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Related papers: Sparse Phase Retrieval from Short-Time Fourier Mea…

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One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…

Instrumentation and Detectors · Physics 2018-05-23 Minmin Wang , Canlin Zhou , Shuchun Si , Zhenkun Lei , Xiaolei Li , Hui Li , YanJie Li

Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier…

Classical Analysis and ODEs · Mathematics 2026-01-19 Shrikant Chand , James Nolen , Hau-Tieng Wu

This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…

Information Theory · Computer Science 2012-10-17 Jun Fang , Yanning Shen , Hongbin Li

In this paper, we propose a differentiable version of the short-time Fourier transform (STFT) that allows for gradient-based optimization of the hop length or the frame temporal position by making these parameters continuous. Our approach…

Signal Processing · Electrical Eng. & Systems 2023-08-07 Maxime Leiber , Yosra Marnissi , Axel Barrau , Mohammed El Badaoui

Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called…

Optimization and Control · Mathematics 2013-07-23 Irène Waldspurger , Alexandre d'Aspremont , Stéphane Mallat

Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…

Information Theory · Computer Science 2023-01-19 Robert Beinert , Saghar Rezaei

A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form…

Information Theory · Computer Science 2017-04-05 Gang Wang , Georgios B. Giannakis , Jie Chen

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…

Data Analysis, Statistics and Probability · Physics 2013-04-09 M. Andrecut

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…

Optimization and Control · Mathematics 2016-11-23 Andreas M. Tillmann , Yonina C. Eldar , Julien Mairal

Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of…

Machine Learning · Computer Science 2023-02-14 Hadi Daneshmand , Francis Bach

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 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

This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…

Information Theory · Computer Science 2016-08-24 Tianyu Qiu , Prabhu Babu , Daniel P. Palomar

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

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new…

Machine Learning · Statistics 2018-01-08 Jinghui Chen , Lingxiao Wang , Xiao Zhang , Quanquan Gu

Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…

Information Theory · Computer Science 2015-12-08 Ljubisa Stankovic , Isidora Stankovic

The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…

Information Theory · Computer Science 2018-07-12 Paul Hand , Oscar Leong , Vladislav Voroninski

Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the…

Computation · Statistics 2024-10-10 Hajime Ueda , Shun Katakami , Masato Okada

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST,…

Numerical Analysis · Mathematics 2017-09-20 Alexander Berrian , Naoki Saito

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…

Image and Video Processing · Electrical Eng. & Systems 2020-07-30 Rakib Hyder , Zikui Cai , M. Salman Asif