Kiryung Lee
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View article: Global Convergence of ESPRIT with Preconditioned First-Order Methods for Spike Deconvolution
Global Convergence of ESPRIT with Preconditioned First-Order Methods for Spike Deconvolution Open
Spike deconvolution is the problem of recovering point sources from their convolution with a known point spread function, playing a fundamental role in many sensing and imaging applications. This paper proposes a novel approach combining E…
View article: Max-Linear Regression by Scalable and Guaranteed Convex Programming
Max-Linear Regression by Scalable and Guaranteed Convex Programming Open
We consider the multivariate max-linear regression problem where the model parameters $\boldsymbol{\beta}_{1},\dotsc,\boldsymbol{\beta}_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y …
View article: Sparse Max-Affine Regression
Sparse Max-Affine Regression Open
This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of $k$-affine functions $ x \mapsto \max_{j \in [k]} \langle a_j^\star, x \rang…
View article: Small-Noise Sensitivity Analysis of Locating Pulses in the Presence of Adversarial Perturbation
Small-Noise Sensitivity Analysis of Locating Pulses in the Presence of Adversarial Perturbation Open
A fundamental small-noise sensitivity analysis of spike localization in the presence of adversarial perturbations and an arbitrary point spread function (PSF) is presented. The analysis leverages the local Lipschitz property of the inverse…
View article: Robust Phase Retrieval by Alternating Minimization
Robust Phase Retrieval by Alternating Minimization Open
We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, w…
View article: Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing
Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing Open
.We consider the problem of reconstructing rank-1 matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the alternating lea…
View article: Stable estimation of pulses of unknown shape from multiple snapshots via ESPRIT
Stable estimation of pulses of unknown shape from multiple snapshots via ESPRIT Open
We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used …
View article: Max-affine regression via first-order methods
Max-affine regression via first-order methods Open
We consider regression of a max-affine model that produces a piecewise linear model by combining affine models via the max function. The max-affine model ubiquitously arises in applications in signal processing and statistics including mul…
View article: Sketching low-rank matrices with a shared column space by convex programming
Sketching low-rank matrices with a shared column space by convex programming Open
In many practical applications including remote sensing, multi-task learning, and multi-spectrum imaging, data are described as a set of matrices sharing a common column space. We consider the joint estimation of such matrices from their n…
View article: Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing
Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing Open
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating Le…
View article: Approximately low-rank recovery from noisy and local measurements by convex program
Approximately low-rank recovery from noisy and local measurements by convex program Open
Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrog…
View article: Max-Linear Regression by Convex Programming
Max-Linear Regression by Convex Programming Open
We consider the multivariate max-linear regression problem where the model parameters $\boldsymbolβ_{1},\dotsc,\boldsymbolβ_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y = \max_{1\le…
View article: Low-Rank Matrix Estimation from Rank-One Projections by Unlifted Convex Optimization
Low-Rank Matrix Estimation from Rank-One Projections by Unlifted Convex Optimization Open
We study an estimator with a convex formulation for recovery of low-rank matrices from rank-one projections. Using initial estimates of the factors of the target $d_1\times d_2$ matrix of rank-$r$, the estimator admits a practical subgradi…
View article: Phase retrieval of low-rank matrices by anchored regression
Phase retrieval of low-rank matrices by anchored regression Open
We study the low-rank phase retrieval problem, where our goal is to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of a …
View article: Low-Rank Matrix Estimation From Rank-One Projections by Unlifted Convex\n Optimization
Low-Rank Matrix Estimation From Rank-One Projections by Unlifted Convex\n Optimization Open
We study an estimator with a convex formulation for recovery of low-rank\nmatrices from rank-one projections. Using initial estimates of the factors of\nthe target $d_1\\times d_2$ matrix of rank-$r$, the estimator admits a practical\nsubg…
View article: Convolutional Framework for Accelerated Magnetic Resonance Imaging
Convolutional Framework for Accelerated Magnetic Resonance Imaging Open
Magnetic Resonance Imaging (MRI) is a noninvasive imaging technique that provides exquisite soft-tissue contrast without using ionizing radiation. The clinical application of MRI may be limited by long data acquisition times; therefore, MR…
View article: Identifiability Conditions for Compressive Multichannel Blind Deconvolution
Identifiability Conditions for Compressive Multichannel Blind Deconvolution Open
In applications such as multi-receiver radars and ultrasound array systems, the observed signals can often be modeled as a linear convolution of an unknown signal which represents the transmit pulse and sparse filters which describe the sp…
View article: Generalized notions of sparsity and restricted isometry property. Part I: a unified framework
Generalized notions of sparsity and restricted isometry property. Part I: a unified framework Open
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose g…
View article: Unified Theory for Recovery of Sparse Signals in a General Transform Domain
Unified Theory for Recovery of Sparse Signals in a General Transform Domain Open
Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In …
View article: Fast and Guaranteed Blind Multichannel Deconvolution Under a Bilinear System Model
Fast and Guaranteed Blind Multichannel Deconvolution Under a Bilinear System Model Open
We consider the multichannel blind deconvolution problem where we observe the output of multiple channels that are all excited with the same unknown input. From these observations, we wish to estimate the impulse responses of each of the c…
View article: Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness
Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness Open
We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which i…
View article: Near-Optimal Compressed Sensing of a Class of Sparse Low-Rank Matrices Via Sparse Power Factorization
Near-Optimal Compressed Sensing of a Class of Sparse Low-Rank Matrices Via Sparse Power Factorization Open
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable reconstruct…
View article: Optimal Sample Complexity for Stable Matrix Recovery
Optimal Sample Complexity for Stable Matrix Recovery Open
Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery wi…
View article: Blind Gain and Phase Calibration via Sparse Spectral Methods
Blind Gain and Phase Calibration via Sparse Spectral Methods Open
Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo …
View article: Spectral Methods for Passive Imaging: Non-asymptotic Performance and\n Robustness
Spectral Methods for Passive Imaging: Non-asymptotic Performance and\n Robustness Open
We study the problem of passive imaging through convolutive channels. A scene\nis illuminated with an unknown, unstructured source, and the measured response\nis the convolution of this source with multiple channel responses, each of\nwhic…
View article: Generalized notions of sparsity and restricted isometry property. Part\n I: A unified framework
Generalized notions of sparsity and restricted isometry property. Part\n I: A unified framework Open
The restricted isometry property (RIP) is an integral tool in the analysis of\nvarious inverse problems with sparsity models. Motivated by the applications of\ncompressed sensing and dimensionality reduction of low-rank tensors, we propose…
View article: Unified Theory for Recovery of Sparse Signals in a General Transform Domain
Unified Theory for Recovery of Sparse Signals in a General Transform Domain Open
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many re…
View article: Blind Recovery of Sparse Signals From Subsampled Convolution
Blind Recovery of Sparse Signals From Subsampled Convolution Open
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in pract…