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In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15], based on mirror descent (or Bregman gradient descent), to…

Optimization and Control · Mathematics 2024-06-21 Jean-Jacques Godeme , Jalal Fadili , Claude Amra , Myriam Zerrad

In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then…

Information Theory · Computer Science 2018-02-12 Bing Gao , Zhiqiang Xu

Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These disturbances, arising due to many factors such as non-idealities…

Optics · Physics 2012-07-24 Artem Migukin , Mostafa Agour , Vladimir Katkovnik

The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…

Functional Analysis · Mathematics 2020-02-17 Philipp Grohs , Sarah Koppensteiner , Martin Rathmair

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…

Information Theory · Computer Science 2017-01-10 David Gross , Felix Krahmer , Richard Kueng

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

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…

Information Theory · Computer Science 2019-10-02 Gilles Baechler , Miranda Kreković , Juri Ranieri , Amina Chebira , Yue M. Lu , Martin Vetterli

The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…

Optimization and Control · Mathematics 2017-08-30 Jian-Feng Cai , Haixia Liu , Yang Wang

Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display…

Image and Video Processing · Electrical Eng. & Systems 2020-03-05 Yaotian Wang , Xiaohang Sun , Jason W. Fleischer

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…

Optimization and Control · Mathematics 2017-04-11 Irène Waldspurger

Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…

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,…

The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present…

Optimization and Control · Mathematics 2023-06-23 Rossen Nenov , Dang-Khoa Nguyen , Peter Balazs , Radu Ioan Bot

This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…

Machine Learning · Computer Science 2018-08-20 Fahad Shamshad , Ali Ahmed

Classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms including the hybrid input-output (HIO) method, the…

Image and Video Processing · Electrical Eng. & Systems 2019-08-20 Çağatay Işıl , Figen S. Oktem , Aykut Koç

In this paper, we consider the problem of phase retrieval, which consists of recovering an $n$-dimensional real vector from the magnitude of its $m$ linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm…

Optimization and Control · Mathematics 2024-06-21 Jean-Jacques Godeme , Jalal Fadili , Xavier Buet , Myriam Zerrad , Michel Lequime , Claude Amra

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

Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…

Information Theory · Computer Science 2017-06-13 Wen-Jun Zeng , H. C. So

This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\langle{a}_i,x\rangle|^2$ for $1\le i \le m$, which is also known as phase retrieval and is NP-hard in general. We put forth…

Optimization and Control · Mathematics 2017-05-31 Gang Wang , Georgios B. Giannakis , Yousef Saad , Jie Chen

Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…

Signal Processing · Electrical Eng. & Systems 2022-06-28 Jonas Kornprobst , Alexander Paulus , Josef Knapp , Thomas F. Eibert