An overview of the CS framework and criteria for
favorable recovery conditions is given. As mentioned before, CS relies
on a sparsifying transform for the to-be-recovered signal and uses
this sparsity prior to compensate for the undersampling during the
recovery process. For the reconstruction of wavefields in the Fourier
(Sacchi et al., 1998; Xu et al., 2005; Zwartjes and Sacchi, 2007), Radon
(Trad et al., 2003), and curvelet
(Hennenfent and Herrmann, 2005; Herrmann and Hennenfent, 2007) domains, sparsity promotion
is a well-established technique documented in the geophysical
literature. The main contribution of CS is the new light shed on the
favorable recovery conditions.
Subsections
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