UPR hybrid model improves phase retrieval performance.
problem Recovering signals from phase-less measurements.
method Model-based data-driven deep architecture (UPR).
result UPR shows potential in improving phase retrieval.
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48 results for “Retrieval Phase”
A new deep learning model improves phase retrieval performance.
problem Recovering signals from phaseless measurements.
method Hybrid model-based data-driven deep architecture (Unfolded Phase Retrieval, UPR).
result Significant improvement in phase retrieval performance.
New linear spectral estimators improve phase retrieval accuracy.
problem Recovering vectors from magnitude measurements.
method Linear Spectral Estimators (LSPEs) for phase retrieval.
result LSPEs provide accurate initialization vectors and sharp error bounds.
New algorithms handle phase retrieval with rank d measurements, revealing phase transitions.
problem Phase retrieval with rank d measurements.
method Random duality theory (RDT) and descending phase retrieval algorithms (dPR).
result Minimal sample complexity ratio for dPR's success exhibits phase transitions.
Combines deep learning and iterative methods for robust phase retrieval.
problem Recovering signals from noisy Fourier intensities.
method Regularization-by-denoising combining iterative phase retrieval and deep learning.
result Outperforms other noise-robust phase retrieval algorithms.
Sharp asymptotics derived for phase retrieval and compressed sensing with random generative priors.
problem Phase retrieval and compressed sensing with random measurement matrices.
method Sharp asymptotics derived for optimal performance and polynomial algorithm for random generative priors.
result Compressed phase retrieval becomes tractable with random generative priors, unlike sparse priors.
Extends phase retrieval methods to handle sensing vector errors.
problem Phase retrieval with errors in sensing vectors.
method Total Least Squares (TLS) framework applied to gradient descent.
result Gradient descent can efficiently solve TLS phase retrieval.
New method solves phase retrieval problems efficiently without lifting.
problem Phase retrieval from phaseless measurements.
method Flexible convex relaxation in signal domain, solving inequalities representing slabs.
result Convex program finds best aligned extreme point of slab intersection.
prDeep uses a deep neural network to robustly retrieve phases from noisy data.
problem Noise limits traditional phase retrieval algorithms' performance.
method Regularization-by-denoising framework and convolutional neural network.
result prDeep is robust to noise and can handle various system models.
New algorithm recovers signals from noisy measurements with optimal precision.
problem Recovering signals from magnitude-only measurements with arbitrary corruption.
method Robust Wirtinger Flow algorithm for joint signal and corruption estimation.
result Guaranteed linear convergence to optimal precision with optimal sample complexity.
Proposes using GANs to solve phase retrieval problems.
problem Solving phase retrieval problems in various contexts.
method Applying conditional GANs with knowledge of measurement process.
result Method provides more robust and detailed solutions.
This paper introduces SRPR for robust phase retrieval with smoothed loss functions.
problem Robust phase retrieval from noisy quadratic measurements with corruptions.
method Smoothed robust phase retrieval (SRPR) using convolution-type smoothed loss functions.
result SRPR has no spurious local solutions and benign landscape under corruptions.
New method uses generative models to improve phase retrieval stability.
problem Improving stability of solutions in phase retrieval problems.
method Unified reconstruction approach using generative models to mitigate overfitting.
result Mitigates overfitting to generative model for varying noise levels.
A New Inexact Proximal Linear Algorithm with Adaptive Stopping Criteria for Robust Phase Retrievalmath.OC
New algorithm solves phase retrieval with adaptive stopping criteria.
problem Robust phase retrieval problem as nonsmooth, nonconvex optimization.
method Inexact proximal linear algorithm with adaptive stopping criteria.
result Proposed methods are more efficient than existing methods.
New algorithm converges to optimal phase retrieval estimator with misspecified link functions.
problem High-dimensional sparse phase retrieval with incorrect model specification.
method Simple variant of thresholded Wirtinger flow algorithm, linear convergence for optimal accuracy.
result Linear convergence to optimal estimator for a broad family of unknown link functions.
Paper proposes a method for estimating complex low-rank matrices from phase-only measurements.
problem Estimating complex low-rank matrices from magnitude-only measurements.
method A hierarchical prior model with a Gaussian-Wishart distribution is used to promote low-rankness. A variational EM algorithm is developed to solve the problem.
result The proposed method is less sensitive to initialization and performs well with random initialization.
