• Publications
  • Influence
Robust Spectral Compressed Sensing via Structured Matrix Completion
  • Y. Chen, Yuejie Chi
  • Computer Science, Mathematics
  • IEEE Transactions on Information Theory
  • 30 April 2013
TLDR
This paper explores the problem of spectral compressed sensing, which aims to recover a spectrally sparse signal from a small random subset of its time domain samples. Expand
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Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming
TLDR
We explore a quadratic (or rank-one) measurement model which imposes minimal memory requirements and low computational complexity during the sampling process, and is shown to be optimal in preserving various low-dimensional covariance structures. Expand
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PETRELS: Parallel Subspace Estimation and Tracking by Recursive Least Squares From Partial Observations
TLDR
We consider the problem of reconstructing a data stream from a small subset of its entries, where the data is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. Expand
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Off-the-Grid Line Spectrum Denoising and Estimation With Multiple Measurement Vectors
  • Yuanxin Li, Yuejie Chi
  • Computer Science, Mathematics
  • IEEE Transactions on Signal Processing
  • 10 August 2014
TLDR
We study the problem of line spectrum denoising and estimation with an ensemble of spectrally-sparse signals composed of the same set of continuous-valued frequencies from their partial and noisy observations. Expand
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Guaranteed Blind Sparse Spikes Deconvolution via Lifting and Convex Optimization
  • Yuejie Chi
  • Mathematics, Computer Science
  • IEEE Journal of Selected Topics in Signal…
  • 9 June 2015
TLDR
Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies of a band-limited or diffraction-limited point spread function, which is either determined by the nature or designed by the users. Expand
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Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
TLDR
We present nonconvex optimization algorithms for low-rank matrix factorization that combine optimization and statistical models with performance guarantees. Expand
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Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization
  • Yuejie Chi, Y. Chen
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 February 2015
TLDR
This paper is concerned with estimation of two-dimensional frequencies from partial time samples, which arises in many applications such as radar, inverse scattering, and super-resolution imaging. Expand
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Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution
TLDR
This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. Expand
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Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval
TLDR
We investigate the efficacy of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem by exploiting the statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain statistical dependency. Expand
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Reshaped Wirtinger Flow and Incremental Algorithm for Solving Quadratic System of Equations
We study the phase retrieval problem, which solves quadratic system of equations, i.e., recovers a vector $\boldsymbol{x}\in \mathbb{R}^n$ from its magnitude measurements $y_i=|\langleExpand
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