Robust matrix rank reduction methods for seismic data processing

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 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.;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.