DeepPhaseCut uses neural networks to improve Fourier phase retrieval.
problem Fourier phase retrieval from magnitude data.
method Unsupervised feed-forward neural network with cycleGAN training.
result Outperforms existing methods in Fourier phase retrieval.
Study phase transitions in RBMs with generic priors.
problem Understanding phase transitions in RBMs with various priors.
method Complete analysis of phase diagram, focusing on retrieval phase and paramagnetic phase boundary.
result Retrieval robustness for a wide range of priors and optimal training set size for generalization.
Paper proposes a new method for sparse phase retrieval with fewer measurements.
problem Sparse phase retrieval in various fields.
method Stochastic alternating minimizing method (StormSpar) with HTP algorithm.
result The method recovers sparse signals from fewer measurements than existing methods.
Paper tackles sparse phase retrieval with a novel Bayesian approach.
problem Sparse phase retrieval from magnitude-only data.
method Quasi-Bayesian approach using a scaled Student distribution.
result Achieves minimax-optimal convergence rates under sub-exponential noise.
Descending phase retrieval algorithms show a phase transition with increasing sample complexity.
problem Theoretical limits of descending phase retrieval algorithms.
method Utilizing Random duality theory (RDT), the study develops a generic program to characterize algorithm performance.
result As sample complexity increases, the parametric manifold transitions from multi to single funneling points, leading to a phase transition in algorithm success.
Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priorscond-mat.dis-nn
The study examines the retrieval capabilities of RBMs and generalized Hopfield networks under various prior distributions.
problem Characterizing the state of RBMs and Hopfield networks under different prior distributions.
method Equivalence between RBMs and generalized Hopfield networks, analysis of phase transitions, and study of retrieval capabilities.
result The retrieval phase is robust and exists at low load for every pattern distribution.
Global stability bounds for matrix frames in phase retrieval problems.
problem Phase retrieval for matrix frames in various applications.
method Computable global stability bounds for the quasi-linear analysis map β, using Whitney stratification of positive semidefinite matrices of low rank.
result Novel conditions for a frame to be generalized phase retrievable.
Near-optimal sample complexity for phase retrieval with generative priors.
problem Phase retrieval with magnitude-only measurements and sparse signals.
method Near-optimal sample complexity with i.i.d. Gaussian measurements and generative models.
result O(k log L) samples suffice for phase retrieval with generative priors.
Deep learning tackles low-photon nanoscale holographic phase retrieval.
problem Low-photon imaging challenges at nanoscale.
method Dataset-free deep learning framework with physical model integration.
result Significantly improves signal recovery from higher noise levels.
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.
problem Recover signals from magnitude measurements with noise and corruption.
method Robust gradient descent applied to Wirtinger Flow algorithm.
result Improves algorithm's robustness to heavy-tailed noise and adversarial corruption.
New framework uses deep generative priors for robust phase retrieval.
problem Highly ill-posed and non-linear phase retrieval problem.
method Regularization through deep generative priors with gradient descent.
result Effective for random Gaussian and Fourier friendly measurements.
New method uses image registration to recover complex signals from amplitude data.
problem Recovering complex-valued signals from amplitude measurements.
method Indirect registration using LDDMM formalism with exterior calculus.
result Algorithm performs well under various conditions including noise and topology.
Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problemcond-mat.dis-nn
Gradient descent variants improve phase retrieval accuracy.
problem Phase retrieval problem in high-dimensional spaces.
method Gradient descent, stochastic gradient descent, Langevin algorithm, dynamical mean-field theory.
result Stochastic variants of gradient descent achieve better generalization in phase retrieval.
Transformer models improve query-document retrieval efficiency and accuracy.
problem Efficiently retrieve relevant documents from large corpora for query matching.
method Designed paragraph-level pre-training tasks to optimize embedding-based Transformer models.
result Transformer models significantly outperform BM-25 and non-Transformer embedding models.
Paper analyzes ADMM convergence for nonconvex Gaussian phase retrieval.
problem Nonconvex optimization in Gaussian phase retrieval.
method Block coordinate descent as ADMM with dual variable fixed.
result Block coordinate descent converges linearly to global minimizer.
