Filters








113,154 Hits in 2.9 sec

Phase Retrieval via Matrix Completion

Emmanuel J. Candès, Yonina C. Eldar, Thomas Strohmer, Vladislav Voroninski
2013 SIAM Journal of Imaging Sciences  
completion.  ...  This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications.  ...  We are indebted to Stefano Marchesini for inspiring and helpful discussions on the phase problem in X-ray 21 crystallography as well as for providing us with the gold balls data set used in Section 4.  ... 
doi:10.1137/110848074 fatcat:ckr67i6czfeifo74ilf756qusu

Phase Retrieval via Matrix Completion

Emmanuel J. Candès, Yonina C. Eldar, Thomas Strohmer, Vladislav Voroninski
2015 SIAM Review  
completion.  ...  This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications.  ...  We are indebted to Stefano Marchesini for inspiring and helpful discussions on the phase problem in X-ray 21 crystallography as well as for providing us with the gold balls data set used in Section 4.  ... 
doi:10.1137/151005099 fatcat:udfer2mfu5b35fjgqpuzn4a5qy

Phase Retrieval via Matrix Completion [article]

Emmanuel J. Candes, Yonina Eldar, Thomas Strohmer, Vlad Voroninski
2011 arXiv   pre-print
completion.  ...  This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications.  ...  We are indebted to Stefano Marchesini for inspiring and helpful discussions on the phase problem in X-ray 21 crystallography as well as for providing us with the gold balls data set used in Section 4.  ... 
arXiv:1109.0573v2 fatcat:x7lvsqtcdvf4pn4pnur4kv5lam

On phase retrieval via matrix completion and the estimation of low rank PSD matrices [article]

Marcus Carlsson, Daniele Gerosa
2019 arXiv   pre-print
We apply this in particular to the phase retrieval problem for Fourier data, which can be formulated as a rank 1 PSD matrix recovery problem.  ...  Given underdetermined measurements of a Positive Semi-Definite (PSD) matrix X of known low rank K, we present a new algorithm to estimate X based on recent advances in non-convex optimization schemes.  ...  phase retrieval problem is lifted onto a linear one with dimension squared; the problem (1) to be solved is now to find a suitable rank 1 PSD-matrix X such that A(X) = b.  ... 
arXiv:1907.09537v2 fatcat:s3zlguchfbfm7c6xsga5ziv4j4

On phase retrieval via matrix completion and the estimation of low rank PSD matrices

Marcus Carlsson, Daniele Gerosa
2019 Inverse Problems  
We apply this in particular to the phase retrieval problem for Fourier data, which can be formulated as a rank 1 PSD matrix recovery problem.  ...  Given underdetermined measurements of a positive semi-definite (PSD) matrix X of known low rank K, we present a new algorithm to estimate X based on recent advances in non-convex optimization schemes.  ...  phase retrieval problem is lifted onto a linear one with dimension squared; the problem (1) to be solved is now to find a suitable rank 1 PSD-matrix X such that A(X) = b.  ... 
doi:10.1088/1361-6420/ab4e6d fatcat:xhkyg5aypzddhc6jqyttgkseoq

Denoised Wigner distribution deconvolution via low-rank matrix completion

Justin Lee, George Barbastathis
2016 Optics Express  
Here, we demonstrate a method for noise suppression in WDD via low-rank noisy matrix completion [3,4].  ...  KEY WORDS: Computational Imaging, phase retrieval, ptychography, noise suppression Wigner Distribution Deconvolution (WDD) was first proposed as a method for phase retrieval in 1989 by Bates and Rodenburg  ...  Here, we demonstrate a method for noise suppression in WDD via low-rank noisy matrix completion [3, 4] .  ... 
doi:10.1364/oe.24.020069 pmid:27607616 fatcat:2zgeu7ndwfctdkghrxdfexd4dm

Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming*

Henrik Ohlsson, Allen Y. Yang, Roy Dong, S. Shankar Sastry
2012 IFAC Proceedings Volumes  
high, albeit the exact solutions to both sparse signal recovery and phase retrieval are combinatorial.  ...  In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted.  ...  In the rest of the section, we briefly review the phase retrieval literature and its recent connections with CS and matrix completion.  ... 
doi:10.3182/20120711-3-be-2027.00415 fatcat:5axcte2tuneuna4zmka7t745me

Low-Rank Phase Retrieval via Variational Bayesian Learning [article]

Kaihui Liu, Jiayi Wang, Zhengli Xing, Linxiao Yang, Jun Fang
2018 arXiv   pre-print
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements.  ...  We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to promote the low-rankness of the matrix.  ...  PhaseLift transforms phase retrieval into a semidefinite program via convex relaxation.  ... 
arXiv:1811.01574v1 fatcat:qqnqopayd5c6vnaxebwtvqts2e

Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage [article]

