Related papers: Phasebook: A Survey of Selected Open Problems in P…
We will answer the most significant open problem in real phase retrieval by projections by showing it requires at least $2n-2$ projections to do phase retrieval in $\RR^n$.
The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in…
Programmable photonic integrated circuits (PICs), offering diverse signal processing functions within a single chip, are promising solutions for applications ranging from optical communications to artificial intelligence. While the scale…
Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the…
The principal limitation in many areas of astronomy, especially for directly imaging exoplanets, arises from instability in the point spread function (PSF) delivered by the telescope and instrument. To understand the transfer function, it…
This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming…
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…
This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…
Most methods tackling the phase retrieval problem of magnitude-only antenna measurements suffer from unrealistic sampling requirements, from unfeasible computational complexities, and, most severely, from the lacking reliability of…
In this paper, we provide a detailed overview of the models used for information retrieval in the first and second stages of the typical processing chain. We discuss the current state-of-the-art models, including methods based on terms,…
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…
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…
The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum…
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,…
We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
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…
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 the recovery of the phase information of a signal from…
Wavefront sensing involves estimating the phase and intensity of light, enabling a wide range of imaging applications, from adaptive optics and astronomy to biomedical imaging. Since conventional image sensors can only measure the spatial…
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…