Title :
Recovery of short, complex linear combinations via ℓ1 minimization
Author_Institution :
ICES, Univ. of Texas, Austin, TX
fDate :
4/1/2005 12:00:00 AM
Abstract :
This note provides a condition under which lscr1 minimization (also known as basis pursuit) can recover short linear combinations of complex vectors chosen from fixed, overcomplete collection. This condition has already been established in the real setting by Fuchs, who used convex analysis. The proof given here is more direct
Keywords :
Hilbert spaces; convex programming; linear programming; minimisation; sparse matrices; convex analysis; l1 minimization; linear combination; Atomic measurements; Dictionaries; Hilbert space; Ice; Linear approximation; Mathematical programming; Minimization methods; Signal synthesis; Software standards; Vectors; Algorithms; approximation; basis pursuit; linear program; redundant dictionaries; sparse representations;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.844057
