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Phaseless Recovery Using the Gauss–Newton Method

Bing Gao, Zhiqiang Xu
2017 IEEE Transactions on Signal Processing  
Numerical experiments also show that Gauss-Newton method has better performance over the other algorithms.  ...  In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step.  ...  We are grateful to Xin Liu for discussions and comments at the beginning of this project, which contributed to the proof of Theorem 3.1.  ... 
doi:10.1109/tsp.2017.2742981 fatcat:swg2tdbua5dalivffv2wwnpzli

Fourier Phase Retrieval: Uniqueness and Algorithms [article]

Tamir Bendory, Robert Beinert, Yonina C. Eldar
2017 arXiv   pre-print
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science.  ...  In this chapter we survey methods to guarantee uniqueness in Fourier phase retrieval. We then present different algorithmic approaches to retrieve the signal in practice.  ...  ) using the damped Gauss-Newton method to obtain x ( ) end while Return: x est ← x ( ) retrieval through waveguide arrays [115, 117, 119, 120] .  ... 
arXiv:1705.09590v3 fatcat:i3arbexpqra47cp6ggi2w4rpzu

Fast Iterative Algorithms for Blind Phase Retrieval: A survey [article]

Huibin Chang and Li Yang and Stefano Marchesini
2022 arXiv   pre-print
(pupil) jointly from phaseless data.  ...  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 authors would like to thank Prof. Guoan Zheng for the helpful discussions.  ... 
arXiv:2211.06619v1 fatcat:qdvfwdy5k5dkxecskdtk6gw5dy

L^0-regularized Variational Methods for Sparse Phase Retrieval [article]

Yuping Duan and Chunlin Wu and Zhi-Feng Pang and Huibin Chang
2016 arXiv   pre-print
Numerous experiments show that our proposed methods can recover sparse signals from phaseless measurements with higher successful recovery rates and lower computation cost compared with the state-of-art  ...  We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements.  ...  ACKNOWLEDGMENT The authors would like to thank Dr. Kishore Jaganathan to provide us the codes for SPR algorithm. Dr. Y.  ... 
arXiv:1612.02538v1 fatcat:h4bsgpojyng67adhlfm5lx54we

Denoising Poisson phaseless measurements via orthogonal dictionary learning

Huibin Chang, Stefano Marchesini
2018 Optics Express  
Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are performed to show the efficiency and robustness of proposed methods, which, by preserving texture features  ...  Fast Alternating Minimization Method (AMM) and Proximal Alternating Linearized Minimization (PALM) are adopted to solve the established model with convergence guarantee, and especially global convergence  ...  Disclosures The authors declare that there are no conflicts of interest related to this article.  ... 
doi:10.1364/oe.26.019773 pmid:30119298 fatcat:nuetvity2fgkxfd6cin7pkvy6m

Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers

Aiye Wang, Zhuoqun Zhang, Siqi Wang, An Pan, Caiwen Ma, Baoli Yao
2022 Cells  
It is found that ADMM-FPM method belongs to a global optimization algorithm with a high degree of parallelism and thus results in a more stable and robust phase recovery under noisy conditions.  ...  Its reconstruction is normally formulated as a blind phase retrieval problem, where both the object and probe have to be recovered from phaseless measured data.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/cells11091512 pmid:35563818 pmcid:PMC9104836 fatcat:kzsxgrwvtfb6zoq4o7kzwezipi

Amplitude-Based Smoothed Sparse Phase Retrieval Algorithm

Zhuolei Xiao, Zhengyan Liu
2022 Wireless Communications and Mobile Computing  
Secondly, the support of the original signal is estimated by differential analysis of the gaps, and the initialization can be obtained through a carefully designed method based on this support.  ...  Numerical experiments show that the proposed SPSAF algorithm has significant improvements in recovery performance, convergence speed, and sampling complexity.  ...  Acknowledgments This research was funded by the Natural Science Research Project of Fuyang Normal University (2021FSKJ02ZD), Natural Science Research Project of Anhui Province (KJ2020A0539, KJ2021A0662  ... 
doi:10.1155/2022/7012261 doaj:f8b27c5890c145bdb96fad7d17a0fef0 fatcat:rzlgxcffcfefznsowvjrinckfa

2020 Index IEEE Transactions on Computational Imaging Vol. 6

2020 IEEE Transactions on Computational Imaging  
Zhu, H., +, TCI 2020 12-23 Gauss-Newton Optimization for Phase Recovery From the Bispectrum.  ...  Yonel, B., +, TCI 2020 711-726 Gauss-Newton Optimization for Phase Recovery From the Bispectrum.  ... 
doi:10.1109/tci.2021.3054596 fatcat:puij7ztll5ai7alxrmqzsupcny

