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Related papers: Phase retrieval with complexity guidance

200 papers

Reconstructing images from their Fourier magnitude measurements is a problem that often arises in different research areas. This process is also referred to as phase retrieval. In this work, we consider a modified version of the phase…

Image and Video Processing · Electrical Eng. & Systems 2021-10-27 Tobias Uelwer , Nick Rucks , Stefan Harmeling

The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…

Optimization and Control · Mathematics 2018-03-22 Sherry Xue-Ying Ni , Man-Chung Yue , Kam-Fung Cheung , Anthony Man-Cho So

Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of…

Signal Processing · Electrical Eng. & Systems 2026-03-02 Kumar Vijay Mishra , Henry Arguello , Brian M. Sadler

Phase retrieval(PR) problem is a kind of ill-condition inverse problem which can be found in various of applications. Utilizing the sparse priority, an algorithm called SWF(Sparse Wirtinger Flow) is proposed in this paper to deal with…

Information Theory · Computer Science 2017-04-12 Ziyang Yuan , Qi Wang , Hongxia Wang

We present a convex relaxation-based algorithm for large-scale general phase retrieval problems. General phase retrieval problems include i.a. the estimation of the phase of the optical field in the pupil plane based on intensity…

Optimization and Control · Mathematics 2018-08-15 Reinier Doelman , H. Thao Nguyen , Michel Verhaegen

The problem of phase retrieval is to determine a signal $f\in \mathcal{H}$, with $\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\omega)|$, where $F(\omega):=\langle f , \varphi_\omega\rangle$ are measurements of $f$ with…

Functional Analysis · Mathematics 2017-02-02 Rima Alaifari , Ingrid Daubechies , Philipp Grohs , Rujie Yin

We aim to find a solution $\bm{x}\in\mathbb{C}^n$ to a system of quadratic equations of the form $b_i=\lvert\bm{a}_i^*\bm{x}\rvert^2$, $i=1,2,\ldots,m$, e.g., the well-known NP-hard phase retrieval problem. As opposed to recently proposed…

Optimization and Control · Mathematics 2019-05-28 Ji Li , Jian-Feng Cai , Hongkai Zhao

We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…

Classical Analysis and ODEs · Mathematics 2023-10-18 Philippe Jaming , Martin Rathmair

Companion paper [118] developed a powerful \emph{Random duality theory} (RDT) based analytical program to statistically characterize performance of \emph{descending} phase retrieval algorithms (dPR) (these include all variants of gradient…

Machine Learning · Statistics 2025-06-24 Mihailo Stojnic

Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half-century. Recent advances in deep learning have introduced new possibilities for a robust and fast…

Machine Learning · Computer Science 2021-11-10 Chang-Jen Wang , Chao-Kai Wen , Shang-Ho , Tsai , Shi Jin , Geoffrey Ye Li

A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…

Numerical Analysis · Mathematics 2017-07-04 Frank E. Curtis , Daniel P. Robinson , Mohammadreza Samadi

High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and…

Image and Video Processing · Electrical Eng. & Systems 2021-09-15 Xuyang Chang , Liheng Bian , Jun Zhang

Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless…

Machine Learning · Statistics 2020-12-22 Naveed Naimipour , Shahin Khobahi , Mojtaba Soltanalian

We introduce a fast Eikonal Phase Retrieval (EPR) formulation that accelerates eikonal phase retrieval by more than two orders of magnitude while retaining controlled accuracy. The method is derived from a second-order asymptotic expansion…

The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements.…

Signal Processing · Electrical Eng. & Systems 2020-03-11 Naveed Naimipour , Shahin Khobahi , Mojtaba Soltanalian

Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase…

Optics · Physics 2007-11-13 S. Marchesini

We consider the problem of signal reconstruction from quadratic measurements that are encoded as +1 or -1 depending on whether they exceed a predetermined positive threshold or not. Binary measurements are fast to acquire and inexpensive in…

Information Theory · Computer Science 2018-03-14 Subhadip Mukherjee , Chandra Sekhar Seelamantula

This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…

Image and Video Processing · Electrical Eng. & Systems 2020-07-17 Martin Reiche , Peter Jung

This paper provides a tutorial of iterative phase retrieval algorithms based on the Gerchberg-Saxton (GS) algorithm applied in digital holography. In addition, a novel GS-based algorithm that allows reconstruction of 3D samples is…

Optics · Physics 2019-11-19 Tatiana Latychevskaia

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