Title:

The Application of OPTSPACE Algorithm and Comparison with LMAFIT Algorithm in Threedimensional Seismic Data Reconstruction via Lowrank Matrix Completion

Author:

Chen Xue

Year:

2016

Degree:

MS

Adviser:

Mukerji

File Size:

5.7 MB

View File:

Access Count:

698

Abstract:

This report is focused on three-dimensional seismic data reconstruction with randomly missing data on a regular grid. Ma (2013) developed a rank-reduction method that transforms three-dimensional seismic data reconstruction problem into low-rank matrix completion (MC) problem with the “texture-patch transformation”, and resolved the MC problem from the perspective of the nuclear-norm minimization. Aiming at achieving a higher-quality reconstruction with small computational complexity in time, this report followed the general framework and the low-rank matrix completion idea in Yang et al. (2011) and Ma (2013), generalized the three-dimensional texture-patch transform, and settled the low-rank matrix completion problem from two other perspectives, the rank-r matrix approximation problem and low-rank factorization problem. Furthermore, this report applied two corresponding matrix completion algorithms, a gradient descent algorithm on the Grassman manifold (OptSpace) and the low-rank matrix fitting algorithm (LMaFit), to resolving the MC problem, and finally compared the performance of the proposed methods by conducting numerical experiments on simulated seismic data and the field data set.


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