Simply denoise: wavefield reconstruction via jittered undersampling

Main contributions

We propose and analyze a coarse sampling scheme, termed jittered undersampling (Dippe and Wold, 1992; Leneman, 1966), which creates, under specific conditions, a favorable recovery situation for seismic wavefield reconstruction methods that impose sparsity in Fourier or Fourier-related domains (see e.g. Sacchi et al., 1998; Xu et al., 2005; Herrmann and Hennenfent, 2007; Zwartjes and Sacchi, 2007). Jittered undersampling differentiates itself from random undersampling according to a discrete uniform distribution, which also creates favorable recovery conditions (Xu et al., 2005; Abma and Kabir, 2006; Zwartjes and Sacchi, 2007), by controlling the maximum gap in the acquired data. This control makes jittered undersampling very well suited to methods that rely on transforms with localized elements, e.g., windowed Fourier or curvelet transform (Candès et al., 2005a, and references therein). These methods are known to be vulnerable to gaps in the data that are larger than the spatio-temporal extent of the transform elements (Trad et al., 2005).