87 citations · 386 across the 17 of their papers we have counts for
23 papers
Optimal Sample Complexity of Subgradient Descent for Amplitude Flow via Non-Lipschitz Matrix Concentration
Paul Hand, Oscar Leong, Vladislav Voroninski
We consider the problem of recovering a real-valued -dimensional signal from phaseless, linear measurements and analyze the amplitude-based non-smooth least squares objectiv…
Compressive Phase Retrieval: Optimal Sample Complexity with Deep Generative Priors
Paul Hand, Oscar Leong, Vladislav Voroninski
Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodo…
Nonasymptotic Guarantees for Spiked Matrix Recovery with Generative Priors
Jorio Cocola, Paul Hand, Vladislav Voroninski
Many problems in statistics and machine learning require the reconstruction of a rank-one signal matrix from noisy data. Enforcing additional prior information on the rank-one comp…
A Provably Convergent Scheme for Compressive Sensing under Random Generative Priors
Wen Huang, Paul Hand, Reinhard Heckel +1
Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, d…
Phase Retrieval Under a Generative Prior
Paul Hand, Oscar Leong, Vladislav Voroninski
The phase retrieval problem asks to recover a natural signal from quadratic observations, where is to be minimized. As is common in many imaging prob…
Rate-Optimal Denoising with Deep Neural Networks
Reinhard Heckel, Wen Huang, Paul Hand +1
Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying princip…
Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs
Nicolas Boumal, Vladislav Voroninski, Afonso S. Bandeira
We consider semidefinite programs (SDPs) with equality constraints. The variable to be optimized is a positive semidefinite matrix of size . Following the Burer--Monteiro ap…
Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk
Paul Hand, Vladislav Voroninski
We examine the theoretical properties of enforcing priors provided by generative deep neural networks via empirical risk minimization. In particular we consider two models, one in…
A Survey of Structure from Motion
Onur Ozyesil, Vladislav Voroninski, Ronen Basri +1
The structure from motion (SfM) problem in computer vision is the problem of recovering the three-dimensional (D) structure of a stationary scene from a set of projective measur…
Corruption Robust Phase Retrieval via Linear Programming
Paul Hand, Vladislav Voroninski
We consider the problem of phase retrieval from corrupted magnitude observations. In particular we show that a fixed can be recovered exactly from corrupted…
An Elementary Proof of Convex Phase Retrieval in the Natural Parameter Space via the Linear Program PhaseMax
Paul Hand, Vladislav Voroninski
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 matric…
Compressed Sensing from Phaseless Gaussian Measurements via Linear Programming in the Natural Parameter Space
Paul Hand, Vladislav Voroninski
We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and ana…
ShapeFit and ShapeKick for Robust, Scalable Structure from Motion
Thomas Goldstein, Paul Hand, Choongbum Lee +2
We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence…
The non-convex Burer-Monteiro approach works on smooth semidefinite programs
Nicolas Boumal, Vladislav Voroninski, Afonso S. Bandeira
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and…
On the low-rank approach for semidefinite programs arising in synchronization and community detection
Afonso S. Bandeira, Nicolas Boumal, Vladislav Voroninski
To address difficult optimization problems, convex relaxations based on semidefinite programming are now common place in many fields. Although solvable in polynomial time, large se…
Exact simultaneous recovery of locations and structure from known orientations and corrupted point correspondences
Paul Hand, Choongbum Lee, Vladislav Voroninski
Let and and consider the bipartite location recovery problem: given a subset of pairwise direction obser…
ShapeFit: Exact location recovery from corrupted pairwise directions
Paul Hand, Choongbum Lee, Vladislav Voroninski
Let and consider the location recovery problem: given a subset of pairwise direction observations $\{(t_i - t_j) / \|t_i - t_j\|_2\}_{i<j \in [n]…
A strong restricted isometry property, with an application to phaseless compressed sensing
Vladislav Voroninski, Zhiqiang Xu
The many variants of the restricted isometry property (RIP) have proven to be crucial theoretical tools in the fields of compressed sensing and matrix completion. The study of exte…
Quantum Tomography From Few Full-Rank Observables
Vladislav Voroninski
We establish that the PhaseLift algorithm recovers pure states from a constant number of full-rank observables with high probability.
Determination of all pure quantum states from a minimal number of observables
Damien Mondragon, Vladislav Voroninski
We show that for any positive integer , the maps , where are the colu…
Sparse Signal Recovery from Quadratic Measurements via Convex Programming
Xiaodong Li, Vladislav Voroninski
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurem…
PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
Emmanuel J. Candes, Thomas Strohmer, Vladislav Voroninski
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We pr…
Phase Retrieval via Matrix Completion
Emmanuel J. Candes, Yonina Eldar, Thomas Strohmer +1
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. O…