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Quantum optical coherence tomography (Q-OCT) offers a factor-of-two improvement in axial resolution and the advantage of even-order dispersion cancellation when it is compared to conventional OCT (C-OCT). These features have been ascribed…

Quantum Physics · Physics 2009-11-13 Baris I. Erkmen , Jeffrey H. Shapiro

A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…

Information Theory · Computer Science 2017-10-17 Oussama Dhifallah , Christos Thrampoulidis , Yue M. Lu

The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping which is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function…

Computational Physics · Physics 2019-10-29 N. A. Lopez , I. Y. Dodin

Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one…

Optimization and Control · Mathematics 2015-02-17 Paul Hand

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…

Numerical Analysis · Mathematics 2025-10-20 Veit Elser

The quaternionic offset linear canonical transform (QOLCT) can be thought as a generalization of the quaternionic linear canonical transform (QLCT). In this paper we define the QOLCT, we derive the relationship between the QOLCT and the…

Classical Analysis and ODEs · Mathematics 2019-09-19 Youssef El Haoui , Said Fahlaoui , Eckhard Hitzer

A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…

Numerical Analysis · Mathematics 2021-12-16 Jian-Feng Cai , Meng Huang , Dong Li , Yang Wang

We consider the problem of recovering an unknown signal $\pmb{x}_0\in \mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex phase retrieval problem via PhaseLift from linear Gaussian measurements perturbed by…

Information Theory · Computer Science 2023-11-23 Gao Huang , Song Li , Hang Xu

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…

Machine Learning · Statistics 2017-05-19 Huishuai Zhang , Yuejie Chi , Yingbin Liang

Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…

Optimization and Control · Mathematics 2019-11-21 Bing Gao , Haixia Liu , Yang Wang

Phase retrieval aims to recover a signal $x \in \mathbb{C}^{n}$ from its amplitude measurements $|<x, a_i > |^2$, $i=1,2,...,m$, where $a_i$'s are over-complete basis vectors, with $m$ at least $3n -2$ to ensure a unique solution up to a…

Optimization and Control · Mathematics 2014-10-09 Penghang Yin , Jack Xin

We propose a numerical interferometry method for identification of optical multiply-scattering systems when only intensity can be measured. Our method simplifies the calibration of optical transmission matrices from a quadratic to a linear…

Signal Processing · Electrical Eng. & Systems 2020-02-17 Sidharth Gupta , Rémi Gribonval , Laurent Daudet , Ivan Dokmanić

The problem of recovering a signal from the magnitude of its short-time Fourier transform (STFT) is a longstanding one in audio signal processing. Existing approaches rely on heuristics that often perform poorly because of the nonconvexity…

Applications · Statistics 2012-09-11 Dennis L. Sun , Julius O. Smith

The ambiguity function (AF) is a critical tool in radar waveform design, representing the two-dimensional correlation between a transmitted signal and its time-delayed, frequency-shifted version. Obtaining a radar signal to match a…

Signal Processing · Electrical Eng. & Systems 2025-10-10 Samuel Pinilla , Kumar Vijay Mishra , Brian M. Sadler

This paper proposes a graph linear canonical transform (GLCT) by decomposing the linear canonical parameter matrix into fractional Fourier transform, scale transform, and chirp modulation for graph signal processing. The GLCT enables…

General Mathematics · Mathematics 2024-07-18 Jian Yi Chen , Bing Zhao Li

The aim of this paper is to pursue the investigation of the phase retrieval problem for the fractional Fourier transform $\ff\_\alpha$ started by the second author. We here extend a method of A.E.J.M Janssen to show that there is a…

Classical Analysis and ODEs · Mathematics 2015-01-19 Simon Andreys , Philippe Jaming

The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…

Information Theory · Computer Science 2025-06-27 Zhiqiang Xu

Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…

Numerical Analysis · Mathematics 2021-11-11 Rima Alaifari , Matthias Wellershoff

In this work, we propose a novel consistency-preserving loss function for recovering the phase information in the context of phase reconstruction (PR) and speech enhancement (SE). Different from conventional techniques that directly…

Audio and Speech Processing · Electrical Eng. & Systems 2024-09-25 Pin-Jui Ku , Chun-Wei Ho , Hao Yen , Sabato Marco Siniscalchi , Chin-Hui Lee

In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is…

Signal Processing · Electrical Eng. & Systems 2018-03-12 Haiye Huo , Wenchang Sun