相关论文: PhaseLift: Exact and Stable Signal Recovery from M…
This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…
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…
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…
Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…
Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
Phase retrieval aims to recover a signal $x \in \mathbb{C}^{n}$ from its amplitude measurements $|<x, a_i > |^2$, $i=1,2,...,m$, where $a_i$'s are over-complete basis vectors, with $m$ at least $3n -2$ to ensure a unique solution up to a…
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 $…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
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…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…
The PhaseLift algorithm is an effective convex method for solving the phase retrieval problem from Fourier measurements with coded diffraction patterns (CDP). While exact reconstruction guarantees are well-established in the noiseless case,…
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.…
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…
This note shows that we can recover a complex vector x in C^n exactly from on the order of n quadratic equations of the form |<a_i, x>|^2 = b_i, i = 1, ..., m, by using a semidefinite program known as PhaseLift. This improves upon earlier…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…