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A Mathematical Introduction to Compressive Sensing

- S. Foucart, H. Rauhut
- Computer Science
- Applied and Numerical Harmonic Analysis
- 8 August 2013

TLDR

Hard Thresholding Pursuit: An Algorithm for Compressive Sensing

- S. Foucart
- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 1 November 2011

TLDR

Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0

- S. Foucart, M. Lai
- Mathematics
- 1 May 2009

Abstract We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal l q -quasinorm is also the sparsest one. This… Expand

A note on guaranteed sparse recovery via ℓ1-minimization

- S. Foucart
- Mathematics
- 1 July 2010

Abstract It is proved that every s-sparse vector x ∈ C N can be recovered from the measurement vector y = A x ∈ C m via l 1 -minimization as soon as the 2s-th restricted isometry constant of the… Expand

Sparse Recovery Algorithms: Sufficient Conditions in Terms of RestrictedIsometry Constants

- S. Foucart
- Mathematics
- 2012

We review three recovery algorithms used in Compressive Sensing for the reconstruction s-sparse vectors x∈ℂ N from the mere knowledge of linear measurements y=A x∈ℂ m , m<N. For each of the… Expand

Stability and Robustness of Weak Orthogonal Matching Pursuits

- S. Foucart
- Mathematics
- 2012

A recent result establishing, under restricted isometry conditions, the success of sparse recovery via orthogonal matching pursuit using a number of iterations proportional to the sparsity level is… Expand

Stability and robustness of ℓ1-minimizations with Weibull matrices and redundant dictionaries

- S. Foucart
- Mathematics
- 15 January 2014

Abstract We investigate the recovery of almost s-sparse vectors x ∈ C N from undersampled and inaccurate data y = A x + e ∈ C m by means of minimizing ‖ z ‖ 1 subject to the equality constraints A z… Expand

Hard thresholding pursuit algorithms: Number of iterations ☆

- Jean-Luc Bouchot, S. Foucart, P. Hitczenko
- Mathematics
- 1 September 2016

Abstract The Hard Thresholding Pursuit algorithm for sparse recovery is revisited using a new theoretical analysis. The main result states that all sparse vectors can be exactly recovered from… Expand

Exponential Decay of Reconstruction Error From Binary Measurements of Sparse Signals

- Richard Baraniuk, S. Foucart, D. Needell, Y. Plan, Mary Wootters
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 30 July 2014

TLDR

Sparse Recovery by Means of Nonnegative Least Squares

- S. Foucart, David Koslicki
- Mathematics, Computer Science
- IEEE Signal Processing Letters
- 27 February 2014

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