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We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…

Statistics Theory · Mathematics 2021-02-18 Antoine Maillard , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…

Information Theory · Computer Science 2016-09-21 Cheng Qian , Nicholas D. Sidiropoulos , Kejun Huang , Lei Huang , H. C. So

In this paper, we consider an intelligent reflecting surface (IRS)-aided single-user system where an IRS with discrete phase shifts is deployed to assist the uplink communication. A practical transmission protocol is proposed to execute…

Information Theory · Computer Science 2019-12-24 Changsheng You , Beixiong Zheng , Rui Zhang

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially…

Machine Learning · Computer Science 2019-02-05 Y. Yu , H. Zhao , R. C. de Lamare , Y. Zakharov , L. Lu

We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time…

Numerical Analysis · Mathematics 2012-01-17 Gaurav Thakur , Hau-Tieng Wu

In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common…

Machine Learning · Computer Science 2019-12-17 Wei Cai , Xiaoguang Li , Lizuo Liu

Accurately recovering images from phaseless measurements is a challenging and long-standing problem. In this work, we present "deepECpr," which combines expectation-consistent (EC) approximation with deep denoising networks to surpass…

Computer Vision and Pattern Recognition · Computer Science 2024-11-27 Saurav K. Shastri , Philip Schniter

We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…

Information Theory · Computer Science 2022-10-03 Antoine Maillard , Florent Krzakala , Yue M. Lu , Lenka Zdeborová

Optical phase determination is an important and established tool in diverse fields such as astronomy, biology, or quantum optics. There is increasing interest in using a lower number of total photons. However, different noise sources, such…

Quantum Physics · Physics 2024-02-21 Q. Pears Stefano , A. G. Magnoni , D. Rodrigues , J. Tiffenberg , C. Iemmi

Extensive research on Reconfigurable Intelligent Surfaces (RIS) has primarily focused on optimizing reflective coefficients for passive beamforming in specific target directions. This optimization typically assumes prior knowledge of the…

Signal Processing · Electrical Eng. & Systems 2025-12-05 Xiao Cai , Hei Victor Cheng , Daniel E. Lucani

Determining the phase of a wave from intensity measurements has many applications in fields such as electron microscopy, visible light optics, and medical imaging. Propagation based phase retrieval, where the phase is obtained from…

Image and Video Processing · Electrical Eng. & Systems 2018-04-10 Zachary David Cleary Kemp

Phase aberration is an inherent side effect of ultrasound imaging due to the speed of sound inhomogeneity nature of human tissues, resulting in focusing error and reduced image contrast. This work introduces a phase aberration correction…

Signal Processing · Electrical Eng. & Systems 2023-08-29 Wei-Hsiang Shen , Yu-An Lin , Pai-Chi Li , Meng-Lin Li

We present a dual-wavelength external holographic microscopy module for quantitative phase imaging of 3D structures with extended thickness range. This is done by simultaneous acquisition of two off-axis interferograms, each of which at a…

Optics · Physics 2019-04-10 Nir A. Turko , Natan T. Shaked

We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…

Information Theory · Computer Science 2016-11-17 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi

We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…

Information Theory · Computer Science 2018-07-18 M. Salman Asif , Chinmay Hegde

We introduce an ultra-sensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA + interferometry uses weak value amplification of the relative delay between two paths…

Quantum Physics · Physics 2025-03-03 Jing-Hui Huang , Kyle M. Jordan , Adetunmise C. Dada , Xiang-Yun Hu , Jeff. S. Lundeen

This paper discusses different approaches used for millimeter wave imaging of two-dimensional objects. Imaging of a two dimensional object requires reflected wave data to be collected across two distinct dimensions. In this paper, we…

Computer Vision and Pattern Recognition · Computer Science 2014-04-21 Sujeet Patole , Murat Torlak

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

Machine learning is attracting surging interest across nearly all scientific areas by enabling the analysis of large datasets and the extraction of scientific information from incomplete data. Data-driven science is rapidly growing,…

Applied Physics · Physics 2025-03-17 Sung Yun Lee , Do Hyung Cho , Chulho Jung , Daeho Sung , Daewoong Nam , Sangsoo Kim , Changyong Song

If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…

Numerical Analysis · Mathematics 2013-05-20 Yuan Sun