Sparsity in time-frequency representations
GE Pfander, H Rauhut - Journal of Fourier Analysis and Applications, 2010 - Springer
Journal of Fourier Analysis and Applications, 2010•Springer
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 ℂ n 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.
representations. As main result we show that an S-sparse Gabor representation in ℂ n 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.
Abstract
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 ℂ n 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.
Springer