Related papers: Fundamental Limits of PhaseMax for Phase Retrieval…
Phase retrieval refers to the problem of reconstructing an unknown vector $x_0 \in \mathbb{C}^n$ or $x_0 \in \mathbb{R}^n $ from $m$ measurements of the form $y_i = \big\vert \langle \xi^{\left(i\right)}, x_0 \rangle \big\vert^2 $, where $…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…
Phaseless super-resolution refers to the problem of superresolving a signal from only its low-frequency Fourier magnitude measurements. In this paper, we consider the phaseless super-resolution problem of recovering a sum of sparse Dirac…
Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed…
We consider a class of multivariate recurrences frequently arising in the worst case analysis of Davis-Putnam-style exponential time backtracking algorithms for NP-hard problems. We describe a technique for proving asymptotic upper bounds…
We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…
We consider the problem of recovering an unknown signal $\pmb{x}_0\in \mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex phase retrieval problem via PhaseLift from linear Gaussian measurements perturbed by…
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…
Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
Phase recovery of modified spectrograms is a major issue in audio signal processing applications, such as source separation. This paper introduces a novel technique for estimating the phases of components in complex mixtures within onset…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…
We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering…
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…
The recovery of a signal from the intensity measurements with some entries being known in advance is termed as {\em affine phase retrieval}. In this paper, we prove that a natural least squares formulation for the affine phase retrieval is…