相关论文: Phase Retrieval from 1D Fourier Measurements: Conv…
A linear and thus convex phase retrieval algorithm for the application in phaseless near-field far-field transformations is presented. The formulation exploits locally known phase relations among sets of measurement samples, which can in…
Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C…
Phase-retrieval techniques aim to recover the original signal from just the modulus of its Fourier transform, which is usually much easier to measure than its phase, but the standard iterative techniques tend to fail if only part of the…
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…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
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…
In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $…
This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…
Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every…
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…
The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding…
We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…