Simply denoise: wavefield reconstruction via jittered undersampling

From discrete to continuous spatial undersampling

So far, undersampling schemes based on an underlying fine interpolation grid were considered. This situation typically occurs when binning continuous randomly-sampled seismic data into small bins that define the fine grid used for interpolation. Despite the error introduced in the data, binning presents some computational advantages since it allows for the use of fast implementations of Fourier or Fourier-related transforms, e.g., FFTW (Frigo and Johnson, 1998) or FDCT (Candès et al., 2005a). However, binning can lead at the same time to an unfavorable undersampling scheme, e.g., regular or poorly-jittered. In this case, one should consider working on the original data with, e.g., an extension to the curvelet transform for irregular grids (Hennenfent and Herrmann, 2006). Despite the extra computational cost for the interpolation, continuous random sampling typically leads to improved interpolation results because it does not create coherent undersampling artifacts (Xu et al., 2005).