Sparse recovery with pre-Gaussian random matrices
Studia Mathematica, Tome 200 (2010) no. 1, pp. 91-102
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For an $m \times N$ 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 $\ell_1$-minimization under the optimal condition $m \ge c s \ln(e N /s)$.
The main ingredient of the proof is a variation of a classical Restricted Isometry Property,
where the inner norm becomes the $\ell_1$-norm and the outer norm depends on probability distributions.
Keywords:
times underdetermined system linear equations independent pre gaussian random coefficients satisfying simple moment conditions proved s sparse solutions system found ell minimization under optimal condition main ingredient proof variation classical restricted isometry property where inner norm becomes ell norm outer norm depends probability distributions
Affiliations des auteurs :
Simon Foucart 1 ; Ming-Jun Lai 2
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author = {Simon Foucart and Ming-Jun Lai},
title = {Sparse recovery with {pre-Gaussian} random matrices},
journal = {Studia Mathematica},
pages = {91--102},
publisher = {mathdoc},
volume = {200},
number = {1},
year = {2010},
doi = {10.4064/sm200-1-6},
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url = {http://geodesic.mathdoc.fr/articles/10.4064/sm200-1-6/}
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TY - JOUR AU - Simon Foucart AU - Ming-Jun Lai TI - Sparse recovery with pre-Gaussian random matrices JO - Studia Mathematica PY - 2010 SP - 91 EP - 102 VL - 200 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm200-1-6/ DO - 10.4064/sm200-1-6 LA - en ID - 10_4064_sm200_1_6 ER -
Simon Foucart; Ming-Jun Lai. Sparse recovery with pre-Gaussian random matrices. Studia Mathematica, Tome 200 (2010) no. 1, pp. 91-102. doi: 10.4064/sm200-1-6
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