Seismic data reconstruction via matrix completion

Yi Yang; Jianwei Ma; Stanley Osher

doi:10.3934/ipi.2013.7.1379

Article Contents

2013, Volume 7, Issue 4: 1379-1392. Doi: 10.3934/ipi.2013.7.1379

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Seismic data reconstruction via matrix completion

1.
Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095
2.
Department of Mathematics, Harbin Institute of Technology, Harbin
3.
Department of Mathematics, University of California, Los Angeles, CA 90095

Received: January 31, 2012

Revised: January 31, 2013

Published: October 2013

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Abstract

In seismic processing, one goal is to recover missing traces when the data is sparsely and incompletely sampled. We present a method which treats this reconstruction problem from a novel perspective. By utilizing its connection with the general matrix completion (MC) problem, we build an approximately low-rank matrix, which can be reconstructed through solving a proper nuclear norm minimization problem. Two efficient algorithms, accelerated proximal gradient method (APG) and low-rank matrix fitting (LMaFit) are discussed in this paper. The seismic data can then be recovered by the conversion of the completed matrix into the original signal space. Numerical experiments show the efficiency and high performance of data recovery for our model compared with other models.

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Mathematics Subject Classification: 15A29, 15A83.

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