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Fast Iterative Algorithms for Blind Phase Retrieval: A Survey

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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Abstract

In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem, where one has to recover both the sample and the probe (pupil) jointly from phaseless data. This survey first presents the mathematical formula of BPR and related nonlinear optimization problems and then gives a brief review of the recent iterative algorithms. It mainly consists of three types of algorithms, including the operator-splitting-based first-order optimization methods, second-order algorithm with Hessian, and subspace methods. The future research directions for experimental issues and theoretical analysis are further discussed.

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References

  • Ahmed, A., Aghasi, A., Hand, P.: Blind deconvolutional phase retrieval via convex programming (2018). NeurIPS (arXiv:1806.08091)

    Google Scholar 

  • Bendory, T., Sidorenko, P., Eldar, Y.C.: On the uniqueness of frog methods. IEEE Sig. Process. Lett. 24(5), 722–726 (2017)

    Article  Google Scholar 

  • Bendory, T., Edidin, D., Eldar, Y.C.: Blind phaseless short-time fourier transform recovery. IEEE Trans. Inf. Theory 66(5), 3232–3241 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146(1–2), 459–494 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Borzi, A., Schulz, V.: Multigrid methods for pde optimization. SIAM Rev. 51(2), 361–395 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  MATH  Google Scholar 

  • Brandt, A., Livne, O.E.: Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition. SIAM, Philadelphia (2011)

    Google Scholar 

  • Cai, J.-F., Huang, M., Li, D., Wang, Y.: The global landscape of phase retrieval II: quotient intensity models (2021). arXiv preprint arXiv:2112.07997

    Google Scholar 

  • Candes, E.J., Li, X., Soltanolkotabi, M.: Phase retrieval via wirtinger flow: Theory and algorithms. IEEE Trans. Inf. Theory 61(4), 1985–2007 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, H., Tai, X.-C., Wang, L.-L., Yang, D.: Convergence rate of overlapping domain decomposition methods for the Rudin-Osher-Fatami model based on a dual formulation. SIAM J. Image Sci. 8, 564–591 (2015)

    Article  MATH  Google Scholar 

  • Chang, H., Lou, Y., Ng, M.K., Zeng, T.: Phase retrieval from incomplete magnitude information via total variation regularization. SIAM J. Sci. Comput. 38(6), A3672–A3695 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, H., Enfedaque, P., Lou, Y., Marchesini, S.: Partially coherent ptychography by gradient decomposition of the probe. Acta Crystallogr. Sect. A: Found. Adv. 74(3), 157–169 (2018a)

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, H., Lou, Y., Duan, Y., Marchesini, S.: Total variation–based phase retrieval for Poisson noise removal. SIAM J. Imaging Sci. 11(1), 24–55 (2018b)

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, H., Marchesini, S., Lou, Y., Zeng, T.: Variational phase retrieval with globally convergent preconditioned proximal algorithm. SIAM J. Imaging Sci. 11(1), 56–93 (2018c)

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, H., Enfedaque, P., Marchesini, S.: Blind ptychographic phase retrieval via convergent alternating direction method of multipliers. SIAM J. Imaging Sci. 12(1), 153–185 (2019a)

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, H., Enfedaque, P., Zhang, J., Reinhardt, J., Enders, B., Yu, Y.-S., Shapiro, D., Schroer, C.G., Zeng, T., Marchesini, S.: Advanced denoising for x-ray ptychography. Opt. Express 27(8), 10395–10418 (2019b)

    Article  Google Scholar 

  • Chang, H., Marcus, M.A., Marchesini, S.: Analyzer-free linear dichroic ptychography. J. Appl. Crystallogr. 53(5), 1283–1292 (2020)

    Article  Google Scholar 

  • Chang, H., Glowinski, R., Marchesini, S., Tai, X.-C., Wang, Y., Zeng, T.: Overlapping domain decomposition methods for ptychographic imaging. SIAM J. Sci. Comput. 43(3), B570–B597 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  • Chapman, H.N.: Phase-retrieval x-ray microscopy by wigner-distribution deconvolution. Ultramicroscopy 66(3), 153–172 (1996)

