Low-rank methods for seismic data reconstruction

Seismic data are usually sampled on a sparse and irregular grid due to the geological, logistical, and economic constraints in seismic data acquisition. I have worked on the reconstruction of multi-dimensional seismic data by solving for a low-rank subspace from the observed incomplete and corrupted data. The figure below shows a small patch of seismic data before and after reconstruction.

Particularly, I am interested in developing efficient matrix/tensor completion algorithms via randomized methods. Below are two examples of my work:

Projected gradient methods for simultaneous source separation/imaging

Conventional seismic sources are fired in a non-overlapping fashion. Simultaneous source acquisition entails firing more than one seismic source with small random time delays. As a result the acquisition efficiency has been significantly improved. The challenge is to separate the signal from each impulsive source.

I have worked on the separation and the direct imaging of simultaneous source data via rank-constrained inversion as follows:

One-way wave-equation migration

A simple piece of python code for post-stack one-way wave-equation migration. I designed the SAIG velocity model to test the method.