Deep neural network estimates support of sparse signals for improved phase retrieval.
problem Sparse phase retrieval from Fourier magnitudes with support estimation.
method Trained deep neural network (DNN) provides extended support estimate larger than the support .
result DNN-based support estimation improves signal reconstruction performance with lower complexity.
Paper analyzes the phase retrieval problem in X-ray imaging.
problem Phase retrieval problem in X-ray imaging of amorphous samples.
method Analysis of well-posedness and development of experimental protocols.
result The phase retrieval problem is generally ill-posed.
Continuous-time mirror descent solves sparse phase retrieval efficiently.
problem Recovering sparse signals from magnitude-only measurements.
method Continuous-time mirror descent applied to unconstrained empirical risk minimization problem.
result Mirror descent recovers -sparse vectors with minimum non-zero entry order of from Gaussian measurements.
Bandit Phase Retrievalstat.ML
Improved regret bounds for bandit phase retrieval.
problem Minimizing cumulative and simple regret in a bandit phase retrieval problem.
method Proved minimax cumulative and simple regret bounds using adaptive algorithms.
result Minimax cumulative regret is and minimax simple regret is .
New proof shows 11 measurements needed for phase retrieval in 4D complex space.
problem Determining the minimal number of intensity measurements for phase retrieval in 4D complex space.
method Leveraged characteristic classes and cohomology groups from differential topology.
result Proved that 11 is the exact minimum number of measurements required for phase retrieval in 4D complex space.
Study shows how anisotropic data affects learning dynamics in phase retrieval.
problem Understanding learning dynamics in phase retrieval with anisotropic Gaussian inputs.
method Developed a tractable reduction to reveal a three-phase trajectory and derived scaling laws.
result Found that anisotropy leads to a three-phase trajectory: fast escape, slow convergence, and spectral-tail learning.
Study phase retrieval under misspecified models using generative priors.
problem Estimating signals from phase measurements with model misspecification.
method Two-step approach: spectral initialization followed by iterative refinement.
result Statistical rate of order under suitable conditions.
Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrievalstat.ML
Gradient descent with random initialization solves phase retrieval problems efficiently.
problem Solving systems of quadratic equations for phase retrieval.
method Gradient descent with random initialization for nonconvex least squares problem.
result Gradient descent achieves near-optimal computational and sample complexities for phase retrieval.
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 vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a pertu…
Solves a challenging problem in imaging and communication.
problem Simultaneous source separation and phase retrieval.
method Uses deep generative models to constrain the search space.
result Demonstrates solving a highly under-determined, non-convex problem.
Optimal spectral initializers impact phase retrieval phase transitions.
problem Understanding the limits of phase retrieval algorithms.
method Developed Random duality theory (RDT) to characterize optimal spectral initializers.
result Optimal spectral initializers can fall into flat regions of the phase retrieval manifold, making phase retrieval difficult.
The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Thresholdmath.FA
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…
Phase retrieval requires at least d+o(d) measurements to recover signals with high probability.
problem Recovering signals from quadratic measurements with noisy data.
method Used Gaussian sensing vectors and spectral methods to analyze the minimum number of measurements needed.
result A sharp phase transition occurs at n = d+o(d), where a simple spectral estimator achieves positive correlation.
Spectral Gradient Descent Mitigates Anisotropy-Driven Misalignment: A Case Study in Phase Retrievalstat.ML
SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.
problem Misalignment during gradient descent in phase retrieval models with anisotropic inputs.
method Spectral gradient descent modifies gradient updates to preserve directional information and remove spike amplification.
result SpecGD removes spike amplification, leading to stable alignment and accelerated noise contraction.
Gradient flow in phase retrieval escapes spurious minima with high probability.
problem Understanding gradient-based optimization in high-dimensional non-convex functions.
method Analytical and numerical study of gradient dynamics in phase retrieval.
result Gradient flow avoids spurious minima by drifting along unstable directions.
Nearly Minimax-Optimal Rates for Noisy Sparse Phase Retrieval via Early-Stopped Mirror Descenteess.SP
Paper studies early-stopped mirror descent for noisy sparse phase retrieval.
problem Recovering a sparse signal from noisy quadratic measurements.
method Early-stopped mirror descent with hyperbolic entropy mirror map.
result Achieves nearly minimax-optimal rate of convergence for -sparse signals.