    Article  Google Scholar 

  • Chen, Y., Candes, E.: Solving random quadratic systems of equations is nearly as easy as solving linear systems. In: Advances in Neural Information Processing Systems, pp. 739–747 (2015)

    Google Scholar 

  • Chen, P., Fannjiang, A.: Fourier phase retrieval with a single mask by douglas–rachford algorithms. Appl. Comput. Harmon. Anal. 44(3), 665-699 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Dierolf, M., Menzel, A., Thibault, P., Schneider, P., Kewish, C.M., Wepf, R., Bunk, O., Pfeiffer, F.: Ptychographic x-ray computed tomography at the nanoscale. Nature 467(7314), 436–439 (2010a)

    Article  Google Scholar 

  • Dierolf, M., Thibault, P., Menzel, A., Kewish, C.M., Jefimovs, K., Schlichting, I., von König, K., Bunk, O., Pfeiffer, F.: Ptychographic coherent diffractive imaging of weakly scattering specimens. New J. Phys. 12(3), 035017 (2010b)

    Article  Google Scholar 

  • Elser, V.: Phase retrieval by iterated projections. J. Opt. Soc. Am. A 20(1), 40–55 (2003)

    Article  Google Scholar 

  • Elser, V., Lan, T.-Y., Bendory, T.: Benchmark problems for phase retrieval. SIAM J. Imaging Sci. 11(4), 2429–2455 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Enfedaque, P., Chang, H., Enders, B., Shapiro, D., Marchesini, S.: High performance partial coherent x-ray ptychography. In: International Conference on Computational Science, pp. 46–59. Springer (2019)

    Google Scholar 

  • Fan, J.-Y., Yuan, Y.-X.: On the quadratic convergence of the levenberg-marquardt method without nonsingularity assumption. Computing 74(1), 23–39 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Fannjiang, A.: Raster grid pathology and the cure. Multiscale Model. Simul. 17(3), 973–995 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Fannjiang, A., Strohmer, T.: The numerics of phase retrieval. Acta Numer. 29, 125–228 (2020)

    Article  MathSciNet  Google Scholar 

  • Fannjiang, A., Zhang, Z.: Fixed point analysis of douglas–rachford splitting for ptychography and phase retrieval. SIAM J. Imaging Sci. 13(2), 609–650 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Fung, S.W., Wendy, Z.: Multigrid optimization for large-scale ptychographic phase retrieval. SIAM J. Imaging Sci. 13(1), 214–233 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, B., Xu, Z.: Phaseless recovery using the Gauss–Newton method. IEEE Trans. Sig. Process. 65(22), 5885–5896 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, B., Wang, Y., Xu, Z.: Solving a perturbed amplitude-based model for phase retrieval. IEEE Trans. Sig. Process. 68, 5427–5440 (2020)

    Article  MATH  Google Scholar 

  • Godard, P., Allain, M., Chamard, V., Rodenburg, J.: Noise models for low counting rate coherent diffraction imaging. Opt. Express 20(23), 25914–25934 (2012)

    Article  Google Scholar 

  • Grohs, P., Koppensteiner, S., Rathmair, M.: Phase retrieval: uniqueness and stability. SIAM Rev. 62(2), 301–350 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Guizar-Sicairos, M., Fienup, J.R.: Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Opt. Express 16(10), 7264–7278 (2008)

    Article  Google Scholar 

  • Guizar-Sicairos, M., Johnson, I., Diaz, A., Holler, M., Karvinen, P., Stadler, H.-C., Dinapoli, R., Bunk, O., Menzel, A.: High-throughput ptychography using eiger: scanning x-ray nano-imaging of extended regions. Opt. Express 22(12), 14859–14870 (2014)

    Article  Google Scholar 

  • Gürsoy, D., Chen-Wiegart, Y.-C.K., Jacobsen, C.: Lensless x-ray nanoimaging: revolutions and opportunities. IEEE Sig. Process. Mag. 39(1), 44–54 (2022)

    Article  Google Scholar 

  • Hackbusch, W.: Multi-grid Methods and Applications, Springer, Berlin, Heidelberg (1985)

