Sparse recovery with pre-Gaussian random matrices

Simon Foucart, and Ming-Jun Lai. "Sparse recovery with pre-Gaussian random matrices." Studia Mathematica 200.1 (2010): 91-102. <http://eudml.org/doc/285906>.

@article{SimonFoucart2010,
abstract = {For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.},
author = {Simon Foucart, Ming-Jun Lai},
journal = {Studia Mathematica},
keywords = {sparse recovery; pre-Gaussian random matrices; underdetermined system of linear equations; -sparse solutions; -minimization},
language = {eng},
number = {1},
pages = {91-102},
title = {Sparse recovery with pre-Gaussian random matrices},
url = {http://eudml.org/doc/285906},
volume = {200},
year = {2010},
}

TY - JOUR
AU - Simon Foucart
AU - Ming-Jun Lai
TI - Sparse recovery with pre-Gaussian random matrices
JO - Studia Mathematica
PY - 2010
VL - 200
IS - 1
SP - 91
EP - 102
AB - For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.
LA - eng
KW - sparse recovery; pre-Gaussian random matrices; underdetermined system of linear equations; -sparse solutions; -minimization
UR - http://eudml.org/doc/285906
ER -