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Simply denoise; wavefield reconstruction via jittered undersampling

Gilles Hennenfent and Felix J. Herrmann
Simply denoise; wavefield reconstruction via jittered undersampling
Geophysics (May 2008) 73 (3): V19-V28


We present a new, discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting 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 sub-Nyquist sampling is key in formulating a versatile wavefield sparsity-promoting recovery scheme that follows the principles of compressive sampling. After the behavior of the jittered-undersampling scheme in the Fourier domain is analyzed, its performance is studied for curvelet recovery by sparsity-promoting 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.

ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 73
Serial Issue: 3
Title: Simply denoise; wavefield reconstruction via jittered undersampling
Affiliation: University of British Columbia, Department of Earth and Ocean Sciences, Vancouver, BC, Canada
Pages: V19-V28
Published: 200805
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 33
Accession Number: 2008-124445
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Annotation: Includes appendices
Illustration Description: illus.
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2018, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 200848
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