• Acta Optica Sinica
  • Vol. 40, Issue 1, 0111007 (2020)
Jian Wang1、*, Zhishen Tong2、3、**, Chenyu Hu2、3、***, Mengchu Xu1、****, and Zengfeng Huang1
Author Affiliations
  • 1School of Data Science, Fudan University, Shanghai 200433, China
  • 2Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
  • 3Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
  • show less
    DOI: 10.3788/AOS202040.0111007 Cite this Article Set citation alerts
    Jian Wang, Zhishen Tong, Chenyu Hu, Mengchu Xu, Zengfeng Huang. Some Mathematical Problems in Ghost Imaging[J]. Acta Optica Sinica, 2020, 40(1): 0111007 Copy Citation Text show less
    References

    [1] Wolf E. Optics in terms of observable quantities[J]. Il Nuovo Cimento (1943-1954), 12, 884-888(1954). http://link.springer.com/article/10.1007/BF02781855

    [2] Bhatia A B, Wolf E. On the circle polynomials of Zernike and related orthogonal sets[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 50, 40-48(1954).

    [3] Wolf E. Coherence properties of partially polarized electromagnetic radiation[J]. Il Nuovo Cimento (1955--1965), 13, 1165-1181(1959).

    [4] Mandel L, Wolf E. Coherence properties of optical fields[J]. Reviews of Modern Physics, 37, 231-287(1965).

    [5] Glauber R J. Photon correlations[J]. Physical Review Letters, 10, 84-86(1963).

    [6] Glauber R J. The quantum theory of optical coherence[J]. Physical Review, 130, 2529-2539(1963).

    [7] Brown R H, Twiss R Q. Correlation between photons in two coherent beams of light[J]. Nature, 177, 27-29(1956).

    [8] Brown R H, Twiss R Q. The question of correlation between photons in coherent light rays[J]. Nature, 178, 1447-1448(1956).

    [9] Strekalov D V, Sergienko A V, Klyshko D N et al. Observation of two-photon “ghost” interference and diffraction[J]. Physical Review Letters, 74, 3600-3603(1995).

    [10] Cheng J, Han S S. Incoherent coincidence imaging and its applicability in X-ray diffraction[J]. Physical Review Letters, 92, 093903(2004).

    [11] Gatti A, Brambilla E, Bache M et al. Ghost imaging with thermal light: comparing entanglement and classical correlation[J]. Physical Review Letters, 93, 093602(2004).

    [12] Bennink R S, Bentley S J, Boyd R W et al. Quantum and classical coincidence imaging[J]. Physical Review Letters, 92, 033601(2004).

    [13] Ferri F, Magatti D, Gatti A et al. High-resolution ghost image and ghost diffraction experiments with thermal light[J]. Physical Review Letters, 94, 183602(2005).

    [14] Kolobov M I. Quantum imaging[M]. New York, NY: Springer, 79-110(2007).

    [15] Shapiro J H, Boyd R W. The physics of ghost imaging[J]. Quantum Information Processing, 11, 949-993(2012).

    [16] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAM Review, 43, 129-159(2001).

    [17] Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 52, 1289-1306(2006).

    [18] Candès E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 52, 489-509(2006).

    [19] Candès E, Tao T. The Dantzig selector: statistical estimation when p is much larger than n[J]. The Annals of Statistics, 35, 2313-2351(2007).

    [20] Candès E J. The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique, 346, 589-592(2008).

    [21] Zhao C Q, Gong W L, Chen M L et al. Ghost imaging lidar via sparsity constraints[J]. Applied Physics Letters, 101, 141123(2012).

    [22] Liu Z T, Tan S Y, Wu J R et al. Spectral camera based on ghost imaging via sparsity constraints[J]. Scientific Reports, 6, 25718(2016).

    [23] Gong W L, Han S S. Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints[J]. Physics Letters A, 376, 1519-1522(2012).

    [24] Katz O, Bromberg Y, Silberberg Y. Compressive ghost imaging[J]. Applied Physics Letters, 95, 131110(2009).

    [25] Wang H, Han S S, Kolobov M I. Quantum limits of super-resolution of optical sparse objects via sparsity constraint[J]. Optics Express, 20, 23235-23252(2012).

    [26] Sun B, Edgar M P, Bowman R et al. 3D computational imaging with single-pixel detectors[J]. Science, 340, 844-847(2013).

    [27] Benzi M. Preconditioning techniques for large linear systems: a survey[J]. Journal of Computational Physics, 182, 418-477(2002).

    [28] Elad M. Optimized projections for compressed sensing[J]. IEEE Transactions on Signal Processing, 55, 5695-5702(2007).

    [29] Duarte-Carvajalino J M, Sapiro G. Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization[J]. IEEE Transactions on Image Processing, 18, 1395-1408(2009).

    [30] Tsiligianni E, Kondi L P, Katsaggelos A K. Preconditioning for underdetermined linear systems with sparse solutions[J]. IEEE Signal Processing Letters, 22, 1239-1243(2015).

    [31] Wang J, Li P. Recovery of sparse signals using multiple orthogonal least squares[J]. IEEE Transactions on Signal Processing, 65, 2049-2062(2016).

    [32] Tong Z S, Wang J. -10-11)[2019-11-01]. https:∥arxiv.xilesou., top/abs/1910, 04926(2019).

    [33] Pati Y C, Rezaiifar R, Krishnaprasad P S. Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. [C]∥Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, November 1-3, 1993, Pacific Grove, CA, USA. New York: IEEE, 40-44(1993).

