GESPAR: Efficient Phase Retrieval of Sparse Signals. We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore, prior information on the signal is needed in order to enable its recovery. In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis. We propose a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse Retrieval. Our algorithm does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images. Simulation results indicate that GESPAR is fast and more accurate than existing techniques in a variety of settings.

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Li, Huiping; Li, Song: Phase retrieval from Fourier measurements with masks (2021)
  2. Li, Hui-ping; Li, Song: Phase retrieval with PhaseLift algorithm (2020)
  3. Ma, Cong; Wang, Kaizheng; Chi, Yuejie; Chen, Yuxin: Implicit regularization in nonconvex statistical estimation: gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution (2020)
  4. Mousavi, Ahmad; Rezaee, Mehdi; Ayanzadeh, Ramin: A survey on compressive sensing: classical results and recent advancements (2020)
  5. Pang, Tongyao; Li, Qingna; Wen, Zaiwen; Shen, Zuowei: Phase retrieval: a data-driven wavelet frame based approach (2020)
  6. Thao, Nguyen Hieu; Luke, David Russell; Soloviev, Oleg; Verhaegen, Michel: Phase retrieval with sparse phase constraint (2020)
  7. Zhou, Zhiyong; Yu, Jun: Phaseless compressive sensing using partial support information (2020)
  8. Bahmani, Sohail; Romberg, Justin: Solving equations of random convex functions via anchored regression (2019)
  9. Burger, Martin; Föcke, Janic; Nickel, Lukas; Jung, Peter; Augustin, Sven: Reconstruction methods in THz single-pixel imaging (2019)
  10. Fan, Jun; Wang, Liqun; Yan, Ailing: An inexact projected gradient method for sparsity-constrained quadratic measurements regression (2019)
  11. Liu, Yong-Jin; Li, Ruonan; Wang, Bo: On the characterizations of solutions to perturbed (l_1) conic optimization problem (2019)
  12. Roig-Solvas, Biel; Makowski, Lee; Brooks, Dana H.: A proximal operator for multispectral phase retrieval problems (2019)
  13. Yuan, Ziyang; Wang, Hongxia; Wang, Qi: Phase retrieval via sparse Wirtinger flow (2019)
  14. Beck, Amir; Hallak, Nadav: Proximal mapping for symmetric penalty and sparsity (2018)
  15. Bolte, Jérôme; Sabach, Shoham; Teboulle, Marc; Vaisbourd, Yakov: First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems (2018)
  16. Chang, Huibin; Lou, Yifei; Duan, Yuping; Marchesini, Stefano: Total variation-based phase retrieval for Poisson noise removal (2018)
  17. Chang, Huibin; Marchesini, Stefano; Lou, Yifei; Zeng, Tieyong: Variational phase retrieval with globally convergent preconditioned proximal algorithm (2018)
  18. Sun, Ju; Qu, Qing; Wright, John: A geometric analysis of phase retrieval (2018)
  19. Yuan, Ziyang; Wang, Hongxia: Phase retrieval for sparse binary signal: uniqueness and algorithm (2018)
  20. Iwen, Mark; Viswanathan, Aditya; Wang, Yang: Robust sparse phase retrieval made easy (2017)

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