Skip to content

Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques

N/ACitations
Citations of this article
52Readers
Mendeley users who have this article in their library.

This artice is free to access.

Abstract

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. First, in a digital setting with random modulation, considering a whole class of sensing bases including the Fourier basis, we prove that the technique is 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 origina signal spectrum by the modulation (hence the name "spread spectrum"). The approach is also efficient as sensing matrices with fast matrix multiplication algorithms can be used, in particular in the case of Fourier measurements. Second, these results are confirmed by a numerical analysis of the phase transition of the ℓ1-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 and magnetic resonance imaging. © 2012 Puy et al.

Cite

CITATION STYLE

APA

Puy, G., Vandergheynst, P., Gribonval, R., & Wiaux, Y. (2012). Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques. Eurasip Journal on Advances in Signal Processing, 2012(1). https://doi.org/10.1186/1687-6180-2012-6

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free