GESPAR swMATH ID: 25722 Software Authors: Yoav Shechtman, Amir Beck, Yonina C. Eldar Description: 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. Homepage: https://arxiv.org/abs/1301.1018 Related Software: PhaseLift; Wirtinger Flow; SparsePR; CoSaMP; PhaseMax; PDCO; PhaseCut; TFOCS; CVX; UNLocBoX; BlockPR; PhaseCode; GloVe; word2vec; FPC_AS; Yall1; FlexBox; BranchHull; FMS; ADMiRA Cited in: 31 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year GESPAR: efficient phase retrieval of sparse signals. Zbl 1394.94522Shechtman, Yoav; Beck, Amir; Eldar, Yonina C. 2014 all top 5 Cited by 67 Authors 3 Wang, Hongxia 2 Bahmani, Sohail 2 Beck, Amir 2 Chang, Huibin 2 Eldar, Yonina Chana 2 Iwen, Mark A. 2 Li, Huiping 2 Li, Song 2 Lou, Yifei 2 Marchesini, Stefano 2 Romberg, Justin K. 2 Viswanathan, Aditya 2 Wang, Yang 2 Yuan, Ziyang 1 Augustin, Sven 1 Ayanzadeh, Ramin 1 Bojarovska, Irena 1 Bolte, Jérôme 1 Brooks, Dana H. 1 Burger, Martin 1 Chen, Yuxin 1 Chi, Yuejie 1 Chouzenoux, Emilie 1 Duan, Yuping 1 Ehler, Martin 1 Fan, Jun 1 Flinth, Axel 1 Föcke, Janic 1 Fornasier, Massimo 1 Hallak, Nadav 1 Jung, Peter 1 Li, Qingna 1 Li, Ruonan 1 Liu, Yong-Jin 1 Luke, David Russell 1 Ma, Cong 1 Makowski, Lee 1 Mendelson, Shahar 1 Mousavi, Ahmad 1 Nickel, Lukas 1 Pang, Tongyao 1 Peng, Wei 1 Pesquet, Jean-Christophe 1 Qu, Qing 1 Repetti, Audrey 1 Rezaee, Mehdi 1 Roig-Solvas, Biel 1 Sabach, Shoham 1 Shechtman, Yoav 1 Shen, Zuowei 1 Sigl, Juliane 1 Soloviev, Oleg A. 1 Sun, Ju 1 Teboulle, Marc 1 Thao, Nguyen Hieu 1 Vaisbourd, Yakov 1 Verhaegen, Michel 1 Wang, Bo 1 Wang, Kaizheng 1 Wang, Liqun 1 Wei, Ke 1 Wen, Zaiwen 1 Yan, Ailing 1 Yao, Yisha 1 Zeng, Tie Yong 1 Zhou, Zhiyong 1 Zhu, Xunzhi all top 5 Cited in 21 Serials 3 SIAM Journal on Optimization 3 Applied and Computational Harmonic Analysis 3 Foundations of Computational Mathematics 3 SIAM Journal on Imaging Sciences 2 Mathematical Problems in Engineering 1 Inverse Problems 1 Journal of Computational and Applied Mathematics 1 Optimization 1 Asia-Pacific Journal of Operational Research 1 IEEE Transactions on Signal Processing 1 Journal of Global Optimization 1 Applied Mathematics. Series B (English Edition) 1 The Journal of Fourier Analysis and Applications 1 Multiscale Modeling & Simulation 1 Inverse Problems in Science and Engineering 1 Optimization Letters 1 Inverse Problems and Imaging 1 Electronic Journal of Statistics 1 Information and Inference 1 Journal of Mathematical Modeling 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 13 Fields 18 Information and communication theory, circuits (94-XX) 17 Operations research, mathematical programming (90-XX) 14 Numerical analysis (65-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 4 Statistics (62-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Computer science (68-XX) 3 Optics, electromagnetic theory (78-XX) 2 Functional analysis (46-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) Citations by Year