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How does additive gaussian measurement noise influence simultaneous orthogonal matching pursuit performance?

par Determe, Jean-François ;Louveaux, Jérôme;Jacques, Laurent;Horlin, François
Référence FNRS Contact Group on "Wavelets and Applications” (16 November, 2016: Louvain-La-Neuve, Belgium)
Publication Non publié, 2016-11

Communication à un colloque

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Résumé :

Results in compressed sensing have shown that the support of high-dimensional sparse signals can be computed on the basis of properly designed linear measurements of these sparse signals, even if the number of measurements is significantly lower than the dimension of the sparse signals. Several computationally effective algorithms have been developed to solve the support recovery problem. In this work, we focus on the support recovery of several sparse signals sharing a common support. We study Simultaneous orthogonal matching pursuit (SOMP), which extends orthogonal matching pursuit (OMP) in order to simultaneously process multiple sparse signals. We summarize recent theoretical results quantifying to what extent additive Gaussian measurement noise degrades SOMP performance. We also present numerical evidence validating the theoretical results.