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Society of Exploration Geophysicists
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GEOPHYSICS
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00168033
19422156
05
2008
73
3
Simply denoise: Wavefield reconstruction via jittered undersampling
Gilles
Hennenfent
University of British Columbia, Department of Earth and Ocean Sciences, Vancouver, Canada. .
Felix J.
Herrmann
University of British Columbia, Department of Earth and Ocean Sciences, Vancouver, Canada. .
We present a new, discrete undersampling scheme designed to favor wavefield reconstruction by sparsitypromoting inversion with transform elements localized in the Fourier domain. The work is motivated by empirical observations in the seismic community, corroborated by results from compressive sampling, that indicate favorable (wavefield) reconstructions from random rather than regular undersampling. Indeed, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control. Thus, we introduce a sampling scheme, termed jittered undersampling, that shares the benefits of random sampling and controls the maximum gap size. The contribution of jittered subNyquist sampling is key in formulating a versatile wavefield sparsitypromoting recovery scheme that follows the principles of compressive sampling. After the behavior of the jitteredundersampling scheme in the Fourier domain is analyzed, its performance is studied for curvelet recovery by sparsitypromoting inversion (CRSI). The findings on synthetic and real seismic data indicate an improvement of several decibels over recovery from regularly undersampled data for the same amount of data collected.
05
2008
V19
V28
10.1190/1.2841038
10.1190/1.2841038
https://library.seg.org/doi/10.1190/1.2841038

https://library.seg.org/doi/pdf/10.1190/1.2841038

http://geophysics.geoscienceworld.org/cgi/doi/10.1190/1.2841038
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