163850
20190316235034.0
10.1186/1687-6180-2012-6
doi
000306285000001
ISI
ARTICLE
Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques
2012
Institute of Electrical and Electronics Engineers
2012
Journal Articles
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random modulation, considering a whole class of sensing bases including the Fourier basis, we prove that the technique is \emph{universal} in the sense that the required number of measurements for accurate recovery is optimal and independent of the sparsity basis. This universality stems from a drastic decrease of coherence between the sparsity and the sensing bases, which for a Fourier sensing basis relates to a spread of the original signal spectrum by the modulation (hence the name ``spread spectrum''). The approach is also \emph{efficient} as sensing matrices with fast matrix multiplication algorithms can be used, in particular in the case of Fourier measurements. Secondly, these results are confirmed by a numerical analysis of the phase transition of the $\ell_1$-minimization problem. Finally, we show that the spread spectrum technique remains effective in an analog setting with chirp modulation for application to realistic Fourier imaging. We illustrate these findings in the context of radio interferometry.
Compressed sensing
Spread spectrum
LTS2
LTS5
CIBM-SP
CIBM-AIT
Puy, Gilles
179918
242927
Vandergheynst, Pierre
120906
240428
Gribonval, RĂ©mi
Wiaux, Yves
163268
240427
6
EURASIP Journal on Advances in Signal Processing
2012
n/a
584008
n/a
http://infoscience.epfl.ch/record/163850/files/EURASIP-Spread_spectrum.pdf
LTS5
252394
U10954
LTS2
252392
U10380
LIFMET
252276
U10984
CIBM
252477
U12623
oai:infoscience.tind.io:163850
article
STI
SB
GLOBAL_SET
179918
179918
179918
179918
179918
179918
163268
163268
163268
179918
179918
179918
179918
179918
161735
161735
EPFL-ARTICLE-163850
EPFL
PUBLISHED
REVIEWED
ARTICLE