Related papers: Phase-Retrieval as a Regularization Problem

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…

One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…

We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple…

Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…

This paper addresses fundamental scaling issues that hinder phase retrieval (PR) in high dimensions. We show that, if the measurement matrix can be put into a generalized block-diagonal form, a large PR problem can be solved on separate…

We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…

The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…

State of the art methods in astronomical image reconstruction rely on the resolution of a regularized or constrained optimization problem. Solving this problem can be computationally intensive and usually leads to a quadratic or at least…

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…

Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…

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.…

Phase retrieval is an ill-posed inverse problem in which classical and deep learning-based methods struggle to jointly achieve measurement fidelity and perceptual realism. We propose a novel framework for phase retrieval that leverages…

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…

Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances…

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…

Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Phase retrieval aims to recover a signal from magnitude or power spectra measurements. It is often addressed by considering a minimization problem involving a quadratic cost function. We propose a different formulation based on Bregman…