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Robust estimation of primaries by sparse inversion via one-norm minimization.

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Title: Robust estimation of primaries by sparse inversion via one-norm minimization.
Authors: Lin, Tim T.1 tlin@eos.ubc.ca, Herrmann, Felix J.1 fherrmann@eos.ubc.ca
Source: Geophysics. May/Jun2013, Vol. 78 Issue 3, pR133-R150. 18p.
Subjects: Estimation theory, Algorithm research, Sparse approximations, Mathematical transformations, Robust control
Abstract: A recently proposed method called estimation of primaries by sparse inversion (EPSI) avoids the need for adaptive subtraction of approximate multiple predictions by directly inverting for the multiple-free subsurface impulse response as a collection of band-limited spikes. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the original EPSI algorithm was not designed to take advantage of this result, and instead it relies on a multitude of inversion parameters, such as the level of sparsity per gradient update. We proposed and tested a new algorithm, named robust EPSI, in which we make obtaining the sparsest solution an explicit goal. Our approach remains a gradient-based approach like the original algorithm, but it is derived from a new biconvex optimization framework based on an extended basis-pursuit denoising formulation. Furthermore, because it is based on a general framework, robust EPSI can recover the impulse response in transform domains, such as sparsifying curvelet-based representations, without changing the underlying algorithm. We discovered that the sparsity-minimizing objective of our formulation enabled it to operate successfully on a variety of synthetic and field marine data sets without excessive tweaking of inversion parameters. We also found that recovering the solution in alternate sparsity domains can significantly improve the quality of the directly estimated primaries, especially for weaker late-arrival events. In addition, we found that robust EPSI produces a more artifact-free impulse response compared to the original algorithm. [ABSTRACT FROM AUTHOR]
Copyright of Geophysics is the property of Society of Exploration Geophysicists and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 88378749
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  Data: <searchLink fieldCode="JN" term="%22Geophysics%22">Geophysics</searchLink>. May/Jun2013, Vol. 78 Issue 3, pR133-R150. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithm+research%22">Algorithm research</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+approximations%22">Sparse approximations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink>
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  Data: A recently proposed method called estimation of primaries by sparse inversion (EPSI) avoids the need for adaptive subtraction of approximate multiple predictions by directly inverting for the multiple-free subsurface impulse response as a collection of band-limited spikes. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the original EPSI algorithm was not designed to take advantage of this result, and instead it relies on a multitude of inversion parameters, such as the level of sparsity per gradient update. We proposed and tested a new algorithm, named robust EPSI, in which we make obtaining the sparsest solution an explicit goal. Our approach remains a gradient-based approach like the original algorithm, but it is derived from a new biconvex optimization framework based on an extended basis-pursuit denoising formulation. Furthermore, because it is based on a general framework, robust EPSI can recover the impulse response in transform domains, such as sparsifying curvelet-based representations, without changing the underlying algorithm. We discovered that the sparsity-minimizing objective of our formulation enabled it to operate successfully on a variety of synthetic and field marine data sets without excessive tweaking of inversion parameters. We also found that recovering the solution in alternate sparsity domains can significantly improve the quality of the directly estimated primaries, especially for weaker late-arrival events. In addition, we found that robust EPSI produces a more artifact-free impulse response compared to the original algorithm. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Geophysics is the property of Society of Exploration Geophysicists and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1190/GEO2012-0097.1
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      – Code: eng
        Text: English
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        PageCount: 18
        StartPage: R133
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      – SubjectFull: Estimation theory
        Type: general
      – SubjectFull: Algorithm research
        Type: general
      – SubjectFull: Sparse approximations
        Type: general
      – SubjectFull: Mathematical transformations
        Type: general
      – SubjectFull: Robust control
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      – TitleFull: Robust estimation of primaries by sparse inversion via one-norm minimization.
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            NameFull: Lin, Tim T.
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            – D: 01
              M: 05
              Text: May/Jun2013
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              Y: 2013
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              Value: 78
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