arXiv research

New algorithms handle phase retrieval with rank d measurements, revealing phase transitions.

UPR hybrid model improves phase retrieval performance.

New method uses generative models to improve phase retrieval stability.

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural …

A new deep learning model improves phase retrieval performance.

Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide accurate initialization vectors. We propose a novel class of estimators suitable fo…

Combines deep learning and iterative methods for robust phase retrieval.

Near-optimal sample complexity for phase retrieval with generative priors.

DeepPhaseCut uses neural networks to improve Fourier phase retrieval.

Global stability bounds for matrix frames in phase retrieval problems.

Descending phase retrieval algorithms show a phase transition with increasing sample complexity.

Gradient descent variants improve phase retrieval accuracy.

Extends phase retrieval methods to handle sensing vector errors.

Study phase retrieval under misspecified models using generative priors.

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are suffici…

This paper introduces SRPR for robust phase retrieval with smoothed loss functions.

New algorithm solves phase retrieval with adaptive stopping criteria.

Paper tackles sparse phase retrieval with a novel Bayesian approach.

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to …

In this paper, we propose the application of conditional generative adversarial networks to solve various phase retrieval problems. We show that including knowledge of the measurement process at training time leads to an optimization at test time that is more robust to initialization than existing approaches involving …

Optimal spectral initializers impact phase retrieval phase transitions.

Deep learning tackles low-photon nanoscale holographic phase retrieval.

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 of a complex-valued linear transformation of the original image. Several recent …

Paper tackles phase retrieval with robust gradient descent for noisy data.

New method uses image registration to recover complex signals from amplitude data.

We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the r…

Study on InstaHide's security, linking to phase retrieval problem.

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP) in methods such as PhaseLift and compete with recently developed non-convex techn…

Continuous-time mirror descent solves sparse phase retrieval efficiently.

Improved regret bounds for bandit phase retrieval.

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval …

Paper studies early-stopped mirror descent for noisy sparse phase retrieval.

This paper introduces and solves the simultaneous source separation and phase retrieval (S$^3$PR) problem. S$^3$PR is an important but largely unsolved problem in a number application domains, including microscopy, wireless communication, and imaging through scattering media, where one has multiple independent coherent…

Study shows how anisotropic data affects learning dynamics in phase retrieval.

Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in terms of retrieval capabilities, both at low and high load. We study the paramagnet…

In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set $\fc$ of $m$ vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a pertu…

In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to …

New error bounds for noisy phase retrieval problems using empirical risk minimization.

We consider the large-scale query-document retrieval problem: given a query (e.g., a question), return the set of relevant documents (e.g., paragraphs containing the answer) from a large document corpus. This problem is often solved in two steps. The retrieval phase first reduces the solution space, returning a subset …

SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.

Gradient flow in phase retrieval escapes spurious minima with high probability.

Paper proposes a new method for PCA using generative models.

In phase retrieval we want to recover an unknown signal $\boldsymbol x\in\mathbb C^d$ from $n$ quadratic measurements of the form $y_i = |\langle{\boldsymbol a}_i,{\boldsymbol x}\rangle|^2+w_i$ where $\boldsymbol a_i\in \mathbb C^d$ are known sensing vectors and $w_i$ is measurement noise. We ask the following weak rec…

This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm for random Gaussian measurements (practically relevant in imaging through scatt…

Guarantees uniform convergence for square-root Lipschitz losses.

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + ε_j$, $j=1, \ldots, m$, with independent sub-exponential noise $ε_j$. The goals are to understand the effect of the sparsity of $x$ on the estimation prec…

Two-stage risk control for ranked retrieval systems.

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 model is motivated by applications such as channel estimation, optics, and u…