Related papers: A Sample Efficient Alternating Minimization-based …
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 to recover the phase information of a signal from the…
Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization…
We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles $\theta_1,...,\theta_n$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \mod 2\pi$. Of…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
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…
The phase retrieval problem is concerned with recovering an unknown signal $\bf{x} \in \mathbb{R}^n$ from a set of magnitude-only measurements $y_j=|\langle \bf{a}_j,\bf{x} \rangle|, \; j=1,\ldots,m$. A natural least squares formulation can…
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,…
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…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Robustness to noise and outliers is a desirable trait in phase retrieval algorithms for many applications in imaging and signal processing. In this paper, we develop novel robust phase retrieval algorithms based on the minimization of…
Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These disturbances, arising due to many factors such as non-idealities…
This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…
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…
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…
The aim of sparse phase retrieval is to recover a $k$-sparse signal $\mathbf{x}_0\in \mathbb{C}^{d}$ from quadratic measurements $|\langle \mathbf{a}_i,\mathbf{x}_0\rangle|^2$ where $\mathbf{a}_i\in \mathbb{C}^d, i=1,\ldots,m$. Noting…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…