Robust matrix rank reduction methods for seismic data processing

• Author / Creator

  Chen, Ke

• An important step of seismic data processing entails signal de-noising. Traditional de-noising methods assume Gaussian noise model and their performance degrades in the presence of erratic (non-Gaussian) noise. This thesis examines the problem of designing reduced-rank noise attenuation algorithms that are resistant to erratic noise.

  I first introduce a robust matrix factorization based on M-estimate and incorporate it into the formulation of the classical Singular Spectrum Analysis (SSA) algorithm. This new algorithm (Robust SSA) permits to de-noise seismic data that have been contaminated by non-Gaussian noise.

  I also propose a second Robust SSA algorithm that attacks the data de-noising and reconstruct problems as low-rank matrix recovery problem that is solved by a convex optimization algorithm. The NP-hard rank minimization problem is replaced by its tightest convex relaxation, the nuclear-norm minimization. An augmented Lagrangian method is used to numerically look for the solution that minimizes the cost function.

• Subjects / Keywords

  • Matrix rank reduction
  • Non-Gaussian noise
  • Seismic data reconstruction
  • Robust statistics
  • Convex optimization
  • Seismic data denoising

• Graduation date

  Fall 2013

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3930P366

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.