部分遮挡三维彩色物体的压缩全息
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摘要
压缩全息将压缩感知理论与全息显示技术结合在一起,利用压缩感知理论,可以由少量的测量数目精确地从2D全息图中恢复3D对象.本文将压缩全息理论从单波长情形拓展到彩色物体的压缩全息,同时研究每层图像在轴向上有较多遮挡的3D对象的3DTV压缩重建,最后通过数值实验验证了本文方法的有效性,并探究复杂物体的填充比例对重建质量的影响,以及不同层之间的遮挡位置和噪声对重建质量的影响.
Compressed holography combines the theory of compressed sensing with the holographic display technology.Using the theory of compressed sensing,3 D objects can be accurately restored from the 2 D hologram only by a small number of measurements. In this paper, the theory of compressed sensing is extended from the single-wavelength case to the compressed holography of the color object, and the 3 DTV compressed reconstruction of 3 D objects with more overlap in the axial direction is studied. Finally, the validity of the method is verified by numerical experiments and the effect of the filling ratio of complex objects on the quality of reconstruction as well as the effect of the position of overlap and noise on the reconstruction quality between different layers are explored.
Compressed holography combines the theory of compressed sensing with the holographic display technology.Using the theory of compressed sensing,3 D objects can be accurately restored from the 2 D hologram only by a small number of measurements. In this paper, the theory of compressed sensing is extended from the single-wavelength case to the compressed holography of the color object, and the 3 DTV compressed reconstruction of 3 D objects with more overlap in the axial direction is studied. Finally, the validity of the method is verified by numerical experiments and the effect of the filling ratio of complex objects on the quality of reconstruction as well as the effect of the position of overlap and noise on the reconstruction quality between different layers are explored.
引文
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[19] BIOUCAS-DIAS J M,FIGUEIREDO M A T. A new Tw IST:Tw o-step iterative shrinkage/thresholding algorithms for image restoration[J]. IEEE Transactions on Image Processing,2007,16(12):2992-3004.
[2] CANDES E J,ROMBERG J K,TAO T. Stable signal recovery from incomplete and inaccurate measurements[J].Communications on Pure and Applied M athematics,2006,59(8):1207-1223.
[3] CANDES E J,TAO T. Near-optimal signal recovery from random projections:Universal encoding strategies[J].IEEE Transactions on Information Theory,2006,52(12):5406-5425.
[4] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[5]田文飚,芮国胜,康健,等.基于Monte Carlo采样的压缩感知弱匹配去噪重构[J].电子学报,2015,43(9):1732-1737.TIAN Wen-biao,RUI Guo-sheng,KANG Jian,et al. M onte carlo matching pursuit denoising inversion for compressed sensing[J]. Acta Electronica Sinica,2015,43(9):1732-1737.(in Chinese)
[6]沈燕飞,朱珍民,张勇东,等.基于秩极小化的压缩感知图像恢复算法[J].电子学报,2016,44(3):572-579.SHEN Yan-fei,ZHU Zhen-min,ZHANG Yong-dong,et al.Compressed sensing image reconstruction algorithm based on rank minimization[J]. Acta Electronica Sinica,2016,44(3):572-579.(in Chinese)
[7]练秋生,韩敏,石保顺,等.融合解析模型和综合模型的压缩感知算法[J].电子学报,2016,44(3):613-619.LIAN Qiu-sheng,HAN M in,SHI Bao-shun,et al. Compressed sensing algorithm fused the cosparse analysis model and the synthesis sparse model[J]. Acta Electronica Sinica,2016,44(3):613-619.(in Chinese)
[8]MARTINEZ-LEON L,CLEMENTE P,MORI Y,et al. Single-pixel digital holography w ith phase-encoded illumination[J]. Optics Express,2017,25(5):4975-4984.
[9]BRADY D J,CHOI K,MARKS D L,et al. Compressive holography[J]. Optics Express,2009,17(15):13040-13049.
[10]CHOI K,HORISAKI R,HAHN J,et al. Compressive holography of diffuse objects[J]. Applied Optics,2010,49(34):H1-H10.
[11] MARTINEZ-LEON L,CLEMENTE P,MORI Y,et al.Single-pixel digital holography w ith phase-encoded illumination[J]. Optics Express,2017,25(5):4975-4984.
[12]伍小燕,于瀛洁,周文静,等.压缩传感无透镜放大全息层析重建[J].光学学报,2014,34(B12):117-124.WU Xiaoyan,YU Yingjie,ZHOU Wenjing,et al. Tomographic reconstruction of lensless amplification hologram based on compressive sensing[J]. Acta Optica Sinica,2014,34(B12):117-124.(in Chinese)
[13]张成,沈川,程鸿,等.彩色全息压缩重构[J].自动化学报,2015,41(2):419-428.ZHANG Cheng,SHEN Chuan,CHENG Hong,et al. Compressed reconstruction of color holography[J]. Acta Automatica Sinica,2015,41(2):419-428.(in Chinese)
[14]翁嘉文,秦怡,杨初平,等.单幅弱相干光数字全息图的压缩感知重建[J].激光与光电子学进展,2015,52(10):110-115.WENG Jiaw en,QIN Yi,YANG Chuping,et al. Reconstruction of single low-coherence digital hologram by compressive sensing[J]. Laser&Optoelectronics Progress,2015,52(10):110-115.(in Chinese)
[15]张立峰,刘昭麟,田沛.基于压缩感知的电容层析成像图像重建算法[J].电子学报,2017,45(2):353-358.ZHANG Li-feng,LIU Zhao-lin,TIAN Pei. Image reconstruction algorithm for electrical capacitance tomography based on compressed sensing[J]. Acta Electronica Sinica,2017,45(2):353-358.(in Chinese)
[16] GABOR D. A new microscopic principle[J]. Nature,1948,161(4098):777-778.
[17]GOODMAN J W. Statistical Optics[M]. US:John Wiley&Sons,2015.
[18]RUDIN L I,OSHER S,FATEMI E. Nonlinear total variation based noise removal algorithms[J]. Physica D:Nonlinear Phenomena,1992,60(1-4):259-268.
[19] BIOUCAS-DIAS J M,FIGUEIREDO M A T. A new Tw IST:Tw o-step iterative shrinkage/thresholding algorithms for image restoration[J]. IEEE Transactions on Image Processing,2007,16(12):2992-3004.