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- Roman Vershynin
- ArXiv
- 2010

2 Preliminaries 7 2.1 Matrices and their singular values . . . . . . . . . . . . . . . . . . 7 2.2 Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Sub-gaussian randomâ€¦ (More)

We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitraryâ€¦ (More)

- Deanna Needell, Roman Vershynin
- Foundations of Computational Mathematics
- 2009

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements â€“ L1-minimization methods and iterative methods (Matchingâ€¦ (More)

This paper improves upon best-known guarantees for exact reconstruction of a sparse signal f from a small universal sample of Fourier measurements. The method for reconstruction that has recentlyâ€¦ (More)

The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite theâ€¦ (More)

- Yaniv Plan, Roman Vershynin
- IEEE Transactions on Information Theory
- 2013

This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We demonstrate that a single convex program gives an accurate estimate of the signal,â€¦ (More)

We demonstrate a simple greedy algorithm that can reliably recover a vector v âˆˆ R from incomplete and inaccurate measurements x = Î¦v + e. Here Î¦ is a N Ã— d measurement matrix with N â‰ª d, and e is anâ€¦ (More)

- Yaniv Plan, Roman Vershynin
- ArXiv
- 2011

We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x âˆˆ R from the signs of O(sâ€¦ (More)

We prove two basic conjectures on the distribution of the smallest singular value of random nÃ—n matrices with independent entries. Under minimal moment assumptions, we show that the smallest singularâ€¦ (More)

- Mark Rudelson, Roman Vershynin
- 2006 40th Annual Conference on Informationâ€¦
- 2006

This paper proves best known guarantees for exact reconstruction of a sparse signal f from few non-adaptive universal linear measurements. We consider Fourier measurements (random sample ofâ€¦ (More)