Sparse phase retrieval via ℓp (0 < p ≤ 1) minimization

2021 ◽  
pp. 2150034
Author(s):  
Manxia Cao ◽  
Wei Huang
Keyword(s):  
Text Analysis ◽  
Phase Retrieval ◽  
Restricted Isometry Property ◽  
Measurement Matrix ◽  
Analysis Model ◽  
Redundant Dictionary ◽  
Retrieval Problem ◽  
Matrix Formula ◽  
Unknown Signal

In this paper, the [Formula: see text]-analysis model for the phase retrieval problem of sparse unknown signals in the redundant dictionary is extended to the [Formula: see text]-analysis model, where [Formula: see text]. It’s shown that if the measurement matrix [Formula: see text] satisfies the strong restricted isometry property adapted to D (S-DRIP) condition, the unknown signal [Formula: see text] can be stably recovered by analyzing the [Formula: see text] [Formula: see text] minimization model.

scholarly journals Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rujia Li ◽  
Liangcai Cao
Keyword(s):  
Phase Retrieval ◽  
Dynamic Range ◽  
A Priori ◽  
Measured Intensity ◽  
Physical Constraints ◽  
Coherent Diffraction Imaging ◽  
Effective Dynamic ◽  
Ill Posed ◽  
Retrieval Problem ◽  
Diffraction Imaging

AbstractPhase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

Phase Retrieval Problem in Fractional Fourier Domain

2010 ◽  
Vol 47 (8) ◽  
pp. 081001
Author(s):  
廖天河 Liao Tianhe ◽  
高穹 Gao Qiong ◽  
崔远峰 Cui Yuanfeng ◽  
宋凯洋 Song Kaiyang
Keyword(s):  
Phase Retrieval ◽  
Fourier Domain ◽  
Retrieval Problem

scholarly journals GARLM: Greedy Autocorrelation Retrieval Levenberg–Marquardt Algorithm for Improving Sparse Phase Retrieval

2018 ◽  
Vol 8 (10) ◽  
pp. 1797 ◽  
Author(s):  
Zhuolei Xiao ◽  
Yerong Zhang ◽  
Kaixuan Zhang ◽  
Dongxu Zhao ◽  
Guan Gui
Keyword(s):  
Fourier Transform ◽  
Local Search ◽  
Phase Retrieval ◽  
Greedy Algorithms ◽  
Optimal Estimation ◽  
Retrieval Algorithm ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Local Search Procedure ◽  
Unknown Signal

The goal of phase retrieval is to recover an unknown signal from the random measurements consisting of the magnitude of its Fourier transform. Due to the loss of the phase information, phase retrieval is considered as an ill-posed problem. Conventional greedy algorithms, e.g., greedy spare phase retrieval (GESPAR), were developed to solve this problem by using prior knowledge of the unknown signal. However, due to the defect of the Gauss–Newton method in the local convergence problem, especially when the residual is large, it is very difficult to use this method in GESPAR to efficiently solve the non-convex optimization problem. In order to improve the performance of the greedy algorithm, we propose an improved phase retrieval algorithm, which is called the greedy autocorrelation retrieval Levenberg–Marquardt (GARLM) algorithm. Specifically, the proposed GARLM algorithm is a local search iterative algorithm to recover the sparse signal from its Fourier transform magnitude. The proposed algorithm is preferred to existing greedy methods of phase retrieval, since at each iteration the problem of minimizing the objective function over a given support is solved by using the improved Levenberg–Marquardt (ILM) method and matrix transform. A local search procedure such as the 2-opt method is then invoked to get the optimal estimation. Simulation results are given to show that the proposed algorithm performs better than the conventional GESPAR algorithm.

The Phase Retrieval Problem

1981 ◽  
Vol 28 (6) ◽  
pp. 735-738 ◽  
Author(s):  
J.G. Walker
Keyword(s):  
Phase Retrieval ◽  
Retrieval Problem

On the ambiguities of phase retrieval problem in Fourier ptychographic microscopy

2020 ◽  
Author(s):  
Leng Ningyi ◽  
Yuan Ziyang ◽  
Yang Haoxing ◽  
Hongxia Wang ◽  
Du Longkun
Keyword(s):  
Phase Retrieval ◽  
Retrieval Problem

scholarly journals The nonsmooth landscape of phase retrieval

2020 ◽  
Vol 40 (4) ◽  
pp. 2652-2695
Author(s):  
Damek Davis ◽  
Dmitriy Drusvyatskiy ◽  
Courtney Paquette
Keyword(s):  
Phase Retrieval ◽  
Optimal Solution ◽  
Subgradient Method ◽  
Relative Distance ◽  
Stationary Points ◽  
Image Recovery ◽  
The Real ◽  
Codimension Two ◽  
Statistical Assumptions ◽  
Retrieval Problem

Abstract We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. Seeking to understand the distribution of the stationary points of the problem, we complete the paper by proving that as the number of Gaussian measurements increases, the stationary points converge to a codimension two set, at a controlled rate. Experiments on image recovery problems illustrate the developed algorithm and theory.

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