Sparse recovery with pre-Gaussian random matrices

• Autorzy: Simon Foucart , Ming-Jun Lai
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 94A12: Signal theory (characterization, reconstruction, filtering, etc.)
• 15B52: Random matrices
• 46B09: Probabilistic methods in Banach space theory
• 60B20: Random matrices (probabilistic aspects; for algebraic aspects see )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 1
• Strony: 91-102

Daty

wydano

2010

Twórcy

autor

Simon Foucart

• Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France

autor

Ming-Jun Lai

• Department of Mathematics, University of Georgia, Athens, GA 30602, U.S.A.

Identyfikatory

DOI

10.4064/sm200-1-6