Sparse Signal Recovery from Phaseless Measurements via Hard Thresholding Pursuit [article]

Jian-Feng Cai, Jingzhi Li, Xiliang Lu, Juntao You
2020 arXiv   pre-print
In this paper, we consider the sparse phase retrieval problem, recovering an s-sparse signal x^♮∈ℝ^n from m phaseless samples y_i=|⟨x^♮,a_i⟩| for i=1,...,m.  ...  Together with a spectral initialization, our algorithm is guaranteed to have an exact recovery from O(s^2log n) samples.  ...  Examples include alternating minimization [33] (or Fienup methods), Wirtinger flow [10] , Kaczmarz [37, 43] , Riemannian optimization [6] , and Gauss-Newton [18, 29] .  ... 
arXiv:2005.08777v2 fatcat:3j4shooxujdehgwbqd3v7xsjme

A Fast and Provable Algorithm for Sparse Phase Retrieval [article]

Jian-Feng Cai, Yu Long, Ruixue Wen, Jiaxi Ying
2024 arXiv   pre-print
In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding  ...  Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.  ...  We would also like to thank the anonymous reviewers for their valuable feedback on the manuscript.  ... 
arXiv:2309.02046v2 fatcat:yhxtnbely5hqfgvotuaqfnvsoe

On DC based Methods for Phase Retrieval [article]

Meng Huang, Ming-Jun Lai, Abraham Varghese, Zhiqiang Xu
2018 arXiv   pre-print
These lead to more effective algorithms than the Wirtinger flow (WF) algorithm and the Gauss-Newton (GN) algorithm and etc..  ...  Our study is a deterministic analysis while the study for the Wirtinger flow (WF) algorithm and its variants, the Gauss-Newton (GN) algorithm, the trust region algorithm is based on the probability analysis  ...  In this example, we use the DC based algorithm and the Gauss-Newton method to retrieve complex variable solutions.  ... 
arXiv:1810.09061v1 fatcat:mmv3ohjnwbh57gxstjznusu4am

Table of Contents

2020 IEEE Transactions on Computational Imaging  
Buller 138 Gauss-Newton Optimization for Phase Recovery From the Bispectrum . . . . . . . . . J. L. Herring, J. Nagy, and L.  ...  Wang 1245 Fast Multi-Focus Ultrasound Image Recovery Using Generative Adversarial Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.1109/tci.2021.3054280 fatcat:7se3scatcrcutgat3tpk5mz2nm

Scalable Solvers of Random Quadratic Equations via Stochastic Truncated Amplitude Flow

Gang Wang, Georgios B. Giannakis, Jie Chen
2017 IEEE Transactions on Signal Processing  
A novel approach termed stochastic truncated amplitude flow (STAF) is developed to reconstruct an unknown n-dimensional real-/complex-valued signal x from m 'phaseless' quadratic equations of the form  ...  initialization using stochastic truncated gradient iterations.  ...  [27] and Gauss-Newton methods [28] , as well as the recently proposed Wirtinger-based variants such as (truncated/reshaped) Wirtinger flow (WF, TWF/RWF) [1] , [16, 29] .  ... 
doi:10.1109/tsp.2017.2652392 fatcat:ndb3pnyr2fcq7ban4jaisfeixu

The Newton method for affine phase retrieval [article]

Bing Gao
2022 arXiv   pre-print
Starting from zero, our algorithm generates iteration point by Newton method, and we prove that the algorithm can quadratically converge to the true signal without any ambiguity for both Gaussian measurements  ...  In addition, we also use some numerical simulations to verify the conclusions and to show the effectiveness of the algorithm.  ...  In paper [11] , we use Gauss-Newton method to solve phase retrieval problem when the measurements are in the real number field.  ... 
arXiv:2201.11001v1 fatcat:3flqhhiirnguvkuz7cqtiwtcdm

Phase Retrieval: An Overview of Recent Developments [article]

Kishore Jaganathan, Yonina C. Eldar, Babak Hassibi
2015 arXiv   pre-print
For both the cases, we review conditions for the identifiability of the signal, as well as practical algorithms for signal recovery.  ...  In particular, we demonstrate that it is possible to robustly and efficiently identify an unknown signal solely from phaseless Fourier measurements, a fact with potentially far-reaching implications.  ...  Acknowledgement: The authors would like to thank Prof.  ... 
arXiv:1510.07713v1 fatcat:l2pfboj4jjhjrkvjjaxcfuxhka
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