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Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert

This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…

Information Theory · Computer Science 2014-10-28 Çağkan Yapar , Volker Pohl , Holger Boche

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 deals with the recovery of complex- or real-valued signals from magnitude measurements. As shown recently, the method PhaseMax enables phase retrieval via convex optimization and without lifting the problem to a higher…

Information Theory · Computer Science 2018-02-02 Ramina Ghods , Andrew S. Lan , Tom Goldstein , Christoph Studer

Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…

Machine Learning · Statistics 2015-06-15 Praneeth Netrapalli , Prateek Jain , Sujay Sanghavi

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

In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…

Information Theory · Computer Science 2016-06-13 Ritesh Kolte , Ayfer Özgür

We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…

Numerical Analysis · Mathematics 2016-12-07 Mark A. Iwen , Brian Preskitt , Rayan Saab , Aditya Viswanathan

We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…

Statistics Theory · Mathematics 2018-04-24 John C. Duchi , Feng Ruan

In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…

Optics · Physics 2012-03-22 Eliyahu Osherovich

We propose a novel iterative phase estimation framework, termed multi-source Griffin-Lim algorithm (MSGLA), for speech enhancement (SE) under additive noise conditions. The core idea is to leverage the ad-hoc consistency constraint of…

Audio and Speech Processing · Electrical Eng. & Systems 2025-07-04 Chun-Wei Ho , Pin-Jui Ku , Hao Yen , Sabato Marco Siniscalchi , Yu Tsao , Chin-Hui Lee

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,…

Information Theory · Computer Science 2023-07-19 Yoav Shechtman , Amir Beck , Yonina C. Eldar

We learn audio representations by solving a novel self-supervised learning task, which consists of predicting the phase of the short-time Fourier transform from its magnitude. A convolutional encoder is used to map the magnitude spectrum of…

Audio and Speech Processing · Electrical Eng. & Systems 2019-10-29 Félix de Chaumont Quitry , Marco Tagliasacchi , Dominik Roblek

Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is…

Information Theory · Computer Science 2019-05-22 Ziyang Yuan , Hongxia Wang

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

The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required…

Information Theory · Computer Science 2016-05-25 Kishore Jaganathan , Yonina C. Eldar , Babak Hassibi

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

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

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

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