Alp Yurtsever and Madeleine Udell and Joel A. Tropp and Volkan Cevher
2017 arXiv   pre-print
This algorithm, SketchyCGM, modifies a standard convex optimization scheme, the conditional gradient method, to store only a small randomized sketch of the matrix variable.  ...  This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution.  ...  Low-Rank Matrix Optimization Methods Matrix completion and phase retrieval are examples of convex low-rank matrix optimization (CLRO) problems.  ... 
arXiv:1702.06838v1 fatcat:phghpmxuarbm5e5vdkapa2bbeq

The Matrix Completion Method for Phase Retrieval from Fractional Fourier Transform Magnitudes

Qi Luo, Hongxia Wang
2016 Mathematical Problems in Engineering  
The matrix completion method is adopted here. Through numerical tests, the matrix completion method is proven effective in both noisy and noise-free situations.  ...  Numerical tests show that the matrix completion method gains a certain advantage in recovering uniqueness and convergence over the GS algorithm in the noise-free case.  ...  Conclusions In this paper we consider solving the FRFT phase retrieval problem with the matrix completion method which utilizes magnitudes of multiple FRFTs.  ... 
doi:10.1155/2016/4617327 fatcat:g4vl2ixmhzbuvfezonabhxqila

Low-Rank Phase Retrieval via Variational Bayesian Learning

Kaihui Liu, Jiayi Wang, Zhengli Xing, Linxiao Yang, Jun Fang
2019 IEEE Access  
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements.  ...  We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to promote the low-rankness of the matrix.  ...  PhaseLift transforms phase retrieval into a semidefinite program via convex relaxation.  ... 
doi:10.1109/access.2018.2889518 fatcat:txhlfqwinvey5fioeszzlrklxm

Multiple Scattering Media Imaging via End-to-End Neural Network [article]

Ziyang Yuan, Hongxia Wang
2018 arXiv   pre-print
Double phase retrieval is a recently proposed efficient method which recovers the unknown object from its phaseless measurements by two steps with phase retrieval.  ...  In this paper, we combine the two steps in double phase retrieval and construct an end-to-end neural network called TCNN(Transforming Convolutional Neural Network) which directly learns the relationship  ...  The double phase retrieval can also be called blind phase retrieval. In this case, the transmission matrix A and x is unknown. The condition of it is worse than phase retrieval.  ... 
arXiv:1806.09968v1 fatcat:yngpcntwgjch5lvo5sbt3yzwlq

Toward high-dimensional-state quantum memory in a cold atomic ensemble

Dong-Sheng Ding, Wei Zhang, Zhi-Yuan Zhou, Shuai Shi, Jian-song Pan, Guo-Yong Xiang, Xi-Shi Wang, Yun-Kun Jiang, Bao-Sen Shi, Guang-Can Guo
2014 Physical Review A. Atomic, Molecular, and Optical Physics  
We reconstruct the storage process density matrix with the fidelity of 85.3% by the aid of a 4-f imaging system experimentally.  ...  ., but to date, all quantum memories only realize the storage and retrieval of the photons lived in a two-dimensional space spanned for example by orthogonal polarizations, therefore only a quantum bit  ...  The complete operators for reconstructing matrix χ Fig. 4 . 4 The columns (1) show the different phase distributions imaged on the SLM 1, the columns (2) represents the phase distributions in Fourier  ... 
doi:10.1103/physreva.90.042301 fatcat:e27ygw2hcncetdvjfy5huejf4m

Phase Recovery Based on the Sparse Measurement

Yi QIAN, Quan-bing ZHANG, Na NI, Shan-feng HU, Ya-ping CHEN
2017 DEStech Transactions on Engineering and Technology Research  
This paper focus on the recovery of the phase of sparse measurements based on the PhaseCut algorithm, and proposes a new method called BlockCut by combining the matrix blocking and the PhaseCut algorithm  ...  corresponding to zero-measurement value and solve the obtained homogeneous linear equations, then substitute the results to the rest equations which correspond to non-zero-measurement value and solve it via  ...  To retrieve the phase of sparse signal, Henrik Ohlssony et al. proposed an approach called CPR by combining the 1 l -minimization problem in Compressive Sensing (CS) with low-rank matrix completion problem  ... 
doi:10.12783/dtetr/icca2016/6056 fatcat:lopu3kazhzhcfh7pujiiogsehu

Binary Sparse Phase Retrieval via Simulated Annealing

Wei Peng, Hongxia Wang
2016 Mathematical Problems in Engineering  
This paper presents the Simulated Annealing Sparse PhAse Recovery (SASPAR) algorithm for reconstructing sparse binary signals from their phaseless magnitudes of the Fourier transform.  ...  Phase lifting technique based on matrix completion [9] is developed to transform phase retrieval problems to be convex.  ...  Reference [22] introduces SA for finding periodic phase relief structures via phase perturbations.  ... 
doi:10.1155/2016/8257612 fatcat:icg75tlpxnbnxfokqivnveqtki
« Previous Showing results 1 — 15 out of 113,154 results