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

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

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

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

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

We present nonconvex optimization algorithms for low-rank matrix factorization that combine optimization and statistical models with performance guarantees.Expand

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

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

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

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=|\langleâ€¦ Expand