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Robust Spectral Compressed Sensing via Structured Matrix Completion
TLDR
This paper develops a novel algorithm, called enhanced matrix completion (EMaC), based on structured matrix completion that does not require prior knowledge of the model order to recover a spectrally sparse signal from a small random subset of its n time domain samples.
Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming
TLDR
This paper explores 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.
Off-the-Grid Line Spectrum Denoising and Estimation With Multiple Measurement Vectors
TLDR
This paper studies 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, and develops two approaches based on atomic norm minimization and structured covariance estimation.
PETRELS: Parallel Subspace Estimation and Tracking by Recursive Least Squares From Partial Observations
TLDR
The proposed algorithm, dubbed Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies the underlying low-dimensional subspace, and then reconstructs the missing entries via least-squares estimation if required, comparing PETRELS with state of the art batch algorithms.
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
TLDR
This tutorial-style overview highlights the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees and reviews two contrasting approaches: two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and global landscape analysis and initialization-free algorithms.
Guaranteed Blind Sparse Spikes Deconvolution via Lifting and Convex Optimization
  • Yuejie Chi
  • Computer Science
    IEEE Journal of Selected Topics in Signal…
  • 9 June 2015
TLDR
A convex optimization framework to simultaneously estimate the point spread function as well as the spike signal is proposed, by mildly constraining the pointspread function to lie in a known low-dimensional subspace and it is proved the proposed algorithm, dubbed as AtomicLift, is guaranteed to recover the Spike signal up to a scaling factor as soon as the number of samples is large enough.
Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization
TLDR
This work develops nonasymptotic convergence guarantees for entropy-regularized NPG methods under softmax parameterization, focusing on tabular discounted Markov decision processes and demonstrates that the algorithm converges linearly at an astonishing rate that is independent of the dimension of the state-action space.
A Nonconvex Approach for Phase Retrieval: Reshaped Wirtinger Flow and Incremental Algorithms
TLDR
An incremental (stochastic) version of RWF (IRWF) is developed and connected with the randomized Kaczmarz method for phase retrieval and it is demonstrated that IRWF outperforms existing incremental as well as batch algorithms with experiments.
Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization
TLDR
It is demonstrated that under some mild spectral separation condition, it is possible to exactly recover all frequencies by solving an atomic norm minimization program, as long as the sample complexity exceeds the order of rlogrlogn.
Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval
TLDR
This paper provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes.
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