    [34] Ferri F, Magatti D, Lugiato L A et al. Differential ghost imaging[J]. Physical Review Letters, 104, 253603(2010).

    [35] Zhang C, Guo S X, Cao J S et al. Object reconstitution using pseudo-inverse for ghost imaging[J]. Optics Express, 22, 30063-30073(2014).

    [36] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems[J]. IEEE Journal of Selected Topics in Signal Processing, 1, 586-597(2007).

    [37] Chen M L, Li E R, Han S S. Application of multi-correlation-scale measurement matrices in ghost imaging via sparsity constraints[J]. Applied Optics, 53, 2924-2928(2014).

    [38] Khamoushi S M M, Nosrati Y, Tavassoli S H. Sinusoidal ghost imaging[J]. Optics Letters, 40, 3452-3455(2015).

    [39] Xu X Y, Li E R, Shen X et al. Optimization of speckle patterns in ghost imaging via sparse constraints by mutual coherence minimization[J]. Chinese Optics Letters, 13, 071101(2015). http://www.opticsjournal.net/Articles/Abstract?aid=OJ150707000077WtZw3y

    [40] Hu C Y, Tong Z S, Liu Z T et al. Optimization of light fields in ghost imaging using dictionary learning[J]. Optics Express, 27, 28734-28749(2019).

    [41] Olshausen B A, Field D J. Natural image statistics and efficient coding[J]. Network: Computation in Neural Systems, 7, 333-339(1996).

    [42] Aharon M, Elad M, Bruckstein A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation[J]. IEEE Transactions on signal processing, 54, 4311-4322(2006).

    [43] Abolghasemi V, Ferdowsi S, Sanei S. A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing[J]. Signal Processing, 92, 999-1009(2012).

    [44] Candès E J, Strohmer T, Voroninski V. Phaselift: exact and stable signal recovery from magnitude measurements via convex programming[J]. Communications on Pure and Applied Mathematics, 66, 1241-1274(2013).

    [45] Candès E J, Eldar Y C, Strohmer T et al. Phase retrieval via matrix completion[J]. SIAM review, 57, 225-251(2015).

    [46] Fannjiang A. Absolute uniqueness of phase retrieval with random illumination[J]. Inverse Problems, 28, 075008(2012).

    [47] Szameit A, Shechtman Y, Osherovich E et al. Sparsity-based single-shot subwavelength coherent diffractive imaging[J]. Nature Materials, 11, 455-459(2012).

    [48] Ohlsson H, Yang A Y, Dong R et al. Compressive phase retrieval from squared output measurements via semidefinite programming[J]. IFAC Proceedings Volumes, 45, 89-94(2012).

    [49] Shechtman Y, Small E, Lahini Y et al. Sparsity-based super-resolution and phase-retrieval in waveguide arrays[J]. Optics Express, 21, 24015-24024(2013).

    [50] Eldar Y C, Kutyniok G[M]. Compressed sensing: theory and applications(2012).

    [51] Hayes M. The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 30, 140-154(1982).

    [52] Gerchberg R W. A practical algorithm for the determination of phase from image and diffraction plane pictures[J]. Optik, 35, 237-246(1972).

    [53] Fienup C, Dainty J[M]. Phase retrieval and image reconstruction for astronomy, 275(1987).

    [54] Fienup J R. Phase retrieval algorithms: a comparison[J]. Applied Optics, 21, 2758-2769(1982).

    [55] Yang G Z, Gu B Y, Dong B Z. Theory of the amplitude-phase retrieval in any linear transform system and its applications[J]. International Journal of Modern Physics B, 7, 3153-3224(1993).

    [56] Rodriguez J A, Xu R, Chen C C et al. Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities[J]. Journal of Applied Crystallography, 46, 312-318(2013).

    [57] Candes E J, Li X D, Soltanolkotabi M. Phase retrieval via Wirtinger flow: theory and algorithms[J]. IEEE Transactions on Information Theory, 61, 1985-2007(2015).

    [58] Cai T T, Li X D, Ma Z M. Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow[J]. The Annals of Statistics, 44, 2221-2251(2016).

    [59] Zhang L, Wang G, Giannakis G B et al. Compressive phase retrieval via reweighted amplitude flow[J]. IEEE Transactions on Signal Processing, 66, 5029-5040(2018).

    [60] Moravec M L, Romberg J K, Baraniuk R G. Compressive phase retrieval[J]. Proceedings of SPIE, 6701, 670120(2007).

    [61] Shechtman Y, Beck A, Eldar Y C. Efficient phase retrieval of sparse signals. [C]∥2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, November 14-17, 2012, Eilat, Israel. New York: IEEE, 13172953(2012).

    [62] Yuan Z Y, Wang H X, Wang Q. Phase retrieval via sparse Wirtinger flow[J]. Journal of Computational and Applied Mathematics, 355, 162-173(2019).

    [63] Dai W, Milenkovic O. Subspace pursuit for compressive sensing signal reconstruction[J]. IEEE Transactions on Information Theory, 55, 2230-2249(2009).

    [64] Needell D, Tropp J A. CoSaMP: iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 26, 301-321(2009).

    [65] Kolte R. -06-10)[2019-11-01]. https:∥arxiv.xilesou., top/abs/1606, 03196(2016).

    Jian Wang, Zhishen Tong, Chenyu Hu, Mengchu Xu, Zengfeng Huang. Some Mathematical Problems in Ghost Imaging[J]. Acta Optica Sinica, 2020, 40(1): 0111007
    Download Citation