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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.
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Keywords:
- adaptive optics /
- additive noise /
- adaptively regularization term /
- nonconvex
[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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[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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