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000163850 0247_ $$2doi$$a10.1186/1687-6180-2012-6
000163850 02470 $$2ISI$$a000306285000001
000163850 037__ $$aARTICLE
000163850 245__ $$aUniversal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques
000163850 269__ $$a2012
000163850 260__ $$bInstitute of Electrical and Electronics Engineers$$c2012
000163850 336__ $$aJournal Articles
000163850 520__ $$aWe advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random modulation, considering a whole class of sensing bases including the Fourier basis, we prove that the technique is \emph{universal} in the sense that the required number of measurements for accurate recovery is optimal and independent of the sparsity basis. This universality stems from a drastic decrease of coherence between the sparsity and the sensing bases, which for a Fourier sensing basis relates to a spread of the original signal spectrum by the modulation (hence the name ``spread spectrum''). The approach is also \emph{efficient} as sensing matrices with fast matrix multiplication algorithms can be used, in particular in the case of Fourier measurements. Secondly, these results are confirmed by a numerical analysis of the phase transition of the $\ell_1$-minimization problem. Finally, we show that the spread spectrum technique remains effective in an analog setting with chirp modulation for application to realistic Fourier imaging. We illustrate these findings in the context of radio interferometry.
000163850 6531_ $$aCompressed sensing
000163850 6531_ $$aSpread spectrum
000163850 6531_ $$aLTS2
000163850 6531_ $$aLTS5
000163850 6531_ $$aCIBM-SP
000163850 6531_ $$aCIBM-AIT
000163850 700__ $$0242927$$g179918$$aPuy, Gilles
000163850 700__ $$0240428$$g120906$$aVandergheynst, Pierre
000163850 700__ $$aGribonval, Rémi
000163850 700__ $$g163268$$aWiaux, Yves$$0240427
000163850 773__ $$j2012$$tEURASIP Journal on Advances in Signal Processing$$k6
000163850 8564_ $$uhttps://infoscience.epfl.ch/record/163850/files/EURASIP-Spread_spectrum.pdf$$zn/a$$s584008$$yn/a
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000163850 937__ $$aEPFL-ARTICLE-163850
000163850 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
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