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Related papers: Phase retrieval with background information

200 papers

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…

Image and Video Processing · Electrical Eng. & Systems 2022-09-21 J. A. Pollock , K. S. Morgan , L. C. P. Croton , M. K. Croughan , G. Ruben , N. Yagi , H. Sekiguchi , M. J. Kitchen

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…

Information Theory · Computer Science 2015-06-16 Afonso S. Bandeira , Dustin G. Mixon

Phase-retrieval from coded diffraction patterns (CDP) is important to X-ray crystallography, diffraction tomography and astronomical imaging, yet remains a hard, non-convex inverse problem. We show that CDP recovery can be reformulated…

Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which…

Computer Vision and Pattern Recognition · Computer Science 2018-05-10 Lokesh Boominathan , Mayug Maniparambil , Honey Gupta , Rahul Baburajan , Kaushik Mitra

The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…

Signal Processing · Electrical Eng. & Systems 2018-02-07 Vladimir Katkovnik , Karen Egiazarian

Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This…

Image and Video Processing · Electrical Eng. & Systems 2020-12-02 Albert Fannjiang , Thomas Strohmer

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…

Numerical Analysis · Mathematics 2025-02-18 Licheng Dai , Xiliang Lu , Juntao You

Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…

Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…

Image and Video Processing · Electrical Eng. & Systems 2025-01-07 Mehmet Onurcan Kaya , Figen S. Oktem

We develop a fast phase retrieval method which can utilize a large class of local phaseless correlation-based measurements in order to recover a given signal ${\bf x} \in \mathbb{C}^d$ (up to an unknown global phase) in near-linear…

Numerical Analysis · Mathematics 2016-07-12 Mark Iwen , Aditya Viswanathan , Yang Wang

Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…

Information Theory · Computer Science 2016-03-07 Yang Chen , Cheng Cheng , Qiyu Sun , Haichao Wang

Phase retrieval is concerned with recovering a function $f$ from the absolute value of its Fourier transform $|\widehat{f}|$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $$ \|…

Functional Analysis · Mathematics 2021-03-29 Stefan Steinerberger

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…

Optics · Physics 2024-09-10 Zhiyuan Hu , Julián Tachella , Michael Unser , Jonathan Dong

The problem of phase retrieval has many applications in the field of optical imaging. Motivated by imaging experiments with biological specimens, we primarily consider the setting of low-dose illumination where Poisson noise plays the…

Numerical Analysis · Mathematics 2024-03-28 Benedikt Diederichs , Frank Filbir , Patricia Römer

In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish…

Information Theory · Computer Science 2025-04-03 Bing Gao

The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…

Machine Learning · Statistics 2024-09-04 Zhong Zheng , Lingzhou Xue

Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…

Computer Vision and Pattern Recognition · Computer Science 2011-08-17 Artem Migukin , Vladimir Katkovnik , Jaakko Astola

We study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…

Information Theory · Computer Science 2018-05-25 Oussama Dhifallah , Christos Thrampoulidis , Yue M. Lu

We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global phase) by their STFT magnitude when the underlying window…

Functional Analysis · Mathematics 2021-01-07 Rima Alaifari , Matthias Wellershoff

I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no…

Optics · Physics 2012-12-04 Stefano Marchesini