相关论文: Enforcing uniqueness in one-dimensional phase retr…

Motivated by the X-ray crystallography technology to determine the atomic structure of biological molecules, we study the crystallographic phase retrieval problem, arguably the leading and hardest phase retrieval setup. This problem entails…

Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…

The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here we study in detail conditions under which a signal can be determined from…

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…

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein…

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…

The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable…

Let $G$ be a finite abelian group. Let $f: G \to {\mathbb C}$ be a signal (i.e. function). The classical uncertainty principle asserts that the product of the size of the support of $f$ and its Fourier transform $\hat f$, $\text{supp}(f)$…

In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…

We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…

Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is…

This paper studies the phase-only reconstruction problem of recovering a complex-valued signal $\textbf{x}$ in $\mathbb{C}^d$ from the phase of $\textbf{Ax}$ where $\textbf{A}$ is a given measurement matrix in $\mathbb{C}^{m\times d}$. The…

This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…

This paper focuses on phase retrieval from phaseless total-field data in biharmonic scattering problems. We prove that a phased biharmonic wave can be uniquely determined by the modulus of the total biharmonic wave within a nonempty domain.…

Suppose that a sequence of numbers $x_n$ (a `signal') is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \xi_n$, where $\xi_n$ is a sequence of independent…

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…

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…

The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…

This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…