arXiv research

New model resolves signal ambiguities in ill-posed systems.

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 …

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…

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 …

UPR hybrid model improves phase retrieval performance.

On most sponsored search platforms, advertisers bid on some keywords for their advertisements (ads). Given a search request, ad retrieval module rewrites the query into bidding keywords, and uses these keywords as keys to select Top N ads through inverted indexes. In this way, an ad will not be retrieved even if querie…

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

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

This paper tackles non-convex phase retrieval with structured assumptions.

GWCA analyzes cross-graph correlations for movie retrieval.

A new deep learning model improves phase retrieval performance.

The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shi…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a fundamental challenge in bio-,astronomical imaging and speech processing. The problem abov…

Paper tackles sparse phase retrieval with a novel Bayesian approach.

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

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

Combines deep learning and iterative methods for robust phase retrieval.

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

Continuous-time mirror descent solves sparse phase retrieval efficiently.

New method uses generative models to improve phase retrieval stability.

SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.

Hadamard Wirtinger Flow recovers sparse signals from fewer measurements.

Generative AI improves stock selection by synthesizing features from diverse data sources.

Study phase retrieval under misspecified models using generative priors.

Deep learning tackles low-photon nanoscale holographic phase retrieval.

This work takes the first steps towards solving the "phaseless subspace tracking" (PST) problem. PST involves recovering a time sequence of signals (or images) from phaseless linear projections of each signal under the following structural assumption: the signal sequence is generated from a much lower dimensional subsp…

GMC benchmark isolates retrieval in Transformers, revealing max-margin alignment.

We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover the $k$-sparse signal vector and its support $\mathcal{T}$. We exploit extended support estimate $\mathcal{E}$ with size larger than $k$ satisfying $\mathcal{E} \supseteq \mathcal{T}$ and obtained by a trained deep neural net…

Finding relevant information from large document collections such as the World Wide Web is a common task in our daily lives. Estimation of a user's interest or search intention is necessary to recommend and retrieve relevant information from these collections. We introduce a brain-information interface used for recomme…

Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information retrieval using deep-learning classifiers, such encodings are learnt on the flattened la…

Study shows overparametrization can shift and bend loss landscapes, affecting signal recovery.

New findings show sparse signals in MRA model require fewer measurements than previously thought.

FinTradeBench benchmarks LLMs for financial reasoning combining company fundamentals and market signals.

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

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 …

New method recovers signals from compressed measurements using generative networks with contractive layers.

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…

Paper presents a unique method to recover signals from their bispectrum.

A bridge between continuous signals and discrete Ising spins for associative memory.

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…

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…

DeepPhaseCut uses neural networks to improve Fourier phase retrieval.

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

Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.

We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in many practical applications. We develop a rank-1 projection algorithm that recovers the signal subject to ensuring cons…

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

Robot learns user preferences from brain signals.

We optimize rank-based metrics using blackbox differentiation.