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Related papers: Numerical methods for phase retrieval

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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

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. Our approach combines multiple structured illuminations…

Information Theory · Computer Science 2011-09-21 Emmanuel J. Candes , Yonina Eldar , Thomas Strohmer , Vlad Voroninski

The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert

The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…

Information Theory · Computer Science 2016-12-21 Dani Kogan , Yonina C. Eldar , Dan Oron

Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…

Image and Video Processing · Electrical Eng. & Systems 2021-06-21 Tobias Uelwer , Tobias Hoffmann , Stefan Harmeling

We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…

Optics · Physics 2021-05-14 Byungjae Hwang , Taeseong Woo , Cheolwoo Ahn , Jung-Hoon Park

In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…

Medical Physics · Physics 2010-03-18 Wenxiang Cong , Ge Wang

Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…

Machine Learning · Computer Science 2023-01-20 Tobias Uelwer , Sebastian Konietzny , Stefan Harmeling

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…

Data Structures and Algorithms · Computer Science 2023-11-21 Yeqi Gao , Zhao Song , Baocheng Sun , Omri Weinstein , Ruizhe Zhang

Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…

Image and Video Processing · Electrical Eng. & Systems 2025-09-19 Stanislas Ducotterd , Zhiyuan Hu , Michael Unser , Jonathan Dong

This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…

Optimization and Control · Mathematics 2016-11-03 Kejun Huang , Yonina C. Eldar , Nicholas D. Sidiropoulos

Coherent X-ray beams with energies $\geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction…

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

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

This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches…

Signal Processing · Electrical Eng. & Systems 2026-01-14 Neil Irwin Bernardo

Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…

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…

A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…

Image and Video Processing · Electrical Eng. & Systems 2020-06-03 Igor Shevkunov , Vladimir Katkovnik , Karen Egiazarian

In this paper, we present a new algorithm, called MagnitudeCut, for recovering a signal from the phase of its Fourier transform. We casted our recovering problem into a new convex optimization problem, and then solved it by the block…

Numerical Analysis · Computer Science 2016-03-02 Jiasong Wu , Jieyuan Liu , Youyong Kong , Xu Han , Lotfi Senhadji , Huazhong Shu

Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…

Computational Physics · Physics 2013-02-04 Zai Yang , Cishen Zhang , Lihua Xie