Sparsity in time-frequency representations

We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an S-sparse Gabor representation in Cn with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S ≤ Cn/ log(n). Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing. Keywords. Time-frequency representations, sparse representations, sparse signal recovery, Basis Pursuit, operator identification, random matrices. AMS Subject Classification. 42C40, 15A52, 90C25.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Götz E. Pfander, Holger Rauhut
• Keywords: Basis Pursuit, CORR 2007, Education, Random Unimodular Window, Time-frequency Representations