    Book  MATH  Google Scholar 

  • Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM J. Optim. 23(4), 2397–2419 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Hesse, R., Luke, D.R., Sabach, S., Tam, M.K.: Proximal heterogeneous block implicit-explicit method and application to blind ptychographic diffraction imaging. SIAM J. Imaging Sci. 8(1), 426–457 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Hirose, M., Shimomura, K., Burdet, N., Takahashi, Y.: Use of Kramers-Kronig relation in phase retrieval calculation in x-ray spectro-ptychography. Opt. Express 25(8), 8593–8603 (2017)

    Article  Google Scholar 

  • Huang, M., Xu, Z.: The estimation performance of nonlinear least squares for phase retrieval. IEEE Trans. Inf. Theory 66(12), 7967–7977 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, M., Xu, Z.: Uniqueness and stability for the solution of a nonlinear least squares problem (2021). arXiv preprint arXiv:2104.10841

    Google Scholar 

  • Huang, X., Yan, H., Harder, R., Hwu, Y., Robinson, I.K., Chu, Y.S.: Optimization of overlap uniformness for ptychography. Opt. Express 22(10), 12634–12644 (2014)

    Article  Google Scholar 

  • Huang, Y., Jiang, S., Wang, R., Song, P., Zhang, J., Zheng, G., Ji, X., Zhang, Y.: Ptychography-based high-throughput lensless on-chip microscopy via incremental proximal algorithms. Opt. Express 29(23), 37892–37906 (2021)

    Article  Google Scholar 

  • Jaganathan, K., Eldar, Y.C., Hassibi, B.: Stft phase retrieval: uniqueness guarantees and recovery algorithms. IEEE J. Sel. Top. Sig. Process. 10(4), 770–781 (2016)

    Article  Google Scholar 

  • Jiang, S., Guo, C., Song, P., Zhou, N., Bian, Z., Zhu, J., Wang, R., Dong, P., Zhang, Z., Liao, J. et al.: Resolution-enhanced parallel coded ptychography for high-throughput optical imaging. ACS Photon. 8(11), 3261–3271 (2021)

    Article  Google Scholar 

  • Jiang, S., Guo, C., Bian, Z., Wang, R., Zhu, J., Song, P., Hu, P., Hu, D., Zhang, Z., Hoshino, K. et al.: Ptychographic sensor for large-scale lensless microbial monitoring with high spatiotemporal resolution. Biosens. Bioelectron. 196, 113699 (2022)

    Article  Google Scholar 

  • Kandel, S., Maddali, S., Nashed, Y.S., Hruszkewycz, S.O., Jacobsen, C., Allain, M.: Efficient ptychographic phase retrieval via a matrix-free levenberg-marquardt algorithm. Opt. Express 29(15), 23019–23055 (2021)

    Article  Google Scholar 

  • Kane, D.J., Vakhtin, A.B.: A review of ptychographic techniques for ultrashort pulse measurement. Progress Quantum Electron.vol. 81, 100364 (2021)

    Google Scholar 

  • Langer, A., Gaspoz, F.: Overlapping domain decomposition methods for total variation denoising. SIAM J. Numer. Anal. 57(3), 1411–1444 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Lee, C.-O., Park, E.-H., Park, J.: A finite element approach for the dual Rudin–Osher–Fatemi model and its nonoverlapping domain decomposition methods. SIAM J. Sci. Comput. 41(2), B205–B228 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Lo, Y.H., Zhou, J., Rana, A., Morrill, D., Gentry, C., Enders, B., Yu, Y.-S., Sun, C.-Y., Shapiro, D.A., Falcone, R.W., Kapteyn, H.C., Murnane, M.M., Gilbert, P.U.P.A., Miao, J.: X-ray linear dichroic ptychography. Proc. Natl. Acad. Sci. 118(3), 2019068118 (2021)

    Article  Google Scholar 

  • Luke, D.R.: Relaxed averaged alternating reflections for diffraction imaging. Inverse Probl. 21(1), 37–50 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Ma, C., Liu, X., Wen, Z.: Globally convergent levenberg-marquardt method for phase retrieval. IEEE Trans. Inf. Theory 65(4), 2343–2359 (2018)

    Article  MATH  Google Scholar 

  • Maiden, A.M., Rodenburg, J.M.: An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109(10), 1256–1262 (2009)

