Math. 68 925
[16]	Han Y, Feng X C, Baciu G, Wang W W 2013 Pattern Recogn. 46 989
[17]	Alliney S, Ruzinsky S A 1994 IEEE Trans. Signal Process. 42 618
[18]	Mallat S M, Zhang Z F 1993 IEEE Trans. Signal Process. 41 3397
[19]	Donoho D 2006 IEEE Trans. Inform. Theory 52 1289
[20]	Donoho D, Tsaig Y 2006 Signal Process. 86 533
[21]	Goldstein T, Osher S 2009 Siam. J. Imag. Sci. 2 323
[22]	Tai X C, Wu C 2009 Scale Space and Variational Methods in Computer Vision Norway, June 1-5, 2009 p502
[23]	Gang P, Zeng H, Xuan L 2008 Chin. Phys. Lett. 25 989
[24]	Zhu Z Y, Da Y L, Li F H, Quan Q M, Cheng L Y, Zhao L C, Li X 2016 Chin. Phys. B 25 090702
[25]	Cheng S Y, Liu W J, Chen S Q, Dong L Z, Yang P, Xu B 2015 Chin. Phys. B 24 084214

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