Rank Minimization via Alternating Optimization - Seismic Data Interpolation

Abstract

Low-rank matrix completion techniques have recently become an effective tool for seismic trace interpolation problems. In this talk, we consider an alternating optimization scheme for nuclear norm minimization and discuss the applications to large scale wave field reconstruction. By adopting a factorization approach to the rank minimization problem we write our low-rank matrix in bi-linear form, and modify this workflow by alternating our optimization to handle a single matrix factor at a time. This allows for a more tractable procedure that can robustly handle large scale, highly oscillatory and critically subsampled seismic data sets. We demonstrate the potential of this approach with several numerical experiments on a seismic line from the Nelson 2D data set and a frequency slice from the Gulf of Mexico data set.

A practical workflow for land seismic wavefield recovery with weighted matrix factorization

“…We use the estimated ground roll as input to our wavefield reconstruction based on weighted matrix factorizations for a rank r = 250, which we find empirically by observing continuity of signals and limited noise in the reconstructed data. We run the reconstruction over all shots simultaneously for 320 iterations of SPG-2 [Lopez et al, 2015] per frequency slice. To avoid reconstruction leakage, we apply steps (1)-( 3) from the previous section again to get the final ground roll recovery.…”

Beating Level-Set Methods for 5-D Seismic Data Interpolation: A Primal-Dual Alternating Approach

“…Steps 3 and 4 focus on a single matrix factor at a time. Alternating approaches are common for matrix factorization ( [21], [16], [12]). The main competing algorithms for constrained matrix completion formulations (2) use a level-set approach along the lines of [1] (see e.g [21]).…”