为了解决全息图像数据在传输过程中占用大量内存并在一定程度上增加设计成本的问题，在数字全息成像技术中，应用压缩感知理论，提出了一种基于迭代去噪收缩阈值算法(IDNST)的数字全息重构方法.IDNST算法引入了去噪迭代因子和正则化收缩因子，利用前2次迭代的值、不断更新的迭代参数以及不断收缩的正则化参数来获得新的迭代值，加快了收敛速度，提高了全息图像的重构精度.仿真结果表明，所提出方法能够高概率地恢复出原始图像.
A novel algorithm, namely iterative de-noising shrinkage-thresholding (IDNST) algorithm, is presented to reconstruct the original image from digital holography in a compressed sensing framework. The proposed algorithm can reduce the computational complexity in classical digital holography process, as well as the data in transmission. The proposed algorithm adopts two new factors, i.e., the de-noising iteration factor and the shrinkage factor of regularization. Furthermore, the proposed algorithm obtains a new iterative value using the previously updated iterative values, the iteration factor and the shrinking regularization parameter. This improves the convergence speed and the reconstruction accuracy. Simulation results show that the original image can be reconstructed from the digital hologram perfectly with high probability by the IDNST algorithm.
［1］CANDES E J. The restricted isometry property and its implication for compressed sensing［J］. Comptes Rendus Mathematique, 2008, 346(9/10): 589-592.
［2］RIVENSON Y, STERN A. Conditions for practicing compressive fresnel holography［J］. Optics Letters, 2011, 36(17): 3365-3367.
［3］JAVIDI B, GARCIA J, MIC V, et al. Phase-shifting gabor holography［J］. Optics Letters, 2009, 34(10): 1492-1494.
［4］李科, 李军. 基于压缩传感的全息图压缩研究［J］. 华南师范大学学报, 2012, 44(4): 61-65.
LI Ke, LI Jun. Hologram compression based on compressive sensing［J］. Journal of South China Normal University, 2012, 44(4): 61-65.
［5］简献忠, 周海, 乔静远, 等. 基于全变差重构算法的数字全息研究［J］. 激光技术, 2014, 38(2): 236-239.
JIAN Xianzhong, ZHOU Hai, QIAO Jingyuan, et al. Study on digital holography based on the total variation reconstruction algorithm［J］. Laser Technology, 2014, 38(2): 236-239.
［6］STERN A, JAVIDI B, RIVENSON Y. Compressive fresnel holography［J］. Journal of Display Technology, 2010, 6(10): 506-509.
［7］BIOUCAS-DLAS J M, FIGUEIREDO M A. A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration［J］. IEEE Transaction on Image Processing, 2008, 16(12): 2992-3004.
［8］BRADY D J, CHOI K, MARKS D L, et al. Compressive holography［J］. Optics Express, 2009, 17(15): 13040-13049.
［9］RIVENSON Y, STERN A, JAVIDI B. Improved depth resolution by single-exposure in-line compressive holography［J］. Applied Optics, 2013, 52(1): 223-231.
［10］RIVENSON Y, STERN A, ROSEN J. Compressive multiple view projection incoherent holography［J］. Optics Express, 2011, 19(7): 6109-6118.
［11］王侠, 王开, 王青云, 等.压缩感知中确定性随机观测矩阵构造［J］.信号处理, 2014, 30(4): 436-442.
WANG Xia, WANG Kai, WANG Qingyun, et al. Deterministic random measurement matrices construction for compressed sensing［J］. Journal of Signal Processing, 2014, 30(4): 436-442.
［12］SONG C B, XIA S T, LIU X J. Subspace thresholding pursuit: A reconstruction algorithm for compressed sensing［C］∥2015 IEEE International Symposium on Information Theory (ISIT). Hong Kong: IEEE, 2015: 536-540.
［13］DAUBECHIES I, DEFRISE M, MOL C D. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint［J］.Communications on Pure and Applied Mathematics, 2004, 57(11): 1413-1457.
［14］FIGUEIREDO M A T, NOWAK R D. An EM algorithm for wavelet-based image restoration［J］. IEEE Transactions on Image Processing, 2003, 12(8): 906-916.
［15］ZHANG Y D, WANG S H, JI G L, et al. Exponential wavelet iterative shrinkage thresholding algorithm for compressed sensing magnetic resonance imaging［J］.Information Sciences, 2015, 322(1): 115-132.
［16］FORNASIER M, RAUHUT H. Iterative thresholding algorithms［J］. Applied and Computational Harmonic Analysis, 2008, 25(2): 187-208.
［17］GAO L F, LI C. An adaptive TV model for image denoising［C］∥International Conference on Natural Computationn. Shenyang: IEEE, 2013: 766-770.