    Article  Google Scholar 

  • Maiden, A., Morrison, G., Kaulich, B., Gianoncelli, A., Rodenburg, J.: Soft x-ray spectromicroscopy using ptychography with randomly phased illumination. Nat. Commun. 4, 1669 (2013)

    Article  Google Scholar 

  • Maiden, A., Johnson, D., Li, P.: Further improvements to the ptychographical iterative engine. Optica 4(7), 736–745 (2017)

    Article  Google Scholar 

  • Marchesini, S.: Invited article: a unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instrum. 78(1), 011301 (2007)

    Article  Google Scholar 

  • Marchesini, S., Wu, H.-T.: Rank-1 accelerated illumination recovery in scanning diffractive imaging by transparency estimation (2014). arXiv preprint arXiv:1408.1922

    Google Scholar 

  • Marchesini, S., Schirotzek, A., Yang, C., Wu, H.-T., Maia, F.: Augmented projections for ptychographic imaging. Inverse Probl. 29(11), 115009 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Marchesini, S., Tu, Y.-C., Wu, H.-T.: Alternating projection, ptychographic imaging and phase synchronization. Appl. Comput. Harmon. Anal. 41(3), 815-851 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Marchesini, S., Krishnan, H., Shapiro, D.A., Perciano, T., Sethian, J.A., Daurer, B.J., Maia, F.R.: SHARP: a distributed, GPU-based ptychographic solver. J. Appl. Crystallogr. 49(4), 1245–1252 (2016)

    Article  Google Scholar 

  • Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  • Nash, S.G.: A multigrid approach to discretized optimization problems. Optim. Methods Softw. 14(1–2), 99–116 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Nashed, Y.S., Vine, D.J., Peterka, T., Deng, J., Ross, R., Jacobsen, C.: Parallel ptychographic reconstruction. Opt. Express 22(26), 32082–32097 (2014)

    Article  Google Scholar 

  • Odstrčil, M., Menzel, A., Guizar-Sicairos, M.: Iterative least-squares solver for generalized maximum-likelihood ptychography. Opt. Express 26(3), 3108–3123 (2018)

    Article  Google Scholar 

  • Ou, X., Zheng, G., Yang, C.: Embedded pupil function recovery for fourier ptychographic microscopy. Opt. Express 22(5), 4960–4972 (2014)

    Article  Google Scholar 

  • Pfeiffer, F.: X-ray ptychography. Nat. Photon 12, 9–17 (2018)

    Article  Google Scholar 

  • Qian, J., Yang, C., Schirotzek, A., Maia, F., Marchesini, S.: Efficient algorithms for ptychographic phase retrieval. Inverse Probl. Appl. Contemp. Math. 615, 261–280 (2014)

    MathSciNet  MATH  Google Scholar 

  • Qu, Q., Zhang, Y., Eldar, Y.C., Wright, J.: Convolutional phase retrieval. In: Proceedings of the 31st International Conference on Neural Information Processing Systems, pp. 6088–6098 (2017)

    Google Scholar 

  • Qu, Q., Zhang, Y., Eldar, Y.C., Wright, J.: Convolutional phase retrieval via gradient descent. IEEE Trans. Inf. Theory 66(3), 1785–1821 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Reinhardt, J., Hoppe, R., Hofmann, G., Damsgaard, C.D., Patommel, J., Baumbach, C., Baier, S., Rochet, A., Grunwaldt, J.-D., Falkenberg, G., Schroer, C.G.: Beamstop-based low-background ptychography to image weakly scattering objects. Ultramicroscopy 173, 52–57 (2017)

    Article  Google Scholar 

  • Rodenburg, J.M.: Ptychography and related diffractive imaging methods. Adv. Imaging Electron Phys. 150, 87–184 (2008)

    Article  Google Scholar 

  • Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics (2003)

    Google Scholar 

  • Shechtman, Y., Eldar, Y.C., Cohen, O., Chapman, H.N., Miao, J., Segev, M.: Phase retrieval with application to optical imaging: a contemporary overview. Sig. Process. Mag. IEEE 32(3), 87–109 (2015)

    Article  Google Scholar 

  • Sun, J., Qu, Q., Wright, J.: A geometric analysis of phase retrieval. In: 2016 IEEE International Symposium on Information Theory (ISIT), pp. 2379–2383. IEEE (2016)

