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利用基于压缩感知的成像系统可以透过静态的散射介质获得高质量的重建图像. 但是当散射介质动态变化时, 因为采样所得的测量值受到散射介质衰减系数非线性变化的影响, 重建图像质量会大大下降. 针对上述情况, 本文提出基于压缩感知成像系统的测量值线性拉伸算法, 该算法能够对所得到的非线性测量值进行分析, 根据测量值大小的不同将测量值划分成数个区域并计算补偿系数, 从而根据补偿系数进行测量值线性拉伸变换, 使测量值线性化. 最后再对变换后的测量值进行压缩感知重建计算. 通过理论分析、计算机仿真和实验证明了所提算法能够有效地应对动态的散射介质, 提高基于压缩感知成像系统在透过动态散射介质时的图像重建质量.Imaging through scattering media has been a focus in research because of its meaningful applications in many fields. Recently, it has been proposed that high quality images can be recovered after passing through stationary scattering media by using the single-pixel imaging system based on compressed sensing. No doubt, it is a very interesting discovery about compressed sensing. However, it is also reported that high quality image can be recovered only with stationary scattering media. Mostly, the scattering media will not remain stationary, for example, the properties of the fog will be dynamically changed when their is wind. Thus, in a dynamic case, the transmittance of the scattering media will be nonlinear over the time, which will make the measured data nonlinear and the reconstructed image quality decrease. In this paper, a novel algorithm of linear transformation for measured data (LTMD) is proposed to make the nonlinear attenuation factor gain a linear transformation after passing through the dynamic scattering media. The factor is proposed from the theoretical calculus based on compressed sensing, and this correction factor can help to eliminate the nonlinear errors caused by dynamic scattering media and make the measured data linear. So the transformed data will greatly upgrade the reconstructed image quality. Simulation results show that high peak singnal to noise ratio images can still be recovered even when the dynamic frequency reaches 300 times in the 900 times of sampling. In experiments, plastic films are used as scattering media, and the number of films can be changed during the sampling to simulate the dynamic state of scattering media. With LTMD, high quality image with a resolution of 64 48 is recovered after passing through dynamic plastic films while the recovered result without LTMD is still hard to be distinguished. The traditional reconstructed algorithms orthogonal matching pursuit, Tval3 and L1-magic are also used in the experiments, and the image is still hard to recover with any of the three traditional algorithms. In a word, the proposed LTMD algorithm uses the correction factor to make the affected nonlinear-measured data linear, so as to increase the reconstructed quality of the imaging system based on the compressed sensing even when passing through scattering media with highly dynamic frequency.
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Keywords:
- imaging /
- compressed sensing /
- scattering media /
- dynamic
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[1] Popoff S, Lerosey G, Fink M, Boccara A C, Gigan S 2010 Nat. Commun. 1 81
[2] Hillman R T, Yamauchi T, Choi W, Dasari R R, Feld M S 2013 Sci. Rep. 3 1909
[3] Chung K, Wallace J, Kim S, Kalyanasundaram S, Andalman A S, Davidson T J, Mirzabekov J J, Zalocusky K A, Mattis J, Denisin A K, Pak S, Bernstein H, Ramakrishnan C, Grosenick L, Gradinaru V, Deisseroth K 2013 Nature 497 332
[4] Gong W L, Bo Z W, Li E R 2013 Appl. Opt. 52 15
[5] Conkey D B, Caravaca-Aguirre A M 2012 Opt. Express 20 1733
[6] Li G M, L S X 2015 Acta Phys. Sin. 64 160502 (in Chinese) [李广明, 吕善翔 2015 64 160502]
[7] Tsaig Y, Donoho D L 2004 Technical Report (Palo Alto: Department of Statistics, Stanford University)
[8] Duarte M F, Davenport M A, Takhar D, Takhar D, Laska J N, Sun T, Kelly K F, Baraniuk R G 2008 IEEE Signal Process. Mag. 25 83
[9] Candes E J, Wakin M B 2008 IEEE Signal Process. Mag. 25 21
[10] Li L Z, Yao X R, Liu X F, Yu W K, Zhai G J 2014 Acta Phys. Sin. 63 224201 (in Chinese) [李龙珍, 姚旭日, 刘雪峰, 俞文凯, 翟光杰 2014 63 224201]
[11] Wen F Q, Zhang G, Tao Y, Liu S, Feng J J 2015 Acta Phys. Sin. 64 084301 (in Chinese) [文方青, 张弓, 陶宇, 刘苏, 冯俊杰 2015 64 084301]
[12] Rodrguez A D, Clemente P, Irles E, Tajahuerce E, Lancis J 2014 Opt. Lett. 39 3888
[13] Dur'an V, Soldevila F, Irles E, Tajahuerce E, Lancis J 2015 Opt. Express 23 14424
[14] Tajahuerce E, Dur'an V, Clemente P, Torres-Company V, Jes L 2014 Opt. Express 22 16945
[15] Ying J P, Liu F, Alfano R R 2000 Appl. Opt. 39 509
[16] Zimnyakov D A, Isaeva A A, Isaeva E A, Ushakova O V, Chekmasov S P, Yuvchenko S A 2012 Appl. Opt. 51 C62
[17] Zhuang J Y, Chen Q, He W J, Feng W Y 2013 Opt. Eng. 52 4
[18] Cands E J, Romberg J K, Tao T 2006 Commun. Pure Appl. Math. 59 1207
[19] Cands E J, Romberg J K, Tao T 2006 IEEE Trans. Infom. Theory 52 489
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