Phase Retrieval Algorithm Fusing Multiple Wavelets and Total Variation Regularization

LIAN Qiusheng1 LI Ying1 CHEN Shuzhen1

(1.Institute of Information Science and Technology, Yanshan University, Qinhuangdao, Hebei, China 066004)

【Abstract】In the process of phase retrieval, the image reconstruction quality can be improved when we use the image sparsity as the prior knowledge. By combining the group sparsity of image in wavelet domain with the gradient sparsity of the image itself, we propose a phase retrieval algorithm fusing orthogonal wavelet db10, sym4 group sparsity and total variation regularization for the coded diffraction pattern model. Aiming at the problem that reconstruction time of the current phase retrieval algorithm is long, we use composite splitting algorithm to decompose nonconvex optimization problem into several sub-problems (including two group hard threshold operators and total variation minimization) that can be solved easily, which reduces the image reconstruction time. Experimental results show that the peak signal-to-noise ratio of the reconstructed image obtained by the proposed algorithm is improved by about 0.8 dB compared with that of BM3D-PRGAMP algorithm under Gaussian noise, and the reconstruction time is reduced by 90%. In Poisson model, the proposed algorithm also has a great advantage, which fully demonstrates that the algorithm is robust to noise.

【Keywords】 optics in computing; phase retrieval; coded diffraction pattern; group sparsity; total variation; composite splitting algorithm;

【DOI】

【Funds】 National Natural Science Foundation of China (61471313) Natural Science Foundation of Hebei Province (F2014203076)

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(Translated by WEI JM)

    References

    [1] Millane R P. Phase retrieval in crystallography and optics [J]. Journal of the Optical Society of America A, 1990, 7 (3): 394–411.

    [2] Akcakaya M, Tarokh V. Sparse signal recovery from a mixture of linear and magnitude-only measurements [J]. IEEE Signal Processing Letters, 2015, 22 (9): 1220–1223.

    [3] Jaganathan K, Oymak S, Hassibi B. Sparse phase retrieval: Uniqueness guarantees and recovery algorithms [J]. IEEE Transactions on Signal Processing, 2017, 65 (9): 2402–2410.

    [4] Maji S K, Yahia H M, Fusco T. A multifractalbased wavefront phase estimation technique for ground-based astronomical observations [J]. IEEETransactions on Geoscience & Remote Sensing, 2016, 54 (3): 1705–1715.

    [5] Leshem B, Xu R, Dallal Y, et al. Direct single-shot phase retrieval from the diffraction pattern of separated objects [J]. Nature Communications, 2016, 7: 10820.

    [6] Gerchberg R, Saxon W. A practical algorithm for the determination of phase from image and diffraction plane pictures [J]. International Journal for Light and Electron Optics, 1972, 35 (2): 237–250.

    [7] Fienup J R. Phase retrieval algorithms: A comparison [J]. Applied Optics, 1982, 21 (15): 2758–2769.

    [8] Roddier F, Roddier C. Wavefront reconstruction using iterative Fourier transforms [J]. Applied Optics, 1991, 30 (11): 1325–1327.

    [9] Guo Y M, Zhang F, Song Q, et al. Application of hybrid iterative algorithom in TIE phase retrieval with large defocusing distance [J]. Acta Optica Sinica, 2016, 36 (9): 0912001. (in Chinese)

    [10] Cheng H, LüQ Q, Zhang W J, et al. Phase retrieval method based on liquid crystal on silicon tunable-lens [J]. Chinese Journal of Lasers, 2017, 44 (3): 0304001. (in Chinese)

    [11] Ohlsson H, Yang A, Dong R, et al. Compressive phase retrieval from squared output measurements via semidefinite programming [C] //International Federation of Automatic Control Symposium on System Identification. Brussels, Belgium, 2012: 89–94.

    [12] Shechtman Y, Beck A, Eldar Y C. GESPAR: Efficient phase retrieval of sparse signals [J]. IEEE Transactions on Signal Processing, 2014, 62 (4): 928–938.

    [13] Pedarsani R, Yin D, Lee K, et al. Phasecode: Fast and efficient compressive phase retrieval based on sparse-graph codes [J]. IEEE Transactions on Information Theory, 2017, 63 (6): 3663–3691.

    [14] Cheng H, Zhang Q B, Wei S. Phase retrieval based on total variation [J]. Journal of Image and Graphics, 2010, 15 (10): 1425–1429. (in Chinese)

    [15] Lian Q S, Zhao X R, Shi B S, et al. Phase retrieval algorithm based on cartoon-texture model [J]. Jouenal of Electronics & Information Technology, 2016, 38 (8): 1991–1998. (in Chinese)

    [16] Candes E J, Li X, Soltanolkotabi M. Phase retrieval from coded diffraction patterns [J]. Applied and Computational Harmonic Analysis, 2015, 39 (2): 277–299.

    [17] Candes E J, Li X, Soltanolkotabi M. Phase retrieval via wirtinger flow: Theory and algorithms [J]. IEEETransactions on Information Theory, 2015, 61 (4): 1985–2007.

    [18] Chen Y, Candes E J. Solving random quadratic systems of equations is nearly as easy as solving linear systems [C]. Advances in Neural Information Processing Systems, 2015: 739–747.

    [19] Tillmann A M, Eldar Y C, Mairal J. DOLPHIn: Dictionary learning for phase retrieval [J]. IEEE Transactions on Signal Processing, 2016, 64 (24): 6485–6500.

    [20] Metzler C A, Maleki A, Baraniuk R G. BM3D-PRGAMP: Compressive phase retrieval based on BM3D denoising [C]. IEEE International Conference on Image Processing, 2016: 2504–2508.

    [21] Katkovnik V. Phase retrieval from noisy data based on sparse approximation of object phase and amplitude [OL]. [2017-9-14]. http: //www.cs.tut.fi/~lasip/DDT/pdfs/Single_column.pdf.

    [22] Yuan M, Lin Y. Model selection and estimation in regression with grouped variables [J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2006, 68 (1): 49–67.

    [23] Yu H J, Jiang M F, Chen H R, et al. Super-pixel algorithm and group sparsity regularization method for compressed sensing MR image reconstruction [J]. Optik, 2017, 140: 392–404.

    [24] Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [J]. Physica D: Nonlinear Phenomena, 1992, 60 (1/2/3/4): 259–268.

    [25] Huang J Z, Zhang S T, Metaxas D. Efficient MRimage reconstruction for compressed MRimaging [J]. Medical Image Analysis, 2011, 15 (5): 670–679.

    [26] Beck A, Teboulle M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems [J]. IEEE Transactions on Image Processing, 2009, 18 (11): 2419–2434.

    [27] Chambolle A. An algorithm for total variation minimization and applications [J]. Journal of Mathematical Imaging and Vision, 2004, 20 (1): 89–97.

    [28] Kowalski M, Siedenburg K, Dorfler M. Social sparsity! Neighborhood systems enrich structured shrinkage operators [J]. IEEE Transactions on Signal Processing, 2013, 61 (10): 2498–2511.

This Article

ISSN:0253-2239

CN:31-1252/O4

Vol 38, No. 02, Pages 298-305

February 2018

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Article Outline

Abstract

  • 1 Introduction
  • 2 Regularization-based phase retrieval model
  • 3 Phase retrieval algorithm fusing multiple wavelets and total variation
  • 4 Experimental results and comparison
  • 5 Conclusions
  • References