    Google Scholar 

  • Thibault, P., Guizar-Sicairos, M.: Maximum-likelihood refinement for coherent diffractive imaging. New J. Phys. 14(6), 063004 (2012)

    Article  Google Scholar 

  • Thibault, P., Menzel, A.: Reconstructing state mixtures from diffraction measurements. Nature 494(7435), 68–71 (2013)

    Article  Google Scholar 

  • Thibault, P., Dierolf, M., Bunk, O., Menzel, A., Pfeiffer, F.: Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy 109(4), 338–343 (2009)

    Article  Google Scholar 

  • Trebino, R., DeLong, K.W., Fittinghoff, D.N., Sweetser, J.N., Krumbügel, M.A., Richman, B.A., Kane, D.J.: Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating. Rev. Sci. Instrum. 68(9), 3277–3295 (1997)

    Article  Google Scholar 

  • Wang, C., Xu, Z., Liu, H., Wang, Y., Wang, J., Tai, R.: Background noise removal in x-ray ptychography. Appl. Opt. 56(8), 2099–2111 (2017)

    Article  Google Scholar 

  • Wen, Z., Yang, C., Liu, X., Marchesini, S.: Alternating direction methods for classical and ptychographic phase retrieval. Inverse Probl. 28(11), 115010 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Wu, C., Tai, X.-C.: Augmented Lagrangian method, dual methods and split-Bregman iterations for ROF, vectorial TV and higher order models. SIAM J. Imaging Sci. 3(3), 300–339 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Xin, L., Zaiwen, W., Ya-Xiang, Y.: Subspace methods for nonlinear optimization. CSIAM Trans. Appl. Math. 2(4), 585–651 (2021)

    Article  MathSciNet  Google Scholar 

  • Xu, J., Zikatanov, L.: Algebraic multigrid methods. Acta Numer. 26, 591–721 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, J., Tai, X.-C., Wang, L.-L.: A two-level domain decomposition method for image restoration. Inverse Probl. Imaging 4(3), 523–545 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Yamashita, N., Fukushima, M.: On the rate of convergence of the levenberg-marquardt method. In: Alefeld, G., Chen, X. (eds.) Topics in Numerical Analysis, pp. 239–249. Springer, Vienna (2001)

    Chapter  Google Scholar 

  • Yan, H.: Ptychographic phase retrieval by proximal algorithms. New J. Phys. 22(2), 023035.(2020)

    Article  MathSciNet  Google Scholar 

  • Yeh, L.-H., Dong, J., Zhong, J., Tian, L., Chen, M., Tang, G., Soltanolkotabi, M., Waller, L.: Experimental robustness of fourier ptychography phase retrieval algorithms. Opt. Express 23(26), 33214–33240 (2015)

    Article  Google Scholar 

  • Zheng, G., Horstmeyer, R., Yang, C.: Wide-field, high-resolution fourier ptychographic microscopy. Nat. Photon. 7, 739–745 (2013)

    Article  Google Scholar 

  • Zheng, G., Shen, C., Jiang, S., Song, P., Yang, C.: Concept, implementations and applications of fourier ptychography. Nat. Rev. Phys. 3(3), 207–223 (2021)

    Article  Google Scholar 

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Acknowledgements

The work of the first author was partially supported by the NSFC (Nos. 11871372, 11501413) and Natural Science Foundation of Tianjin (18JCYBJC16600). The authors would like to thank Prof. Guoan Zheng for the helpful discussions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tianjin Normal University, Tianjin, China

    Huibin Chang & Li Yang

  2. SLAC National Laboratory, Menlo Park, CA, USA

    Stefano Marchesini

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  1. Huibin Chang
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  2. Li Yang
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Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Hong Kong Center for Cerebrocardiovascular Health Engineering (COCHE), Shatin, Hong Kong

    Xue-Cheng Tai

  4. Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA

    Laurent Younes

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Chang, H., Yang, L., Marchesini, S. (2023). Fast Iterative Algorithms for Blind Phase Retrieval: A Survey. In: Chen, K., Schönlieb, CB., Tai, XC., Younes, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-98661-2_116

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