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09/05/2023
A Fast and Provable Algorithm for Sparse Phase Retrieval
We study the sparse phase retrieval problem, which aims to recover a spa...
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09/04/2023
Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion
In recent years, patch-based image restoration approaches have demonstra...
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06/06/2023
Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret
We investigate a generalized framework for estimating latent low-rank te...
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05/10/2023
Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression
High-dimensional linear regression under heavy-tailed noise or outlier c...
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03/14/2023
Asymptotically Sharp Upper Bound for the Column Subset Selection Problem
This paper investigates the spectral norm version of the column subset s...
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10/26/2022
Provable Sample-Efficient Sparse Phase Retrieval Initialized by Truncated Power Method
We study the sparse phase retrieval problem, recovering an s-sparse leng...
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08/09/2022
Two Stage Continuous Domain Regularization for Piecewise Constant Image Restoration
The finite-rate-of-innovation (FRI) framework which corresponds a signal...
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07/15/2022
Approximation Theory of Total Variation Minimization for Data Completion
Total variation (TV) minimization is one of the most important technique...
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04/20/2022
Nearly optimal bounds for the global geometric landscape of phase retrieval
The phase retrieval problem is concerned with recovering an unknown sign...
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04/07/2022
Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion
We study the robust matrix completion problem for the low-rank Hankel ma...
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03/02/2022
Computationally Efficient and Statistically Optimal Robust Low-rank Matrix and Tensor Estimation
Low-rank matrix estimation under heavy-tailed noise is challenging, both...
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12/15/2021
The global landscape of phase retrieval II: quotient intensity models
A fundamental problem in phase retrieval is to reconstruct an unknown si...
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12/15/2021
The global landscape of phase retrieval I: perturbed amplitude models
A fundamental task in phase retrieval is to recover an unknown signal ∈ ...
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12/15/2021
Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization
In this work we propose a nonconvex two-stage stochastic alternating min...
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12/03/2021
Fast Projected Newton-like Method for Precision Matrix Estimation with Nonnegative Partial Correlations
We study the problem of estimating precision matrices in multivariate Ga...
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08/27/2021
Provable Tensor-Train Format Tensor Completion by Riemannian Optimization
The tensor train (TT) format enjoys appealing advantages in handling str...
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03/16/2021
Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization
We investigate a generalized framework to estimate a latent low-rank plu...
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12/12/2020
Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond
Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix ...
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07/17/2020
Provable Near-Optimal Low-Multilinear-Rank Tensor Recovery
We consider the problem of recovering a low-multilinear-rank tensor from...
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05/18/2020
Sparse Signal Recovery From Phaseless Measurements via Hard Thresholding Pursuit
In this paper, we consider the sparse phase retrival problem, recovering...
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11/08/2019
Off-the-Grid Compressed Sensing MRI Reconstruction via Data Driven Tight Frame Regularization
Recently, the finite-rate-of-innovation (FRI) based continuous domain re...
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10/13/2019
Fast and Robust Spectrally Sparse Signal Recovery: A Provable Non-Convex Approach via Robust Low-Rank Hankel Matrix Reconstruction
Consider a spectrally sparse signal x that consists of r complex sinusoi...
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06/12/2019
Optimal low rank tensor recovery
We investigate the sample size requirement for exact recovery of a high ...
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06/09/2019
Fast Cadzow's Algorithm and a Gradient Variant
The Cadzow's algorithm is a signal denoising and recovery method which w...
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03/10/2019
Fast Single Image Reflection Suppression via Convex Optimization
Removing undesired reflections from images taken through the glass is of...
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11/22/2018
Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections
Random projections are able to perform dimension reduction efficiently f...
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10/20/2018
Data-Driven Tight Frame for Cryo-EM Image Denoising and Conformational Classification
The cryo-electron microscope (cryo-EM) is increasingly popular these yea...
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09/27/2018
Towards the optimal construction of a loss function without spurious local minima for solving quadratic equations
The problem of finding a vector x which obeys a set of quadratic equatio...
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09/11/2018
Exploiting the structure effectively and efficiently in low rank matrix recovery
Low rank model arises from a wide range of applications, including machi...
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04/06/2016
Hankel Matrix Nuclear Norm Regularized Tensor Completion for N-dimensional Exponential Signals
Signals are generally modeled as a superposition of exponential function...
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09/15/2015
Precise Phase Transition of Total Variation Minimization
Characterizing the phase transitions of convex optimizations in recoveri...
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04/29/2015
Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging
Compressed sensing has shown great potentials in accelerating magnetic r...
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03/10/2015
Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction
Objective: Improve the reconstructed image with fast and multi-class dic...
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03/10/2015
Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction
This paper explores robust recovery of a superposition of R distinct com...
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12/02/2013
Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional (d≥ 2) Off-the-Grid Frequencies
Recent research in off-the-grid compressed sensing (CS) has demonstrated...
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01/28/2013
Guarantees of Total Variation Minimization for Signal Recovery
In this paper, we consider using total variation minimization to recover...
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12/05/2010